Question

Let m= 350kg

A particular satellite with a mass of m is put into orbit around Ganymede (the largest moon of Jupiter) at a distance 300 km from the surface. What is the gravitational force of attraction between the satellite and the moon? (Ganymede has a mass of 1.48x1023 kg and a radius of 2631 km.)

B. What is the satellite’s centripetal acceleration?

C.What is the satellite’s period of rotation?

Answer 1

here,

mass of satellite , m1 = 300 kg

mass of Ganymede , m2 = 1.48 * 10^23 kg

radius , r = 2631 km = 2.631 * 10^6 m

A = 300 km = 3 * 10^5 m

a)

the gravitational force , F = G * m1 * m2 /( r + A)^2

F = 6.67 * 10^-11 * 1.48 * 10^23 * 300 /( 2.631 * 10^6 + 3 * 10^5)^2 N

F = 344.7 N

b)

the satellite's centripital accelration , a = F/m1

a = 344.7/300 m/s^2 = 1.15 m/s^2

c)

the satellite period of rotation , T = 2*pi*sqrt((r+A)^3 /(G*m2))

T = 2*pi*sqrt(( 2.631 * 10^6 + 3 * 10^5)^3 /( 6.67 * 10^-11 * 1.48 * 10^23))

T = 1 * 10^4 s