Question

The space shuttle is located exactly half way between the earth and the moon. Which statement is true regarding the gravitational pull on the shuttle?

Answer 1

The correct answer is option B)

Step-by-step explanation:

Considering the given question as -

The space shuttle is located exactly half way between the earth and the moon. Which statement is true regarding the gravitational pull on the shuttle? A) The moon pulls more on the shuttle. B) The earth pulls more on the shuttle. C) Both are equal due to equal distances. D) Both are equal due to the mass of the shuttle.

We know that gravitational pull (F) between any two bodies of mass
`M_(1)` and
`M_(2)` is given by -

F =
`(GM_(1)M_(2) )/(r^(2) )` where 'r' is the distance between the two bodies.

Let ,

`M_(e)` : Mass of the earth

`M_(m)` : Mass of the moon

m : Mass of the satellite

`r_(e)` : Distance of satellite from earth

`r_(m)` : Distance of satellite from moon

Given that
`r_(e)`=
`r_(m)`

Let
`r_(e)`=
`r_(m)`=r

Force on satellite by the earth is -

`F_(e)` =
`(GM_(e)m )/(r^(2) )`

Force on satellite by the moon is -

`F_(m)` =
`(GM_(m)m )/(r^(2) )`

∵ Mass of earth (
`M_(e)`) > Mass of moon (
`M_(m)`)

∴
`F_(e)` >
`F_(m)`

∴ The gravitational pull of earth on satellite is more than that of the moon.