Question

Mars has a mass of 6.4 x 10^23 kg. It has a moon named Deimos with a mass of .48 x 10^15 kg.

a. If their centers are 23,460 km apart, what is the force of gravity acting on Deimos?

b. A scientific satellite of mass 800 kg orbits Mars 400 km ab one its surface. If mars has a radius of 3396 km, what is the force of gravity acting on the scientific satellite?

c. The satellite is in a circular orbit around Mars. How does the kinetic energy of the satellite change as it orbits Mars?

d. How does the gravitational force on the satellite change as it orbits Mars?

Answer 1

a) According to Newton's law of gravitation,

`F=GM_1M_2/R^2= 3.72\cdot 10^13` N

b)
`F=Gm_1m_2/(r+R)^2= 2369.97` N

c) It remains the same because the velocity doesn't change.

d) Also constant because its orbit is circular.

Answer 2

PART A)

From gravitational force formula we know that

`F = (Gm_1m_2)/(r^2)`

now we have

`m_1 = 6.4 * 10^(23) kg`

`m_2 = 0.48 * 10^(15) kg`

`r = 23460 km`

now we have

`F = (6.67* 10^(-11)(6.4* 10^(23))(0.48* 10^(15)))/((23460* 10^3)^2)`

`F = 3.72* 10^(13) N`

Part B)

again from same formula as we used above to find the force

`F = (Gm_1m_2)/(r^2)`

now we have

`m_1 = 6.4 * 10^(23) kg`

`m_2 = 800 kg`

`r = (3396 + 400) = 3796 km`

now we have

`F = (6.67* 10^(-11)(6.4* 10^(23))(800))/((3796* 10^3)^2)`

`F = 2370 N`

PART C)

here in circular orbit the speed of the satellite will remain the same always

So here kinetic energy of satellite will always remain same

There is no change in kinetic energy of satellite

Part d)

Since satellite is revolving in circular orbit so the distance will always remain the same

As well as the two masses is also constant

So here the gravitational force between them is always same and it will not change