Energy difference between orbits?

[m84uily]

Homework Statement

The space shuttle is in a 100 km-high circular orbit. It needs to reach a 610 km-high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.50×104 kg.
How much energy is required to boost it to the new orbit?

Me(mass of earth) = 5.98E24 = 5980000000000000000000000
Re(radius of earth) = 6.37E6 = 6370000
G(gravitational constant) = 6.67E-11 = 0.0000000000667
hi = 100km = 100 000m
hf = 610km = 610 000m
m = 6.5E4 = 65000

Homework Equations

Ugi + Ki = Ugf + Kf
Ug = -Gm1m2/r
K = (1/2)m(v^2)

The Attempt at a Solution

Ugi + Ki = Ugf + Kf

Ugi + Ki = Ugf

Ugi - Ugf = -Ki

-Gm(Me) / (Re + hi) + Gm(Me)/(Re + hf) = -(1/2)m(vi^2)

GmMe = 25926290000000000000

Re + hi = 6470000

Re + hf = 6980000

- 4007154559505.4095826893353941267 + 3714368194842.4068767908309455587 = - (1/2)m(vi^2)

-292786364663.002705898504448568 = - (1/2)m(vi^2)

585572729326.005411797008897136 = m(vi^2)

9008811.2204000832584155214944 = (vi^2)

3001.4681774758304537554833575167

Ki = (1/2)(65000)(3001.4681774758304537554833575167)^2

 

[m84uily]

Is it just the difference in gravitational potential energies?

|Ugi - Ugf| = 292786364663.002705898504448568 ?