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.

Reply 1

Vyzrikx

3

Could you explain what you have done to arrive at D?

Reply 2

ThatKid777

OP

9

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

Reply 3

Vyzrikx

3

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 8 months ago)

Reply 4

ThatKid777

OP

9

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!!!!!!!!!!!!!

OCR A Gravitational fields help

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