Gravitation-Based Model for Information Retrieval

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非球面系数

非球面系数
非球面系数（non-spherical coefficients）是描述地球近似为椭球形的数学工具。

地球并非完全的球形，它的形状更接近于椭球，而非球面系数则是用来描述地球形状上的差异。

地球形状的研究一直是人类研究之一。

早在公元前3世纪，古希腊学者亚里士多德就已经提出了地球是一个球体的概念。

但是随着科学技术的进步，人们发现地球并非完全球形。

地球呈现椭球形状，拥有极半径和赤道半径等不同的参数，因此需要通过非球面系数对其进行描述。

非球面系数可用于地球测量学、地球物理学、大地测量学、地质学及地球大气科学等领域，如大气运动、海洋潮汐和地球重力场等都与非球面系数有着密切的关联。

目前，国际上应用较广泛的非球面系数是由欧洲航天局（ESA）推出的Earth Gravitational Model（EGM）系列数据。

该数据利用了全天球地球重力场模型，包括高低分辨率等不同版本，可广泛用于卫星测高、大地测量等方面，并在许多卫星导航系统中得到应用。

非球面系数的研究将有助于我们更深入地了解地球的形状及其变化，促进全球定位、导航和遥感技术的发展，进一步拓展地球科学的研究领域。

GravityModel

The Gravity Model∗James E.AndersonBoston College and NBERJanuary18,2011AbstractGravity has long been one of the most successful empirical models in economics.In-corporating deeper theoretical foundations of gravity into recent practice has led toa richer and more accurate estimation and interpretation of the spatial relations de-scribed by gravity.Wider acceptance has followed.Recent developments are reviewedhere and suggestions are made for promising future research.JEL Classiﬁcation:F10,R1.Contact information:James E.Anderson,Department of Economics,Boston Col-lege,Chestnut Hill,MA02467,USA.Keywords:Incidence,multilateral resistance,trade costs,migration.∗This review was prepared for Annual Review of Economics,vol.3.I thank Jeﬀrey H.Bergstrand,Keith Head,J.Peter Neary and Yoto V.Yotov for helpful comments.The gravity model in economics was until relatively recently an intellectual orphan,un-connected to the rich family of economic theory.This review is a tale of the orphan’s reunion with its heritage and the beneﬁts that continue toﬂow from connections to more distant relatives.Gravity has long been one of the most successful empirical models in economics,order-ing remarkably well the enormous observed variation in economic interaction across space in both trade and factor movements.The goodﬁt and relatively tight clustering of coeﬃ-cient estimates in the vast empirical literature suggested that some underlying economic law must be at work,but in the absence of an accepted connection to economic theory,most economists ignored gravity.The authoritative survey of Leamer and Levinsohn(1995)cap-tures the mid-90’s state of professional thinking:“These estimates of gravity have been both singularly successful and singularly unsuccessful.They have produced some of the clearest and most robust empiricalﬁndings in economics.But,paradoxically,they have had virtually no eﬀect on the subject of international economics.Textbooks continue to be written and courses designed without any explicit references to distance,but with the very strange im-plicit assumption that countries are both inﬁnitely far apart and inﬁnitely close,the former referring to factors and the latter to commodities.”Subsequently,gravityﬁrst appeared in textbooks in2004(Feenstra,2004),following on success in connecting gravity to economic theory,the subject of Section3.Reviews are not intended to be surveys.My take on the gravity model,thus licensed to be idiosyncratic,scants or omits some topics that others have found important while it emphasizes some topics that others have scanted.My emphases and omissions are intended to guide the orphan to maturity.An adoptive parent’s biases may have contaminated my judgment,caveat emptor.My focus is on theory.Incorporating the theoretical foundations of gravity into recent practice has led to richer and more accurate estimation and interpretation of the spatial relations described by gravity,so where appropriate I will point out this beneﬁt.The har-vest reaped from empirical work applying the gravity model is recently surveyed elsewhere (Anderson and van Wincoop,2004;Bergstrand and Egger,2011).From a modeling standpoint,gravity is distinguished by its parsimonious and tractable representation of economic interaction in a many country world.Most international economic theory is concentrated on two country cases,occasionally extended to three country cases with special features.The tractability of gravity in the many country case is due to its modularity:the distribution of goods or factors across space is determined by gravity forces conditional on the size of economic activities at each location.Modularity readily allows for disaggregation by goods or regions at any scale and permits inference about trade costs not dependent on any particular model of production and market structure in full general equilibrium.The modularity theme recurs often below,but is missing from some other prominent treatments of gravity in the literature.1Traditional GravityThe story begins by setting out the traditional gravity model and noting clues to its union with economic theory.The traditional gravity model drew on analogy with Newton’s Law of Gravitation.A mass of goods or labor or other factors of production supplied at origin i,Y i, is attracted to a mass of demand for goods or labor at destination j,E j,but the potential ﬂow is reduced by the distance between them,d ij.Strictly applying the analogy,X ij=Y i E j/d2ijgives the predicted movement of goods or labor between i and j,X ij.Ravenstein(1889) pioneered the use of gravity for migration patterns in the19th century UK.Tinbergen(1962) was theﬁrst to use gravity to explain tradeﬂows.Departing from strict analogy,traditional gravity allowed the exponents of1applied to the mass variables and of−2applied to bilateral distance to be generated by data toﬁt a statistically inferred log-linear relationship betweendata onﬂows and the mass variables and distance.Generally,across many applications,the estimated coeﬃcients on the mass variables cluster close to1and the distance coeﬃcients cluster close to−1while the estimated equationﬁts the data well:most data points cluster close to theﬁtted line in the sense that80−90%of the variation in theﬂows is captured by theﬁtted relationship.Theﬁt of traditional gravity improved when supplemented with other proxies for trade frictions,such as the eﬀect of political borders and common language.Notice that bilateral frictions alone would appear to be inadequate to fully explain the eﬀects of trade frictions on bilateral trade,because the sale from i to j is inﬂuenced by the resistance to movement on i’s other alternative destinations and by the resistance on move-ment to j from j’s alternative sources of supply.Prodded by this intuition the traditional gravity literature recently developed remoteness indexes of each country’s‘average’eﬀectivedistance to or from its partners(id ij/Y i was commonly deﬁned as the remoteness of coun-try j)and used them as further explanatory variables in the traditional gravity model,with some statistical success.The general problem posed by the intuition behind remoteness indexes is analogous to the N-body problem in Newtonian gravitation.An economic theory of gravity is required for an adequate solution.Because there are many origins and many destinations in any application,a theory of the bilateralﬂows must account for the relative attractiveness of origin-destination pairs.Each sale has multiple possible destinations and each purchase has multiple possible origins:any bilateral sale interacts with all others and involves all other bilateral frictions.This general equilibrium problem is neatly solved with structural gravity models.For expositional ease,the discussion focuses below on goods movements except when migration or investment is speciﬁcally treated.2Frictionless Gravity LessonsTaking a step toward structure,an intuitively appealing starting point is the description of a completely smooth homogeneous world in which all frictions disappear.Developing the implications of this structure yields a number of useful insights about the pattern of world trade.A frictionless world implies that each good has the same price everywhere.In a homoge-neous world,economic agents everywhere might be predicted to purchase goods in the same proportions when faced with the same prices.In the next section the assumptions on pref-erences and/or technology that justify this plausible prediction are the focus,but here the focus is on the implications for trade patterns.In a completely frictionless and homogeneous world,the natural benchmark prediction is that X ij/E j=Y i/Y,the proportion of spending by j on goods from i is equal to the global proportion of spending on goods from i,where Y denotes world spending.Any theory must impose adding up constraints,which for goods requires that the sum of sales to all destinations must equal Y i,the total sales by origin i,and the sum of purchases from all origins must equal E j,the total expenditure for each destination j.Total sales andexpenditures must be equal:i.e.,iY i=jE j=Y.One immediate payoﬀis an implication for inferring trade frictions.Multiplying both sides of the frictionless benchmark prediction X ij/E j=Y i/Y by E j yields predicted friction-less trade Y i E j/Y.The ratio of observed trade X ij to predicted frictionless trade Y i E j/Y represents the eﬀect of frictions along with random inﬂuences.(Bilateral trade data are notoriously rife with measurement error.)Fitting the statistical relationship between the ratio of observed to frictionless trade and various proxies for trade costs is justiﬁed by this simple theoretical structure as a proper focus of empirical gravity models.Thus far,the treatment of tradeﬂows has been of a generic good that most of the literature has implemented as an aggregate:the value of aggregate bilateral trade in goods for example.But the model applies more naturally to disaggregated goods(and factors)becausethe frictions to be analyzed below are likely to diﬀer markedly by product characteristics. The extension to disaggregated goods,indexed by k,is straightforward.X kij =Y kiE kjY k=s kib kjY k.(1)Here s ki =Y ki/Y k is country i’s share of the world’s sales of goods class k and b kj=E kj/Y kis country j’s share of the world spending on k,equal to the world’s sales of k,Y k.The notation and logic also readily apply to the disaggregation of countries into regions, and indeed a prominent portion of the empirical literature has examined bilateralﬂows between city pairs or regions,motivated by the observation that much economic interaction is concentrated at very short distances.The model can interpreted to reﬂect individual decisions aggregated with a probability model;see section5.1below.In aggregate gravity applications(i.e.,most applications),it has been common to use origin and destination mass variables equal to Gross Domestic Product(GDP).This is con-ceptually inappropriate and leads to inaccurate modeling unless the ratio of gross shipments to GDP is constant(in which case the ratio goes into a constant term).A possible direction for aggregate modeling is to convert trade to the same value-added basis as GDP,but this seems more problematic than using disaggregated gravity to explain the pattern of gross shipments and then uniting estimated gravity models within a superstructure to connect to GDP.That is the strategy of the structural gravity model research program reviewed here.Equation(1)generates a number of useful implications.1.Big producers have big market shares everywhere,2.small sellers are more open in the sense of trading more with the rest of the world,3.the world is more open the more similar in size and the more specialized the countriesare,4.the world is more open the greater the number of countries,and5.world openness rises with convergence under the simplifying assumption of balancedtrade.Implication1,that big producers have big market shares everywhere,follows because, reverting to the generic notation and omitting the k superscript,the frictionless gravity prediction is that:X ij/E j=s i.Implication2,that small sellers are more open in the sense of trading more with the rest of the world follows fromi=jX ij/E j=1−Y j/Y=1−s jusingjE j=iY i,which implies balanced trade for the world.Implication3is that the world is more open the more similar in size and the more special-ized the countries are.It is convenient to deﬁne world openness as the ratio of internationalshipments to total shipments,ji=jX ij/Y.Dividing(1)through by Y k and suppressingthe goods index k,world openness is given byji=jX ij/Y=jb j(1−s j)=1−jb j s j.Using standard statistical propertiesj b j s j=Nr bsV ar(s)V ar(b)+1/N,where N is the number of countries or regions,V ar denotes variance,r bs is the correlationcoeﬃcient between b and s and1/N=is i/N=jb j/N,the average share.This equationfollows from the shares summing to one and using standard properties of covariance.Here, V ar(s)and V ar(b)measures size dis-similarity and the correlation of s and b,r bs,is aninverse measure of specialization.Substituting into the expression for world openness:ji=jX ij/Y=1−1/N−Nr bsV ar(s)V ar(b)(2)Implication3follows from equation(2)because on the right-hand side the similarity of country size shrinks the variances while specialization shrinks the correlation r bs.The country-size similarity property has been prominently stressed in the monopolistic competition and trade literature.(It is sometimes taken as evidence for monopolistic com-petition in a sector rather than as a consequence of gravity no matter what explains the pattern of the b’s and s’s.)The specialization property has also been noted in that liter-ature as reﬂecting forces that make for greater net international trade,the absolute value of s j−b j.Making comparisons across goods classes,variation in the right-hand side of(2) results from variation in specialization and in the dispersion of the shipment and expenditure shares.Notice again that the cross-commodity variation in world openness arises here in a frictionless world,a reminder that measures of world home bias in a world with frictions must be evaluated relative to the frictionless world benchmark.Country-size similarity also tends to increase bilateral trade between any pair of countries, all else equal.This point(Bergstrand and Egger,2007)is seen most clearly with aggregate trade that is also balanced,hence s j=b j.Equation(1)can be rewritten asX ij=s iji s ijj(Y i+Y j)2Y,where s iji ≡Y i/(Y i+Y j),the share of i in the joint GDP of i and j.The product s ijis ijjis maximized at s iji =s ijj=1/2,so for given joint GDP size,bilateral trade is increasingin country similarity.(With unbalanced trade or specialization,an analogous similarity property holds for the bilateral similarity of income and expenditure shares.Letγj=E j/Y j. Then the same equation as before holds with the right-hand side multiplied byγj.)A more novel implication of equation(2)is implication4,that world openness is ordinarilyincreasing in the number of countries.Increasing world openness due to a rise in the number of countries reﬂects the property that smaller countries are more naturally open and division makes for more and smaller countries.This eﬀect is seen by diﬀerentiating the left-hand side ofji=jX ij/Y=1−jb j s j,yielding−j(b j ds j+s j db j).Increasing the number of countries tends to imply reducingthe share of each existing country while increasing the share(from zero)of the new country. The preceding diﬀerential expression should thus ordinarily be positive.The qualiﬁcation‘ordinarily’is needed because the pattern of share changes will depend on the underlying structure as revealed by the left-hand side of equation(2).On the one hand,the average share1/N decreases as N rises,raising world openness.On the otherhand,the change in the number of countries will usually change r bsin waysthat depend on the type of country division(or confederation)as well as indirect eﬀects on shares as prices change.(The apparent direct eﬀect of N in theﬁrst term on the right-handside of equation(2)vanishes because1/N scalesV ar(b)V ar(s).)A practical implication of this discussion is that inter-temporal comparisons of ratios of world international trade to world income,to be economically meaningful,should be con-trolled for changes in the size distribution and the number of countries,a correction of large practical importance in the past50to100years.Alternatively,measures of openness meant to reﬂect the eﬀects of trade frictions should be constructed in relation to the frictionless benchmark.Applied to aggregate trade data,gravity yields implication5,that world openness rises with convergence under the simplifying assumption of balanced trade for each country,b j= s j,∀j.The right-hand side of equation(2)becomes NV ar(s)+1/N under balanced trade, and per-capita income convergence lowers V ar(s)toward the variance of population.Baier and Bergstrand(2001)use the convergence property to partially explain postwar growth in world trade/income,ﬁnding relatively little action,although presumably more recent data inﬂuenced by the rise of China and India might give more action.Pointing toward a connection with economic theory,the shares s i and b j and the plau-sible hypothesis of the frictionless model must originate from an underlying structure of preferences and technology.Also,the deviation of observed X ij from the frictionless pre-diction reﬂects frictions as they act on the pattern of purchase decisions of buyers and the sales decisions of sellers,which originate from an underlying structure of preferences and technology.3Structural GravityModeling economies with trade costs works best if it moves backward from the end user. Start by evaluating all goods at user prices,applying demand-side structure to determine the allocation of demand at those prices.Treat all costs incurred between production and end use as being incurred by the supply side of the market,even though there are often signiﬁcant costs directly paid by the user.What matters economically in the end is the full cost between production and end use,and the incidence of that cost on the producer and the end user.Many of these costs are not directly observable,and the empirical gravity literature indicates the total is well in excess of the transportation and insurance costs that are observable(see Anderson and van Wincoop,2004,for a survey of trade costs).The supply side of the market under this approach both produces and distributes the delivered goods,incurring resource costs that are paid by end users.The factor markets for those resources must clear at equilibrium factor prices,determining costs that link to end-user prices.Budget constraints require national factor incomes to pay for national expenditures plus net lending or transfers including remittances.Below the national accounts,individual economic agents also meet budget constraints.Goods markets clear when prices are found such that demand is equal to supply for each good.The full general equilibrium requires a set of bilateral factor prices and bilateral goods prices such that all markets clear and all budget constraints are met.This standard description of general economic equilibrium is too complex to yield some-thing like gravity.A hugely useful simpliﬁcation is modularity,subordinating the economic determination of equilibrium distribution of goods within a class under the superstructure determination of the distribution of production and expenditure between classes of goods. Anderson and van Wincoop(2004)call this property trade separability.Observing that goods are typically supplied from multiple locations,even withinﬁne census commodity classes,it is natural to look for a theoretical structure that justiﬁes grouping in this way. The structural gravity model literature has uncovered two structures that work,one on the demand side and one on the supply side,detailed in sections3.1and3.2.Modularity(trade separability)permits the analyst to focus exclusively on inference about distribution costs from the pattern of distribution of goods(or factors)without having to explain at the same time what determines the total supplies of goods to all destinations or the total demand for goods from all origins.This is a great advantage for two reasons.First, it simpliﬁes the inference task enormously.Second,the inferences about the distribution of goods or factors is consistent with a great many plausible general equilibrium models of national(or regional)production and consumption.Modularity also requires a restriction on trade costs,so that only the national aggregate burden of trade costs within a goods class matters for allocation between classes.The most popular way to meet this requirement is to restrict the trade costs so that the distribution of goods uses resources in the same proportion as the production of those same goods.Samuel-son(1952)invented iceberg melting trade costs in which the trade costs were proportional to the volume shipped,as the amount melted from the iceberg is proportional to its volume. The iceberg metaphor still applies when allowing for aﬁxed cost,as if a chunk of the ice-berg breaks oﬀas it parts from the mother glacier.Mathematically,the generalized iceberg trade cost is linear in the volume shipped.Economically,distribution continues to require resources to be used in the same proportion as in production.Fixed costs are realistic and potentially play an important role in explaining why many potential bilateralﬂows are equalto zero.More general nonlinear trade cost functions continue to satisfy the production propor-tionality restriction and thus meet the requirements of modularity,but depart from the iceberg metaphor.Bergstrand(1985)derived a joint cost function that is homogeneous of degree one with Constant Elasticity of Transformation(CET).This setup allows for substi-tution eﬀects in costs between destinations rather than the cost independence due toﬁxed coeﬃcients in the iceberg model.Bilateral costs have a natural aggregator that is an iceberg cost facing monopolistically competitiveﬁrms.A nice feature of the joint cost model is its econometric tractability under the hypothesis of proﬁt maximizing choice of destinations. Although potentially more realistic,the joint cost reﬁnement turns out to make relatively little diﬀerence empirically.Arkolakis(2008)develops a nonlinear(in volume)trade cost function in which hetero-geneous customers are obtained byﬁrms with a marketing technology featuring aﬁxed-cost component(running a national advertisement)and a variable-cost component(leaﬂetting or telemarketing)subject to diminishing returns as the less likely customers are encountered. Because of the Ricardian production and distribution technology,resource requirements in distribution remain proportional to production resource requirements.Arkolakis shows that the marketing technology model can rationalize features of theﬁrm-level bilateral shipments data that cannot be explained with the linearﬁxed-costs model.His setup is not economet-rically tractable but is readily applicable as a simulation model.In all applications based on the preceding cost functions,proxies for costs are entered in some convenient functional form,usually loglinear in variables such as bilateral distance,con-tiguity,membership of a country,continent or regional trade agreement,common language and common legal traditions.See Anderson and van Wincoop(2004)for more discussion.More generality in trade costs that violates the production proportionality restriction comes at the price of losing modularity.See Matsuyama(2007)for recent exploration of the implications of non-iceberg trade costs in a2country Ricardian model.See Deardorﬀ(1980)for a very general treatment of the resource requirements of trade costs as a setting for his demonstration that the law of comparative advantage holds quite generally.3.1Demand-Side StructureThe second requirement for modularity can be met by restricting the preferences and/or technology such that the cross eﬀects in demand between classes of goods(either interme-diate orﬁnal)ﬂow only through aggregate price indexes.This demand property is satisﬁed when preferences or technology are homothetic and weakly separable with respect to a par-tition into classes whose members are deﬁned by location,a partition structure called the Armington assumption.Thus for example steel products from all countries are members of the steel class.Notice that the assumption implies that goods are purchased from multiple sources because they are evaluated diﬀerently by end users,and goods are diﬀerentiated by place of origin.It is usual to impose identical preferences across countries.Diﬀerences in demand across countries,such as a home bias in favor of locally produced goods,can be accommodated, understanding that‘trade costs’now include the eﬀect of a demand side home bias.In practice it is very diﬃcult to distinguish demand-side home bias from the eﬀect of trade costs, since the proxies used in the literature(common language,former colonial ties,or internal trade dummies,etc.)plausibly pick up both demand and cost diﬀerences.Henceforth trade cost is used without qualiﬁcation but is understood to potentially reﬂect demand-side home bias.Declines in trade costs can be understood as reﬂecting homogenization of tastes.Separability implies that each goods class has a natural quantity aggregate and a nat-ural price aggregate,with substitution between goods classes occurring as if the quantity aggregates were goods in the standard treatment.The separability assumption implies that national origin expenditure shares within the steel class are not altered by changes in the prices of non-steel products,though of course the aggregate purchase of steel is aﬀected by the aggregate cross eﬀect.Homotheticity ensures that relative demands are functions onlyof relative aggregate prices.Theﬁrst economic foundation for the gravity model was based on specifying the expendi-ture function to be a Constant Elasticity of Substitution(CES)function(Anderson,1979). Expenditure shares in the CES case are given byX ij E j =βi p i t ijP j1−σ(3)where P j is the CES price index,σis the elasticity of substitution parameter,βi is the ‘distribution parameter’for varieties shipped from i,p i is their factory gate price and t ij>1 is the trade cost factor between origin i and destination j.The CES price index is given byP j=i(βi p i t ij)1−σ1/(1−σ).(4)Notice that the same parameters characterize expenditure behavior in all locations;prefer-ences are common across the world by assumption.Notice also that the shares are invariant to income,preferences are homothetic.With frictionless trade,t ij=1,∀(i,j)and therefore all the buyers’shares of good i must equal the sellers share of world sales(at destination prices),Y i/Y.Thus the frictionless benchmark is justiﬁed by assuming identical homothetic preferences.For intermediate goods,the same logic works replacing expenditure shares with cost shares.The‘distribution parameters’βi bear several interpretations.They could be exogenous taste parameters.Alternatively,in applications to monopolistically competitive products,βi is proportional to the number ofﬁrms from i oﬀering distinct varieties(Bergstrand,1989). Countries with more activeﬁrms get bigger weights.In long run monopolistic competition the number ofﬁrms is endogenous.Due toﬁxed entry costs,bigger countries have more active ﬁrms in equilibrium,all else equal.The number of activeﬁrms contributes to determining the Y i’s that are given in the gravity module.The other building block in the structural gravity model is market clearance:at deliveredprices Y i=jX ij.Multiplying both sides of(3)by E j and summing over j yields a solutionforβi p1−σi,βi p1−σi =Y ij(t ij/P j)1−σE j.Deﬁne the denominator asΠ1−σi.Substituting into(3)and(4)yields the structural gravity model:Xij =EjYiYtijPjΠi1−σ(5)(Πi )1−σ=jtijPj1−σEjY(6)(Pj )1−σ=itijΠi.1−σYiY.(7)The second ratio on the right-hand side of(5)is a decreasing function(under the empirically valid restrictionσ>1)of direct bilateral trade costs relative to the product of two indexes of all bilateral trade costs in the system.Anderson and van Wincoop(2003)called the terms P j andΠi inward and outwardmultilateral resistance respectively.Note that{P1−σj ,Π1−σi}can be solved from(6)-(7)forgiven t1−σij’s,E j’s and Y i’s combined with a normalization.1Under the assumption of bilateral trade cost symmetry t ij=t ji,∀i,j and balanced trade E j=Y j,∀j,the natural normalization isΠi=P i.Anderson and van Wincoop estimated their gravity equation for Canada’s provinces and US states with a full information estimator that utilized(7)withΠi=P i. Subsequent research has focused mostly on estimating(5)with directional countryﬁxedeﬀects to control for E j/P1−σj and Y i/Π1−σi.Multilateral resistance is on the face of it an index of inward and outward bilateral trade costs,but because of the simultaneity of the system(6)-(7),all bilateral trade costs in the world contribute to the solution values.This somewhat mysterious structure has a simple1For any solution to the system{P0j ,Π0i},{λP0j,Π0i/λ}is also a solution.Thus a normalization is needed.Anderson and Yotov(2010a)ﬁnd that the system(6)-(7)solves quite quickly,not surprisingly because it is quadratic in the1−σpower transforms of the P’s andΠ’s.。

格林定律英语词根词缀

格林定律英语词根词缀The Law of Gravitation, proposed by Isaac Newton in 1687,is known as the "Universal Law of Gravitation" or more commonly, "The Law of Gravity". The Law of Gravity states that "every object in the universe attracts every other object with a force proportional to the product of the two objects' masses and inversely proportional to the square of the distance between them." This can be expressed mathematically in the form of the famous equation:F =G (m₁m₂)/r²Where "F" is the force of attraction between two objects, "G" is the gravitational constant, "m₁" and "m₂" are the masses of the two objects, and "r" is the distance between them.The concept of gravitation is based on the Greek root "gravitas" which means "weight" or "heaviness". The prefix "gra-" means their tendency to come together or approach each other, while the suffix "-ation" implies action or process. Therefore, gravitation literally means to come near each other due to their weight.In physics, the root word "grav-", combined with the prefix "in-", forms the word "inertia" which means an object's tendency to remain at rest or in motion unless an outside force acts on it. Inertia is caused by an object's mass, and since gravitation is related to mass, it follows that inertia has something to do with gravitation. The Latin root word "levi-" means "to raise" or "to lift" and this forms the basis of the term "levity". Levity is the opposite ofgravity, and describes an object's ability to float or be suspended in the air as opposed to being pulled down by the force of gravity.Gravity is also related to the root word "cel-" which means "to move rapidly". This produces the words "acceleration" and "accelerate" which means to increase the speed of something, or to cause it to move faster. According to Newton's law of gravitation, an object will accelerate towards the source of the gravitational pull.Finally, the root word "cent-" which means "center" or "point" is related to gravity as well. This produces the word "centripetal" which means directed toward the center. According to Newton's law of gravitation, all objects in the universe are moving towards each other due to the gravitational pull they experience.In conclusion, the law of gravity is a universal law that governs all objects in the universe, and its concept is based on numerous English words that are derived from Latin and Greek roots. By understanding the roots of these words and their meanings, we can gain a better appreciation for the universality of gravitation.。

特斯拉动态引力理论原文

Introduction:
There is a new theory of gravity called Dynamic Theory of Gravity [DTG]. Based on classical thermodynamics Ref:[1] [2] [3] [9] it has been shown that the fundamental laws of Classical Thermodynamics also require Einstein’s
p 4 = mv 4 ,
(1a)
where the velocity in the fifth dimension is given by:
•
γ v4 = , αD
•
(1b)ቤተ መጻሕፍቲ ባይዱ
and γ is a time derivative where gamma itself has units of mass density or kg/m3, and αo is a density gradient with units of kg/m4. In the absence of curvature, (1) becomes:
(5)
and for orbiting Hubble telescope (ht) of a height h the following expression:
ln[1 + z ht ] = −
M em HL R⊕ G M⊕ − . + c 2 (R + h ) + R R h ⊕ c ⊕ em
Abstract:
In a new theory called Dynamic Theory of Gravity, the cosmological distance to an object and also its gravitational potential can be calculated. We first measure its redshift on the surface of the Earth. The theory can be applied as well to an object in orbit above the Earth, e.g., a satellite such as the Hubble telescope. In this paper, we give various expressions for the redshifts calculated on the surface of the Earth as well as on an object in orbit, being the Hubble telescope. Our calculations will assume that the emitting body is a star of mass M = MX-ray(source) = 1.6×108 Msolar masses and a core radius R = 80 pc, at a cosmological distance away from the Earth. We take the orbital height h of the Hubble telescope to be 450 Km.

动态称量

Dynamic Weighing Experiments -The Wayto New Physics of GravitationA. L. Dmitriev, E. M. Nikushchenko and S. A. BulgakovaSt-Petersburg State University of Information Technologies, Mechanics and Optics49, Kronverksky Prospect, St-Petersburg, 197101, Russia+7.812.3154071, alex@dmitriyev.ruAbstract. Dynamic weighing is a measuring of size of the average gravity force acting on a test body which is in the state of accelerated movement. The acceleration of a body, or its microparticles, can be caused both by forces of gravitation, and by a direct, electromagnetic in nature, influence on the part of other bodies. It is just dynamic weighing of bodies which is informative in studying the features of electromagnetic and gravitational forces interaction. The report gives a brief review of results of experiments with weighing of accelerated moving bodies –in case of shock phenomena, in state of rotation, and in heating. Special attention is given to measurements of free fall accelerations of a mechanical rotor. I n majority of the laboratory experiments executed with the purpose of checking the equivalence principle, the axis of a rotor was oriented verticallly. In our experiment we measured the free fall accelerations of the closed container inside which a mechanical rotor (gyroscope) with a horizontal axis of rotation was installed. There was observed an appreciable, essentially exceeding errors of measurements increase of acceleration of free falling of the container at angular speed of rotation of a rotor up to 20 000 rev/min. The physical conditions of free vertical falling ofa body essentially differ from conditions of rotary (orbital) movement of a body in the field of gravity and the resultobtained by us does not contradict the results of measurements of a gyroscope precession on satellites. Experiments with dynamic weighing of bodies give useful information on complex properties of the gravity force which are beyond the scope of well-known theories. Their careful analysis will allow to expand and supplement the concepts based on the general theory of relativity, and probably to open a way to new physics of gravitation and to new principles of movement.Keywords:Gravity Force, Weighing, Acceleration, Free Falling, Gyro, Equivalence Principle .PACS:, 04.80.-y.INTRODUCTIONThough physics is an experimental science, in modern physics of gravitation the scale of theoretical researches has considerably surpassed the scale of experiments. In a solid, over 600 pages, recently published review «100 Years of Gravity and Accelerated Frames » the experimental (and besides -astrophysical) tests of gravitational theories are given less than 30 pages(Hsu and Fine, 2005). Attempts to establish some new properties of gravitation in laboratory experiments, from the point of view of classical GR, are usually considered as unpromising. Meanwhile, the grounds for criticism of experimental basis of GR –equivalency principle –do exist. Thus, in all Eotvos-experiments the measurements of forces of gravitation were made in the extremely limited physical conditions, at constant temperature and small accelerations of test bodies (Chen and Cook, 1993;Haugan and Lammerzahl, 2001). The approximation of appropriate GR results in the area of high accelerations of bodies, strictly speaking, is incorrect. The interrelation of the external accelerations, for example, of elastic forces applied to a test body, and force of gravitation acting on this body, follows from the deep unity of electromagnetic and gravitational interactions and, according to the phenomenological description, can be considered as gravitational analogue of Faraday’ law of induction and Lentz’ rules (Dmitriev, 2001, 2009a). The search for non-classical effects in gravitation in experiments with precision weighing of accelerated moving bodies (oscillating, rotating, being heated up etc.) is logical and expedient. Yet Mendeleev(1950)pointed out: « I f it is possible to achieve something in understanding of gravitation and weight, then in no other way and most likely by the most precise weighings and observations of oscillations taking place at that time».CP1208, Space, Propulsion & Energy Sciences International Forum–SPESIF-2010, edited by G. A. Robertson© 2010 American Institute of Physics 978-0-7354-0749-7/10/$30.00There are distinguished two ways of exact weighing of bodies: static and dynamic. In static weighing the test body is motionless relative to the Earth and weight of the body is determined by the size of elastic or electromagnetic force compensating the gravity; this technique directly corresponds to definition of concept « weight of a body ». I n dynamic weighing the beam of weights and a test body make slowly fading oscillations, and average value of the weight measured is determined by elongations’method, by fixing and averaging some extreme values of readings displayed on the scale of weights; in that case the test body experiences some well marked accelerations, which are described by an infinite set of time derivatives from body displacement. Obviously, the physical conditions of dynamic and static weighing essentially differ, though in practical metrology of weight the results of both techniques of weighing are often believed to be identical. Just dynamic weighing is informative in researches into interrelation of gravitational and electromagnetic (elastic) forces.Of special interest are the measurements of acceleration of free falling of the test bodies underlying the ballistic methods of gravimetry. At free falling a body the interaction of gravitational and foreign forces, by definition, is excluded, but this ideal state is achieved only under condition of absence of own oscillatory or rotary movement of a test body.Preconditions of search of interaction of electromagnetic and gravitational forces are the results of various Gravity Electro-Magnetism theories which are based on modified GR’equations (Bini et al ., 2008;Schmid, 2009). Though the observable effects predicted in such theories are usually extremely small, some worthy positive results were obtained in some laboratory experiments (Tajmar et al .,2008;Woodward, 2009).The interrelation of gravitational and electromagnetic forces is especially important in the analysis of properties and reasons of inertia, propulsions’ problems, and search for new principles of movement. Correctly executed gravitational laboratory experiment can and should be the basis for formulations of new concepts in gravitation including, supplementing and developing the known GR approaches.ACCELERATION OF EXTERNAL FORCES, GRAVITYAND INERTIAL MASS OF A BODYIn distinction from "geometrical", the "field" concept of gravitation describes the gravitational interaction of bodies similarly to other kinds of physical interactions -electric and magnetic. Thus the concept of the "material" gravitational field related to sources -the gravitational mass -and characterized by the set of parameters (potential, velocity, impulse, moment) is considered. The advantage of the field, basically phenomenological concept of gravitation consists in an opportunity to use for its development some separate analogies of the gravitational and electromagnetic phenomena, and in their direct experimental check. Thus, gravitational fields, certainly, should have the properties similar, but not identical to properties of electromagnetic fields.I n (Dmitriev, 2001)on the basis of the noted analogies the assumption of original reaction of the gravity force acting on a test body, on its acceleration a G caused by action of external not gravitational (for example, elastic) forces is put forward. Change p,c g 'G of acceleration of the gravity, similar to the phenomenon of Faraday’s inductionlaw in view of Lenz’ rule, at simple linear approximation, is equal to p,c p,c g a ' D G G , (1)where indexes p,c indicate mutual, passing p or a contrary (opposite) c ,orientation of a vector 0g Gof normal acceleration of a gravity and vector a G of acceleration of external force, Figure 1.Rough estimations of the order of value of dimensionless factors p D and c D , which the gravitational interrelation ofgravitational and electromagnetic fields specify, were executed in mechanical experiments with weighing of two coupled mechanical rotors with the zero full moment, with a horizontal axis of rotation, and in the analysis of the shock phenomena (Dmitriev, 2002).For metal not magnetic test bodies it is 2c 10 D |,7p c ()10 D D |.By consideration of thermal chaotic movement of microparticles of solid bodies the consequence of equation (1), in view of an inequality p c D !D , is the negative temperature dependence of gravity, also observed in the experiment(Dmitriev, Nikushchenko and Snegov,2003; Dmitriev,2008).Measurements of anisotropy of weight of a crystalwith a big spatial difference of speeds of longitudinal acoustic waves also specify to nonzero value of a difference p c ()D D (Dmitriev and Chesnokov, 2004).(a) (b)FIGURE 1. a)Changes p g 'G in gravity force acceleration acting on test body while body is falling down with acceleration a G and b)Changes c g 'G in gravity force acceleration while body is moving up with acceleration a G .Definition of factors p D and c D of electromagnetic (elastic) and gravitational forces interaction has allowed to givea simple physical interpretation to inertial mass of a body. In (Dmitriev, 2008b;2009b)in the description of balance of the elastic (electromagnetic) and gravitational forces acting on the test mass on the part of remote mass (for example, stars), according to idea of Mach about the gravitational nature of inertial forces, the ratio between inertial i m and gravitational g m masses is obtained,i g p c m m () D D . (2)Equation (2)shows the direct proportionality of inertial and gravity masses of a body, and the relation of theses masses, contrary to the known postulate of "geometrical" model of gravitation, generally speaking, is not a constant. Equation (1)shows the relation of change of gravity acceleration with acceleration a Gof external forces, but in so doing it is necessary to take into account that the absolute size p,c g 'of an increment of acceleration should alsodepend on magnitude 0g of normal gravity acceleration. Generally, in view of influence of forces of the gravitationcaused by remote surrounding masses (stars), in movement of a test body on a vertical there should be carried out the equationp,c p,c 0A (g g )c D , (3)where g c -a projection of acceleration of forces of gravitation on the part of the remote masses located in a solid angle 2S , on the direction of the accelerated movement of body. Here the dimensional factors p,c A are universal andcharacterize the action on a test body of not only the gravitational field of the Earth, but also the fields of the gravitation created in all surrounding masses.The resultant forces of gravitation acting on the motionless or moving with the constant speed test body from direction of remote masses, uniformly distributed in space in a full solid angle 4S , it is approximately equal to zero, while the magnitude g c determines the inertial properties of a body, Figure 2, where the resulting accelerations ’ vectors g c G and g c c G , caused by action of the remote masses located in the left and the right half-spaces in the solid angles 2S , are equal in magnitude and are oppositely directed.Equations (2) and (3)are in agreement with the principle of Mach according to which the inertial properties of bodies are determined by action on them of forces of the gravitation created by all surrounding masses, including rather remote ones.FIGURE 2.Mutual orientation of a vector of acceleration of not gravitational forces a G and increments vectors p c g , g ''G G ofaccelerations of the gravitation forces acting on test mass from the direction of remote masses (stars).INERTIAL MASS ANISOTROPYAs is known, GR excludes the practical observablity of anisotropy of inertia (Hughes, 1960). Consequence of equations (2) and (3)is an appreciable difference of inertial mass of a test body at its accelerated movement relative to the Earth in horizontal and vertical directions (Dmitriev, 2009b). Let's show it on an example of harmonious oscillator.For the harmonious, caused by the action of external elastic force, oscillatory movement along a vertical, theaverage, for the period of oscillation, inertial mass i ˆmof a test body is equal to 0i g p c g ˆmm (A A )(g )2c . (4)In oscillatory movement of this test body along the horizontal, its average inertial mass i m is equal to i g p c m m (A A )g c . (5)In equations (4) and (5)the resulting magnitude g c of projections of accelerations of gravity forces created by the remote masses in a solid angle 2S , is believed approximately constant and independent from the direction in space. The relative difference of "vertical" and "horizontal" inertial masses, taking 0g g c !!, is equal to 0i i i i ˆg m m 2ˆmm 2g |c . (6)Experimental estimations of magnitude of inertial mass’ anisotropy of a body can be made, comparing the periods of oscillations of linear mechanical oscillator with vertical and horizontal orientations of its axis. For the same purpose it is convenient to use the rotation oscillator, for example a pendulum of high-quality mechanical balance watch, by changing orientation of the balance axis.The period T of free oscillations of system a balance -spiral of mechanical watch is equal toT 2 , (7)where I -the moment of inertia of balance i I m v and C -factor of elasticity of the spiral.According to equations (6) and (7)the period ˆTof oscillations of balance in a vertical plane should be more than the period T of oscillations of balance moving in a horizontal plane, that is the ideal mechanical watch in position « on an edge » goes more slowly, than in position "flatwise".The position-sensitivity of mechanical watch is influenced many factors, including, the moment of inertia and quality of a spiral, conformity of an axis of rotation and the centre of inertia of a pendulum, friction in axes of a suspension bracket of a pendulum etc (Paramonov, 1977). With high quality of watch and its careful adjustment,the influence of the specified factors can be reduced practically to zero, and in that case the comparison of daily motion of balance watch in vertical and horizontal positions can be used for an estimation of magnitude of anisotropy of inertial masses (equation 6).In view of equations (4)-(7), the relative difference J of the daily motion of an ideal watch is equal to 0ˆg T T 12ˆ4g TT J | . (8) In Figure 3,the results of measurements of position sensitivity of twenty one samples of mechanical watch «Raketa 2609 » manufactured by “Petrodvortsovy watch factory” are given. The difference of an average daily motion of watch in positions "flatwise" and « on an edge » was measured;each of them was measured as an average for two different positions of the head and plane of a dial of watch. The average magnitude of watch motion delay in position «on an edge» has come to about 15 seconds over one day which corresponds to 41.710 J |.specimen numberD i f f e r e n c e o f t i m e m o t i o n , s e c o n d i n 24 h o u r FIGURE 3. A difference of a daily motion of mechanical balance watch «Raketa 2609 » in positions "flatwise" and «on an edge».The question of what part of the given value J is caused by action of physical factors (anisotropy of inertial mass in a gravitational field of the Earth), and what –by technical imperfection of the mechanism of watch still remains open. The difficulty is that even with an appreciable influence on a motion of watch of anisotropy of inertial mass of the pendulum of watch, the position-dependence of a daily motion of watch can be reduced almost to zero by technical means of adjustment. Thus the "physical" delay of a watch motion can be artificially compensated by adjustment of watch,which complicates an objective estimation of magnitude of such effect.Therefore the careful analysis of all technical factors influencing the position sensitivity of balance watches and clockworks used in such experiments is necessary for obtaining of objective data. Nevertheless, the given average result is in agreement with physical preconditions noted above and can be the basis for setting up precision experiments with use of mechanical oscillators on measurements of prospective anisotropy of inertial mass.Note, if the result shown in Figure 3gives a true estimation of magnitude order of a relative difference of inertial mass in horizontal and vertical directions, then, according to equation (8), gravitational field-intensity g c created by all indefinitely remote masses located in a solid angle 2S relative to a point of observation, the said intensity is approximately one thousand times the magnitude of normal acceleration of gravity on the surface of the Earth. In view of gravitational analogue of the Faraday’s induction law (equation (1)), such rather strong "interstellar" gravitational field, apparently, is also the main physical reason of inertial properties of bodies.The precision measurements of anisotropy of inertial mass of bodies in a non-uniform gravitational field will confirm validity or a fallacy of the above estimation and as a consequence the validity of the phenomenological "field" concept of gravitation in the description of inertial properties of bodies.FREE FALLING OF A MECHANICAL ROTOR WITH A HORIZONTAL AXISIt is known, that weight of motionless bodies is directly determined by accelerationg of free falling. For ɨscillatingand rotating test bodies the measurement of such acceleration is not trivial.To laboratory weighings of rotors of mechanical gyroscopes the set of works (Nitschke and Wilmarth, 1990;Quinn and Picard, 1990;Faller et al., 1990) is devoted. Such measurements were usually carried out with the purpose of experimental check of an equivalence principle, or various gravitoelectric(gravitomagnetic)models. In most cases, in these experiments the axis of a rotor was oriented vertically and, as a whole, the positive effect was absent(Luo et al., 2002). In paper (Dmitriev and Snegov, 2001)the results of exact weighing of two coaxial rotors with a horizontal axis and with the zero total are given, and its weights which have shown little change, dependent on angular speed of rotation of a moment J6rotor. The explanation of these results the possible precession a gyroscope is complicated, connected to rotation the. Earth, which essentially could to influence indications of weights, owing to inexact performance of equality J06In much smaller degree the precession effects influence on results of measurement of size of acceleration by freely falling of rotor. Thus physical conditions of interaction of a falling rotating rotor with the centre of gravitation (Earth) essentially differ from conditions of weighing of a rotor on based laboratory weights.In described simple experiment (Dmitriev, Nikushchenko and Bulgakova, 2009)the acceleration of free falling of container with the two, located coaxially, rotors of mechanical gyroscopes placed inside it was measured Figure4; the device and characteristics of the container are given in (Dmitriev and Snegov, 2001).FIGURE4.The device of the container. 1 -electric coils of the engine of a gyroscope, 2 -a massive cylindrical part of a rotor, 3 -the case of the first gyroscope, 4 -plugs of power supplies of engines of gyroscopes, 5 -the case of the secondgyroscope (it is shown without a section), 6 -the case of the container.On the container the compact highly stable generator of pulses connected to two differ-coloured light-emitting diodes, located along a trajectory of falling of the container is fixed.Appearance of the container with the device for throwing down is shown in Figure5.Distance on centre to centre of aperture stop (holes), established before light-emitting diodes is l76.25mm, frequency of impulses F56.25Hz, duration of impulse optical signals0.13ms.The trajectory of the falling container was photographed by the digital camera with exposure0.60.8s.An example of such photos is shown in Figure6. Coordinates of marks (the centres of holes) were digitized by computer.FIGURE 5.Container with the device for throwing. FIGURE 6.An example of the container falling trajectory photo.The calculation of acceleration g of free falling container was carried out under the formula 2212()F g N ' ' , (9)where 12,''-absolute lengths of the next sites of the trajectories,containing N marks; the scale of the image wasdefined by distance A between light-emitting diodes.For reduction of influence of aberration of the image owing to distorsion, the average scale of the image paid off on three readout of length A -in the top, central and bottom parts of a trajectory. The size g in separate measurement was determined as average value of acceleration, designed on two trajectories appropriate to two groups of color marks on the image.The example of the measured values of acceleration of free falling container in conditions (1)0Z , (2)0Z z and (3)0Z (upon termination of time rotation of rotor) is shown in Figure 7.FIGURE 7.The example of the measured values of acceleration of free falling container. 1.0Z (N. 1-4 ), 20Z z ( N. 6-10 ), 3.0Z (N. 12-16 ).The maximal angular velocity of rotation of a rotor 20000rpm Z |, rotation time of rotor is 14-15 mines, duration of one cycle of measurements from 4-5 pictures about 2 minutes.It was processed over 200 pictures, thus the increase of acceleration of free falling of a rotor was regularly observed at transition from a condition (1) to a condition (2) with average size 2g 102ɫP V' r . At smooth reduction ofspeed Z of rotation of a rotor the size g'also decreased, falling up to zero at0Z. In the specified in figure measurements both rotors rotated in one direction and the maximal full moment of rotation of rotors was 2J0.2kg m/s6| .The reason of an appreciable divergence of the measured absolute value of acceleration g of a gravity at0Z(about 990 cm / s2) and standard, at latitude of Saint Petersburg (about 982 cm / s2 A ), apparently, are discrepancies indisplay of scale, errors of absolute value of frequency F of the generator and also the small local (technical) changes of g. Geographical orientation of a vector of the moment of rotation of a rotor, N-S or W-O, did not influence on results of measurements g'. Daily dependence of size g'also it was not observed.At horizontal orientation of an axis of rotation of a rotor the each of its particles simultaneously participates in two linear oscillations in horizontal and vertical planes.Thus of acceleration of particles at their vertical oscillations by an infinite set of derivatives on time from linear displacement are described. As it was marked in (Dmitriev, 2001;2008a;2009a)in these conditions it is possible to expect display of "nonclassical" properties of gravitation,which mentioned some more Mendeleev (1950).Free falling of masse oscillated along a vertical physically essentially differs from circular (orbital) movement of such masse. Therefore the result received by us does not contradict the results of exact measurements of precession a gyroscope in a circumterraneous orbit.Relative change g/g'of acceleration of free falling of the container in the described experiment is equal to210|. Taking into account that the mass of a rotor (500gram) amounts to1/3mass of the whole container, the relative change g/g'reduced to the rotor mass is equal to2310| . It is possible to assume that if in a capacity of such "rotors" to use the nuclei of atoms with spatially oriented spins(the set of such atoms forms a macro-dimensions test body) then at high concentration of oriented nuclei in a test body the spatial dependence of acceleration of free falling of a body on orientation of rotors will be much higher than the specified one.Further experimental researches into free falling of rotating (oscillating) in a vertical plane of either masses or samples of materials with oriented nuclear spins, with use of precision measuring instruments, for example, interferometric ones, seem rather expedient.CONCLUSIONSThe experimental results described above are obtained by simple technical means and are certainly of a preliminary character. At the same time, it is known that viable ideas in physics quite often prove themselves in technically simple experiments. Logical transition from statics to dynamics, realized in experimental gravitation, opens the prospect of establishment of new properties of gravitation which in the future can get the big scientific and practical values. It creates the prospects of effective solutions and propulsion-problems. The leading role in achievement of such targets belongs to experiment. The practical step to new physics of gravitation should be precision experimental researches into dynamic effects in gravitation. Among them it is necessary to note: x Measurement of temperature dependence of gravitation force;x Static and dynamic measurements of weights of test bodies rotating or oscillating in a vertical plane;x Measurement of anisotropy of crystals weights and measurements of anisotropy of inertial mass of bodies;x Measurement of acceleration of a free falling rotor at various orientations of axis of rotation, and also the samples with artificial orientation of nuclear moments (spins);x Measurements of spatial dependence of restitution coefficient at elastic impacts of solid bodies.Experiments with weighing of accelerated moving bodies will give useful information on complex, going beyond the scope of well-known theories properties of gravitation. Careful analysis of these results will allow to expand and complement the concepts based on the general theory of relativity, and probably to open the ways to new physics of gravitation and new principles of movement.NOMENCLATUREc A =coefficient of interaction of elastic and gravity forces by counter of a G and total vector of gravity force [-12m s ]p A = coefficient of interaction of elastic and gravity forces by passing of a G and total vector of gravity force [-12m s ]a G = acceleration vector of external force [-12m s ]c D =degree of interaction of elastic and gravity forces by counter of a G and 0g G (#)p D =degree of interaction of elastic and gravity forces by passing of a G and 0g G (#)C =factor of elasticity of the spiral [2-2kg m s ]g '=average difference of measured values of acceleration of free falling container [-2m s ]F =frequency [-1s ]g =acceleration of free falling container [-2m s ]g =average acceleration of free falling container [-2m s ]0g =normal acceleration of gravity [-2m s ]g c =resulting magnitude of projections of accelerations of gravity forces created by the remote masses in a solid angle 2S [-2m s ]J =the relative difference of the daily motion of an ideal watch (#)I =moment of inertia [2kg m ]J 6= full angular momentum [2-1kg m s ]A =distance [m ]g m =gravitational mass [kg ]i m =inertial mass [kg ] i m =average vertical inertial mass [kg ]i m =average horizontal inertial mass [kg ]N =number of marks (#)T =period of free oscillations [s ] T =period of oscillations of balance in a vertical plane [s ]T =period of oscillations of balance moving in a horizontal plane [s ]Ȧ=angular velocity [-1rad s ]12,''=lengths of the next sites of the trajectories [m ]'G c g ,'G p g = increments of acceleration of gravity [-2m s ]c G g ,c c G g =the resulting accelerations’ vectors, caused by action of the remote masses located in the left and the right half-spaces [-2m s ]REFERENCESBini, D., Cherubini, C., Chicone, C. and Mashhoon, B., “Gravitational I nduction,”/PS_cache/arxiv/pdf/0803/0803.0390v2.pdf,(2008).Chen, Y. T., and Cook, A., Gravitational Experiments in the Laboratory, Cambridge University Press, Cambridge, (1993).Dmitriev, A. L., “On the I nfluence of External Elastic (Electromagnetic) Forces on the Gravity,”Russian Physics Journal,44(12), (2001), pp.1323-1327.Dmitriev, A. L., and Snegov V. S., “Weighing of a Mechanical Gyroscope with Horizontal and Vertical Orientations of the SpinAxis,”Measurement Techniques ,44(8), (2001), pp.831-833.Dmitriev, A. L., “Inequality of the Coefficients of Restitution for Vertical and Horizontal Quasielastic Impacts of a Ball Against a Massive Plate,” International Applied Mechanics ,38(6), (2002), pp.747 –749.Dmitriev, A. L., Nikushchenko, E. M., and Snegov, V. S., “Influence of the Temperature of a Body on its Weight,” Measurement Techniques ,46(2), (2003), pp.115 –120.Dmitriev,A. L. and Chesnokov,N. N., “The effect of the orientation of an anisotropic crystal on its weight,”Measurement Techniques , 47(9),(2004), pp.899-901.Dmitriev, A. L., “Measurements of the Influence of Acceleration and Temperature of Bodies on their Weight,” in proceedings of Space Technology and Application International Forum (STAIF-2008), edited by M. El-Genk, AIP Conference Proceedings 969,New York, (2008a),pp. 1163-1169.Dmitriev, A. L., “On the Nature of Inertial Mass,”/ftp/arxiv/papers/0806/0806.0796.pdf,(2008b).。

科技英语翻译___课后答案

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工业用机器人与数控机床有许多共同的特性。

第1节翻译练习2With non-changeover control both the boiler plant and the chiller plant operate to provide simultaneous heating and cooling throughout the year.The online service delivers substantially more value to our global audience of e-business professionals in the chemical, plastics and allied industries.This device can mimic photosynthesis to produce usable energy from sunlight.采用非转换控制，锅炉设备和制冷装置都在运行，全年可同时供暖和制冷。

该网络服务主要向全球从事化学、塑料及相关工业的专业电子商务用户提供更有价值的服务。

这种装置能够模拟光合作用，利用阳光产生可用的能源。

第1节翻译练习3The longitudinal axis of the turbine generator is perpendicular to the axis of the steam generator. In the right conditions, membranes are self-assembling.Winding of the spring induces residual stresses through bending.汽轮发电机的纵轴与锅炉轴线垂直。

a little history of science 蓝思值

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深空探测中的轨道设计和轨道力学

深空探测中的轨道设计和轨道力学一、本文概述Overview of this article《深空探测中的轨道设计和轨道力学》这篇文章旨在深入探讨深空探测任务中轨道设计和轨道力学的关键要素和实际应用。

随着人类探索宇宙的步伐不断加快，深空探测已成为空间科学领域的重要研究方向。

轨道设计和轨道力学作为深空探测任务的核心技术，对于实现高效、精确的探测任务具有至关重要的作用。

The article "Orbital Design and Orbital Mechanics in Deep Space Exploration" aims to delve into the key elements and practical applications of orbital design and mechanics in deep space exploration missions. With the accelerating pace of human exploration of the universe, deep space exploration has become an important research direction in the field of space science. Orbital design and mechanics, as the core technologies of deep space exploration missions, play a crucial role in achieving efficient and accurate exploration tasks.本文首先将对深空探测任务进行简要介绍，阐述轨道设计和轨道力学在深空探测中的重要性和应用背景。

随后，文章将重点讨论轨道设计的基本原理和方法，包括轨道选择、轨道优化、轨道转移等方面的内容。

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ABSTRACT
This paper proposes GBM (gravitation-based model), a physical model for information retrieval inspired by Newton’s theory of gravitation. A mapping is built in this model from concepts of information retrieval (documents, queries, relevance, etc) to those of physics (mass, distance, radius, attractive force, etc). This model actually provides a new perspective on IR problems. A family of effective term weighting functions can be derived from it, including the well-known BM25 formula. This model has some advantages over most existing ones: First, because it is directly based on basic physical laws, the derived formulas and algorithms can have their explicit physical interpretation. Second, the ranking formulas derived from this model satisfy more intuitive heuristics than most of existing ones, thus have the potential to behave empirically better and to be used safely on various settings. Finally, a new approach for structured document retrieval derived from this model is more reasonable and behaves better than existing ones.
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Categories and Subject Descriptors
H.3.3 [Information Search and Retrieval]: Retrieval models
General Terms
Algorithms, Experimentation, Theory
Keywords
Information retrieval models, Gravitation-based model, theory of gravitation, mass estimation, structured document retrieval
பைடு நூலகம்1 1
Beijing Institute of Technology
f-qyu@
the perspective of set theory and Boolean algebra, while the perspective used in the vector space model is vector and linear algebra. Most of other categories of models take the probabilistic perspective, which is the most dominating perspective on information retrieval today. It may be extremely hard to answer questions like “what is the essence of information retrieval”, and “what is the right perspective of it”. However, it is clear that, till now, we know more about information retrieval each time when a new perspective is adopted. It would also be helpful to view information retrieval from more new perspectives. Although many of the models (and the formulas and algorithms derived from them) have been successfully applied to various tasks, there are still some problems faced by them: First, the retrieval formulas (formal or ad-hoc) conducted by most IR models fail to satisfy even some basic intuitive heuristic constraints [5]; Second, the retrieval formulas derived or motivated from many IR models commonly lack intuitive interpretations, especially physical interpretations. At the same time, we are living in a physical world which is dominated by fundamental physical laws. Can we get help from “the God” in acquiring deeper understanding of information retrieval? In this paper, we try to view information retrieval from the perspective of physics, a quite different perspective from existing ones. We propose a new framework which models documents, queries, and their relationships using basic concepts in physics. In particular, documents and queries are modeled as objects with specific structures; and the relationship between a query and a document is modeled as the attractive force between them. A basic rule used here is Sir Isaac Newton’s theory of gravitation (see Section2.1 for a brief introduction of it), a fundamental law of the universe. The primary goal of the model is to help learning more about information retrieval from a new perspective. It is encouraging that we can really benefit from the nature. With the new perspective and model, we get the following preliminary achievements, 1. We have derived a family of effective ranking formulas which satisfy all the heuristic constraints1 proposed in [5]. Experimental results show that these formulas are among the most effective ranking functions proposed till now.
1. INTRODUCTION
Information retrieval (IR) models, which define the representation of documents, queries, and the relevance relationship between them, are in a core position in information retrieval (IR). In the past several decades, many categories of IR models (and their variants) have been proposed and studied [2], including Boolean models, vector space models [3][4], probabilistic and logic models [10][14][6][1], and language models [12][13][7][24], etc. The key behind all the models is the primary perspective on information retrieval. The Boolean model views IR problems from