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where A is the area of a squircle with minor radius r, is the gamma function. A = ( k + 1 ) ( k + 2 ) π r 2 {\displaystyle A=(k+1)(k+2)\pi r^{2}} where A is the area of an epicycloid with the smaller circle of radius r and the larger circle of radius kr ( k ∈ N {\displaystyle k\in \mathbb {N} } ), assuming the initial point lies on the ...
The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. The Schwarzschild radius is given as =, where G is the gravitational constant, M is the object mass, and c is the speed of light.
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.
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.
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.
Mars has an axial tilt of 25.19°, quite close to the value of 23.44° for Earth, and thus Mars has seasons of spring, summer, autumn, winter as Earth does. As on Earth, the southern and northern hemispheres have summer and winter at opposing times. However, the orbit of Mars has significantly greater eccentricity than that of Earth. Therefore ...
Deimos (/ ˈ d aɪ m ə s /; systematic designation: Mars II) [11] is the smaller and outer of the two natural satellites of Mars, the other being Phobos. Deimos has a mean radius of 6.2 km (3.9 mi) and takes 30.3 hours to orbit Mars. [5] Deimos is 23,460 km (14,580 mi) from Mars, much farther than Mars's other moon, Phobos. [12]
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.