Question

Mars rotates on its axis once every 1.02 days (almost the same as Earth does). (a) Find the distance from Mars at which a satellite would remain in one spot over the Martian surface. (Use 6.42 x 10^23 kg for the mass of Mars).
(b) Find the speed of the satellite.

Answer 1

Answer:

$r= 2.03*10^7m$

V = 1.45x10^3 m/s

Explanation:

number of days in sec = 1.02days * 86400s = 88128 s              

Mass of Mars is 6.42*10^23 Kg

gravitational constant G = 6.674*10^{-11}

$T^{2} = \frac {4pi^2}{GM} *r^3$

$\frac {88128^2}{(9.22*10^{-13})} = r^3$

$r= 2.03*10^7m$

(b) $V=\frac{2 \pi*r}{T}$

$V=\frac{(2 \pi(2.03*10^7))}{(88128)} = 1.45x10^3 m/s$

V