# OCR A Gravitational fields help

Help with this OCR MCQ question. I've tried for hours and nothing has worked. There could be a misconception in my understanding.

Scientists are planning to launch a rocket from the surface of the Earth into an orbit at a
distance of 18000 km above the centre of the Earth. The radius of the Earth is 6400 km and it has mass 6.0 x10^24 kg.
What is the minimum work done to move the 150kg mass of the rocket into this orbit?

A) 3.3x10^9 J
B) 7.7 x 10^9 J
C) 9.4 x 10 ^9 J
D) 1.7x10 ^10 J

I got D as my answer but the MS says its B.
Could you explain what you have done to arrive at D?
Original post by Vyzrikx
Could you explain what you have done to arrive at D?

I added the kinetic energy of the rocket (to get it into orbit) and the gravitational potential energy
KE of rocket (using derivation of you can get from setting mv^2/r = GMm/r^2, reply to this if you're not familiar with it):

GMm/2r = E_k = 1.67x10^9
----------------------------------------------------------------------------
Work Done to get rocket into orbital distance = mass of rocket X change in gravitational potential of rocket

gravitational potential = -GM/r

potentials are at Earth's surface (6400km away from centre of the Earth) and 18000km away from centre of the Earth

= 150 * ((Gx6x10^24)/(6400x10^3) - (Gx6x10^24)/(18000x10^3))
= (150 x G x 6x10^24)(1/6400x10^3 - 1/18000x10^3)
= 6.05x10^9
---------------------------------------------------------------------------------
Minimum total Work Done = E_k + (work done to get into orbit)
= 6.05x10^9 + 1.67x10^9 = 7.7x10^9 (B)
(edited 9 months ago)
Original post by Vyzrikx
KE of rocket (using derivation of you can get from setting mv^2/r = GMm/r^2, reply to this if you're not familiar with it):

GMm/2r = E_k = 1.67x10^9
----------------------------------------------------------------------------
Work Done to get rocket into orbital distance = mass of rocket X change in gravitational potential of rocket

gravitational potential = -GM/r

potentials are at Earth's surface (6400km away from centre of the Earth) and 18000km away from centre of the Earth

= 150 * ((Gx6x10^24)/(6400x10^3) - (Gx6x10^24)/(18000x10^3))
= (150 x G x 6x10^24)(1/6400x10^3 - 1/18000x10^3)
= 6.05x10^9
---------------------------------------------------------------------------------
Minimum total Work Done = E_k + (work done to get into orbit)
= 6.05x10^9 + 1.67x10^9 = 7.7x10^9 (B)

Damn I forgot to consider the change in GPE thankyou!!!!!!!!!!!!!