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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.
[8] [13] Long years of continuous observation has found that the determination of even zonal, normalized gravity coefficient C l=2, m=0, and odd zonal, normalized gravity coefficient C l=3, m=0 are crucial for outlining the time-variable gravity due to such mass exchange, [24] [8] [31] [32] where is the degree while is the order.
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.
The sixteen equatorial quadrangles are the smallest, with surface areas of 4,500,000 square kilometres (1,700,000 sq mi) each, while the twelve mid-latitude quadrangles each cover 4,900,000 square kilometres (1,900,000 sq mi). The two polar quadrangles are the largest, with surface areas of 6,800,000 square kilometres (2,600,000 sq mi) each.
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).
For planet Earth, which can be approximated as an oblate spheroid with radii 6 378.1 km and 6 356.8 km, the mean radius is = (( ) ) / = . The equatorial and polar radii of a planet are often denoted r e {\displaystyle r_{e}} and r p {\displaystyle r_{p}} , respectively.
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.
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.