Question

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (kg)

Answer 1

`6.27*10^(23)kg`

Step-by-step explanation:

assume

M= mass of Mars

m=mass of phobos

r=orbital radius

T=period

we can apply F=ma to this orbital motion (considering the cricular motion laws)

where,

`F=(GMm)/(r^(2) )` and a=rω^2

where ω=
`(2\pi )/(T)` and G is the universal gravitational constant.

G = 6.67 x 10-11 N m2 / kg2

`F=ma\\(GMm)/(r^(2) )=mr((2\pi )/(T) )^(2)\\  M=(r^(3))/(G)  ((2\pi )/(T) )^(2)\\M=((9.4*10x^(6) )^(3)*(2\pi )^(2) )/((2.8*10^(4)) ^(2) *6.67*10^(-11) ) \\M=6.27*10^(23)kg`