Physics
posted by Ana on .
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.
(a) Assuming a circular orbit, what is the orbital period of this satellite?
5310 s
(b) What is the satellite's speed in its orbit?
7790m/s
(c) What is the minimum energy necessary to place the satellite in orbit, assuming no air friction?
I was able to get a and b, but i don't know about c.
Thanks

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/(rRearth) 
how do i get small r?

is it R_e + height?

Yes, earth radius + height

(6.67E11*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?

(6.67E11*220*5.98E24)/[2(6.38E6+2.0E5)]
note 2 in denominator
+ (6.67E11*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.