PAT space question

Hi, currently trying to one of the PAT summer assignments and struggling with this question, could anyone help me with where I should start?

The neutral point between the Earth and the Moon is the point where the gravitational pull of the Moon is equal to the gravitational pull of the Earth. If the energy a 1000 kg spacecraft needs in order to reach the neutral point from Earth is 6.0 × 10^10 J and to reach the neutral point from the Moon is 0.25 × 10^10 J, what is the minimum energy needed to send a 1 kg rock from the Moon to the Earth?
(a) 0.25×10^7 J (b) 5.75×10^7 J (c) 6.0×10^7 J (d) 6.25×10^7 J

(edited 8 months ago)

Reply 1

Ignorabimus

1000kg -> 1kg
Energy -> ?

Reply 2

Ignorabimus

maybe add some '^' behind the 10s, your copy and paste kinda broke.

Reply 3

emily-darlington

Hi,
Sorry I've edited it now!!

Original post by Ignorabimus

maybe add some '^' behind the 10s, your copy and paste kinda broke.

Reply 4

Ignorabimus

Original post by emily-darlington

Hi,
Sorry I've edited it now!!

Does the 1000kg to 1kg make sense for you?

Spoiler

Reply 5

emily-darlington

Is escape velocity directly proportional to mass of the object escaping?

Reply 6

Ignorabimus

Original post by emily-darlington

Is escape velocity directly proportional to mass of the object escaping?

esacpe velocity is sqrt (2GM/d) G- gravitational constant, M -mass d-distance

Reply 7

Ignorabimus

Mass goes from 1000kg to 1kg, so diving by 1000. If you put that into the escape velocity, it will be a sqrt 1000 decrease, whihc is roughly a 32x decrease, which doesnt match any of the possible answers, as the asnwers are all 10e7

Reply 8

emily-darlington

I think it might be because the M in escape velocity is the mass of the planets?
And the question is talking about energy, so for the rocket/ rock the energy is 1/2 mv^2, which means it is directly proportional,
once it leaves the moon's gravitational field, it will get attracted by the earth's, so I think the answer is 0.25*10^10/1000, which is answer (A)!