Dot Point book help (1 Viewer)

[adomad]

there is this question in the dot point book that i don't understand how to get.
for those of you who have the book, its 1.6.2

A satellite of mass 500kg, is boosted from an orbit of altitude of 10 000km to one of altitude 20 000km. Given the diameter of the Earth as 12756km, its mass 5.94x10^24, calculate the change in the gravitational potential energy of the satellite

help please guys and girls!

the answer is +4.61x10^9J

 

[boxhunter91]

change in GPE= GPEFinal-GPEInitial

 

[adomad]

yeah, i did that but i get 980.866x10^6

 

[darkchild69]

Initial GPE = Gm1m2/r

m1 = mass of satelitte (500kg)
m2 = mass of Earth (6x10^24kg)
r = distance between centre of Earth and orbit (radius of Earth + altitude) -- in the question they gave u diameter, the sneaky bastards, you need to divide this by 2 to get the radius. You also need to multiply in by 1000 (x10^3) to convert from km to m.

= 6.67x10^-11*500*6x10^24/(10000+6378)x10^3

= - 1.22x10^10J

Final GPE:

= 6.67x10^-11*500*6x10^24/(20000+6378)x10^3

= - 7.59x10^9J

Change GPE = final GPE - initial GPE

= -7.59x10^9J - (-1.22x10^10)J

= 4.61x10^9J

 

[boxhunter91]

It works maybe you didnt change into metres? Or you didnt use the correct radius(ie you left as diameter) read darkchild's post and see where you went wrong.

 

[adomad]

It works maybe you didnt change into metres? Or you didnt use the correct radius(ie you left as diameter) read darkchild's post and see where you went wrong.

Ah, i feel so stupid LOL, yeah i ddin't change diameter to radius LOL THANKS GUYS!!