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Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
where G is the universal constant of gravitation (commonly taken as G = 6.674 × 10 −11 m 3 kg −1 s −2), [10] M is the mass of Mars (most updated value: 6.41693 × 10 23 kg), [11] m is the mass of the satellite, r is the distance between Mars and the satellite, and is the angular velocity of the satellite, which is also equivalent to (T ...
[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. The eccentricity is greater than that of every other planet except Mercury, and this causes a large difference between the aphelion and perihelion distances—they are respectively 1.666 and 1.381 AU.
[2] [3] The general equation describing the radius of the sphere of a planet: [4] / where a {\displaystyle a} is the semimajor axis of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun).
It takes 250 days (0.68 years) in the transit to Mars, and in the case of a free-return style abort without the use of propulsion at Mars, 1.5 years to get back to Earth, at a total delta-v requirement of 3.34 km/s. Zubrin advocates a slightly faster transfer, that takes only 180 days to Mars, but 2 years back to Earth in case of an abort.
6.6743 × 10 −11 m 3 /(kg·s 2) To properly use this formula, the units must be consistent; for example, M {\displaystyle M} must be in kilograms, and r {\displaystyle r} must be in meters. The answer will be in meters per second.
The gravitational constant GM (μ) for Mars has the value of 42 830 km 3 s −2, its equatorial radius is 3 389.50 km and the known rotational period (T) of the planet is 1.025 956 76 Earth days (88 642.66 s). Using these values, Mars' orbital altitude is equal to 17 039 km. [73]
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.