Question

A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Mars so that scientists can study a surface feature. Mars rotates once every 24.6 h. Use the data of this table to find the altitude of the satellite. Please show how you figured this out step by step!

Useful Planetary Data Mean 10-19 ..3 Mean Distance Radius (m Mass (kg) Period (s) Body from Sun (m) 2.48 X 10 7.60 x 106 5.79 x 1010 2.97 Mercury 9.18 X 1023 1.94 X 107 3.156 x 107 1.08 X 10 1.496 x 10 2.28 X 10 7.78 X 10 4.88 X 1024 6.06 x 106 Venus 2.99 6.38 106 3.37 10 Earth 5.98 X 1024 2.97 6.42 x 1023 5.94 X 107 Mars 2.98 1.90 X 1027 6.99 X 107 3.74 X 108 2.97 Jupiter 5.85 X 107 2.33 X 107 2.21 107 Saturn 5.68 X 1026 9.95 x 108 1.43 X 1012 2.99 Uranus 8.68 X 1025 2.64 x 109 2.87 x 1012 2.95 5.22 10 7.82 x 109 1.08 1026 Neptune 4.50 x 1012 2.99 1.27 x 1023 7.36 x 1022 5.91 X 1012 Pluto 1.14 X 106 2.96 1.74 X 10 Moon 6.96 x 108 Sun 1.991 X 1030 aIn August 2006, the International Astronomical Union adopted a definition of a planet that separates Pluto from the other cight planets. Pluto is now defined as a "dwarf planet" like the asteroid Ceres

Answer 1

forca for orbit is provided by fora The centripetal Gravitahonal mv Rth CMm So RE Tdiu of mars mass M S Satellite So, Rth r: Tadiuo of eea alhitude M v 2 We get Rth (T Rth) M penod T 2T Atso V Put v GGM V2 4272 41273 Cn M Synchonous satellite, pemod o f ntahon of plamet for a is equal to period of 7evolution of satell}k - Put this in ) 24 .6 X3600s So / M=6.4 2 X1o23 to qet above witth 2.04X10T m 2+h Y r- R- Y- 3 37X 10 m h .04 X 10

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