How Accurate Are Calculations for Satellite Orbit Energy and Rocket Altitudes?

[six789]

this is the problem...
What is the change in gravitational potential energy of a 6200kg satellite that lifts off from Earth's surface into a circular orbit of altitude2500km?

i did this...
r = rE +h
=6.38 x10^6m + 2.5 x10^6m
r=8.88 x10^6m

Eg= -GMm
r
=-6.673x10-11N m2/kg2 (5.98 x10^24kg)(6200kg)
8.88 x10^6m
Eg=-2.786127793 x10^11J

Eg=mgh
=6200kg(9.82m/s2)(-2.5 x10^6m)
Eg=-1.52055 x10^11J

Change in Gravitational Potential Energy
∆ Eg = Eg - Eg
=-2.786127793 x10^11J – (-1.52055 x10^11J)
∆ Eg =-1.265577793 x10^11J

but the answer on my book is 1.1x10^11J, can anyone check this, coz I am not sure where is the mistake.. thanks for the help

 

[Janus]

Your problem is here:

Eg=mgh
=6200kg(9.82m/s2)(-2.5 x10^6m)
Eg=-1.52055 x10^11J

You should have just the used the same form used in the prior Eg formula

$$E_g = \frac{GMm}{R}$$

with a different value for R

 

[six789]

satellites

thanks for the help... i get the answer now...

 

[six789]

another problem is... a rocket is launched vertically from Earth's surface with a velocity of3.4km/s. How high it go a)from Earth's centre and b) from Earth's surface.
a)r = 2GM
V^2
= 2(6.673x10^-11N m^2/kg^2) (5.98 x10^24kg)
(3400m/s)^2
r=7.0x107m

i don't know what to do with b), i am thinking to add the raduis of the earth, but my answer is wrong... the answer should be 650km.