Question

Calculate the period of a satellite orbiting the moon, 94 km above the moon's surface. ignore effects of the earth. the radius of the moon is 1740 km. express your answer using three significant figures and include the appropriate units.

Answer 1

R= radius of moon

 

h= distance of satellite from moon's surface,

 

M = mass of moon,

 

G= Gravitational constant

 

Time period of a satellite = T = 2π(r)/v

 

let orbit radius = R + h =r

R = 1740 + 94 = 1844 km = 1.844 E6 m

 

M = mass of moon = 7.348E22 kg

 

T = 2π√[R³/(GM)]

 

=  (2*(3.14)*((1740+94)*(10^3))^3/2)/ sqrt ((6.67*10^-11)*(7.34 × 10^22)) = 7032 sec = 1.9999337638883334 hr or approximately 2 hrs.