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Download PDF by A. Lemaître (auth.), Jean J. Souchay, Rudolf Dvorak (eds.): Dynamics of Small Solar System Bodies and Exoplanets

By A. Lemaître (auth.), Jean J. Souchay, Rudolf Dvorak (eds.)

ISBN-10: 3642044573

ISBN-13: 9783642044571

This ebook bargains an updated evaluate of present examine on Dynamics of Small sun approach our bodies and Exoplanets. In course-tested huge chapters the authors conceal subject matters of theoretical celestial mechanics, physics and dynamics of asteroids, comets, balance of exoplanets and numerical integration codes utilized in dynamical astronomy.

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Additional resources for Dynamics of Small Solar System Bodies and Exoplanets

Example text

The frequencies change drastically if Mercury is assumed to have a liquid core [8]. 13 The Gravitational Resonances Another interesting family of resonances concerns the commensurabilities between the orbital period of a first object (called here the satellite) orbiting a second body (called here the planet) with the rotation period of this planet; typically the geostationary situation of an artificial satellite in gravitational resonance 1:1. 1 The Potential of the Earth The apparition of such a resonance comes from the fact that the planets are neither spherical nor homogeneous.

I, j, k being different and ∈ {1, 2, 3}). From the balance of energy, we know that s j B j + sk Bk > 0 and then two cases are possible: – s j B j > 0 and sk Bk < 0: it means that if we enter the region k, by our previous discussion, we are going out quite immediately. So the capture in the region j is the only possibility. – s j B j > 0 and sk Bk > 0: the capture in regions j and k is possible, both behaviors are associated with probabilities of capture given by the following expressions: sj Bj s j B j + sk Bk sj Bj =− si Bi sk Bk = s j B j + sk Bk sk Bk .

34) S 52 A. Lemaˆıtre • The equation ∂H ∂S = 0 gives the value of S at the equilibrium: n 2 C (1 − cos K ) S =n− (2 δ1 + δ2 ) sin (2K − 2 i) + 2δ2 sin (K − i) . C 4S (35) ˙ = 0) in (34), the obliquity Let us notice that if we neglect the precession rate (Ω at the equilibrium K coincides with the inclination i, and the two frequencies are exactly equal: S = nC. ˙ = 0, there is a difference between K and i and (35) shows On the opposite, if Ω the correction to add on the exact commensurability. If the inclination i is very small (sin i i and cos i 1), the equilibrium equation gives an analytical solution for K : K = δ1 + δ2 δ1 + δ2 − ˙ S Ω n2 C i.

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Dynamics of Small Solar System Bodies and Exoplanets by A. Lemaître (auth.), Jean J. Souchay, Rudolf Dvorak (eds.)


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