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Vesta (radius 262.7 ± 0.1 km), the second-largest asteroid, appears to have a differentiated interior and therefore likely was once a dwarf planet, but it is no longer very round today. [74] Pallas (radius 255.5 ± 2 km ), the third-largest asteroid, appears never to have completed differentiation and likewise has an irregular shape.
The Schwarzschild radius of an object is proportional to its mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi), [8] whereas Earth's is approximately 9 mm (0.35 in) [8] and the Moon's is approximately 0.1 mm (0.0039 in).
Global study of residual Bouguer anomaly data indicates that crustal thickness of Mars varies from 5.8 km to 102 km. [5] Two major peaks at 32 km and 58 km are identified from an equal-area histogram of crustal thickness. [5] These two peaks are linked to the crustal dichotomy of Mars. [5]
For example, if a TNO is incorrectly assumed to have a mass of 3.59 × 10 20 kg based on a radius of 350 km with a density of 2 g/cm 3 but is later discovered to have a radius of only 175 km with a density of 0.5 g/cm 3, its true mass would be only 1.12 × 10 19 kg.
μ = Gm 1 + Gm 2 = μ 1 + μ 2, where m 1 and m 2 are the masses of the two bodies. Then: for circular orbits, rv 2 = r 3 ω 2 = 4π 2 r 3 /T 2 = μ; for elliptic orbits, 4π 2 a 3 /T 2 = μ (with a expressed in AU; T in years and M the total mass relative to that of the Sun, we get a 3 /T 2 = M) for parabolic trajectories, rv 2 is constant and ...
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 first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
For example, the recently discovered planet, Gliese 581 c, has at least 5 times the mass of Earth, but is unlikely to have 5 times its surface gravity. If its mass is no more than 5 times that of the Earth, as is expected, [6] and if it is a rocky planet with a large iron core, it should have a radius approximately 50% larger than that of Earth.