A satellite of mass 220 kg is launched from a site on Earth's equator into an orbit at 200 km above the surface of Earth.

You have to lift the body to orbit and then speed it up to orbit speed.

m v^2/r = G m M/r^2 in orbit
so (1/2)m v^2 = G m M/(2r) = Ke in orbit
Change in Potential energy to lift it to orbit
= G m M/(r-Rearth)

how do i get small r?

is it R_e + height?

Yes, earth radius + height

(6.67E-11*220*5.98E24)/(6.38E6+2.0E5)-(6.38E6)=

1.33295653E10J

Is this right? I want to make sure if this is right before I insert into the site.

both terms should be positive

What do you mean?

(6.67E-11*220*5.98E24)/[2(6.38E6+2.0E5)]

note 2 in denominator
+ (6.67E-11*220*5.98E24) / 2^10^5

8.78*10^16 [ 1/1.32E7 + 1/2E5 ]

so is it 6770873457?

Change in Potential energy to lift it to orbit

= G m M [1/Rearth - 1/r ]

8.78*10^16 [ 1/1.32E7 + 1/6.38E6 - 1/6.58E6 ]

this is my last try....is it 6904053501?

7.07*10^9 Joules

We are close to each other. My arithmetic is failing, after bedtime.

Your professor must like arithmetic !

Yes, we are. Some of the problems are very difficult but thank you so much for your help. I really appreciate.