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Mars has an orbit with a semimajor axis of 1.524 astronomical units (228 million km) (12.673 light minutes), and an eccentricity of 0.0934. [ 1 ] [ 2 ] The planet orbits the Sun in 687 days [ 3 ] and travels 9.55 AU in doing so, [ 4 ] making the average orbital speed 24 km/s.
where L is the semi-major axis, T is the orbital period, c is the speed of light, and e is the orbital eccentricity (see: Two-body problem in general relativity). The other planets experience perihelion shifts as well, but, since they are farther from the Sun and have longer periods, their shifts are lower, and could not be observed accurately ...
On the other hand, an observer on Mars would see the Moon rotate, with the same period as its orbital period, and would see far side features that can never be seen from Earth. Since Earth is an inferior planet, observers on Mars can occasionally view transits of Earth across the Sun. The next one will take place in 2084.
Substituting the mass of Mars for M and the Martian sidereal day for T and solving for the semimajor axis yields a synchronous orbit radius of 20,428 km (12,693 mi) above the surface of the Mars equator. [3] [4] [5] Subtracting Mars's radius gives an orbital altitude of 17,032 km (10,583 mi). Two stable longitudes exist - 17.92°W and 167.83°E.
The orbital radius and angular velocity of the planet in the elliptical orbit will vary. This is shown in the animation: the planet travels faster when closer to the Sun, then slower when farther from the Sun. Kepler's second law states that the blue sector has constant area.
Using the Vicarious Hypothesis, Kepler determined the eccentricities of the Sun and equant to be 11,332 and 7,232 arbitrary units, respectively, for the Martian orbital radius of 100,000 units. Using these positions for the Sun and equant, the model constructed using the Vicarious Hypothesis agreed with the twelve observations within 2' of arc ...
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The basic orbit determination task is to determine the classical orbital elements or Keplerian elements, ,,,,, from the orbital state vectors [,], of an orbiting body with respect to the reference frame of its central body. The central bodies are the sources of the gravitational forces, like the Sun, Earth, Moon and other planets.