Results 141 to 150 of about 200,604 (171)

Types of Motion in the Oblate Planet Problem

1985
We consider a mass point in the gravitational field of an oblate planet and in a meridianal plane. The Hamiltonian of the problem is: $$ \frac{1}{2}\left( {p_r^2 + \frac{{p_{\theta }^2}}{{{r^2}}}} \right) - \frac{1}{r} - \frac{\varepsilon }{{{r^3}}}\left( {1 - 3{{\sin }^2}\theta } \right) $$ .
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Motion of a Space Probe Near an Oblate Planet

1970
For orbits with semi-latus rectum of the order of \( \frac{1}{6} \) the planet’s equatorial radius, conventional first order theories of satellite motion about an oblate planet produce errors of the order of 1300 J 2 2 outside the planet’s radius, J2 being the oblateness coefficient.
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A Mathematical Theory of the Orbits About an Oblate Planet

Journal of the Society for Industrial and Applied Mathematics, 1965
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Qualitative properties of orbits about an oblate planet

Communications on Pure and Applied Mathematics, 1964
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Satellite Motions About an Oblate Planet

Journal of the Aerospace Sciences, 1961
The drag-free path of a vehicle in the vicinity of an oblate planet is discussed. Although the solution found is approximate in the sense that it is a truncated power series in the oblateness parameter / , there is no restriction on either the eccentricity or the inclination angle.
Anthony, M. L., Fosdick, George E.
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Planar Motions About an Oblate Planet

ARS Journal, 1961
Two cases of plane motion (equatorial and polar) of a vehicle about an oblate planet are discussed. Further, the results of these drag free plane motion studies may be applied to the determination of radial position, speed, and angular momentum for a motion whose initial velocity vector is inclined at an arbitrary angle to the equatorial plane ...
Anthony, M. L., Fosdick, G. E.
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On the Density of an Oblate Spheroidal Planet and the Motion of a Satellite

American Mathematical Monthly, 1929
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Solar Oblateness and the Perihelion Advances of Planets

Nature, 1967
Observations of the oblateness of the Sun suggest that it may have a rapidly spinning core. An experiment to test this suggestion, by comparing the perihelion advance of a small artificial planet of high eccentricity and Mercury, is discussed.
J. J. GILVARRY, P. A. STURROCK
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Epicyclic Motion of Satellites About an Oblate Planet

Journal of Guidance, Control, and Dynamics, 2001
An analytic formulation is presented of a near circular orbit of a satellite about an axisymmetric potential. The model has a simple analytic form that is capable of describing all of the gravitational perturbative effects. Unlike more rigorous treatments, our approach has a simple geometric interpretation and greater mathematical simplicity than ...
Yoshikazu Hashida, Philip L. Palmer
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Free modes of layered oblate planets

Journal of Geophysical Research, 1963
The equations governing the motion of an elastic gravitating nonhomogeneous isotropic field are considered, and a general solution for the Laplace or Fourier transform of the displacement vector is given in spherical coordinates. The perturbation method is used to set the boundary conditions for an oblate layered spheroid and it is seen that, except ...
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