How Much Energy Is Required to Launch a Satellite into Orbit?

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To launch a 200 kg satellite into a 205 km orbit, the minimum energy required, excluding air friction, involves calculating both kinetic and potential energy. The kinetic energy at orbit is approximately 6.07 billion joules, while the potential energy is about 12.11 billion joules, resulting in a total energy of -6.049 billion joules. The initial kinetic energy, calculated using Earth's rotational velocity, is around 21.53 million joules. There is uncertainty regarding whether to use the total radius of Earth plus altitude or just Earth's radius for initial potential energy calculations. Clarification on this point is necessary for accurate energy assessments.
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1. Homework Statement

A satellite of mass 200 kg is launched from a site on Earth's equator into an orbit at 205 km above the surface of Earth. What is the minimum energy necessary to place the satellite in orbit, assuming no air friction? I also figured the orbital period to be 5300 s and the orbital velocity to be 7788 m/s

2. Homework Equations
P = -GMm/r
K = .5*m*v^2

3. The Attempt at a Solution
I plugged the numbers into the kinetic energy equation
.5*200 kg*(7788 m/s)^2
and got 6.07 E 9
 
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What's the potential energy of the satellite in orbit?
What's the total energy of the satellite in orbit?
What's the kinetic and potential energy of the satellite sitting at the equator?
 
final kinetic = 6.065 E 9 J
final potential = 1.211 E 10 J
final total energy = -6.049 E9 J

initial kinetic = 2.153 E 7 J (using Earth's rotational period of 463.9 s to find Earth's v)
now here's where I am not sure
for initial potential energy do you use the total radius or just the radius of the earth?
 
crr2010 said:
final kinetic = 6.065 E 9 J
final potential = 1.211 E 10 J
final total energy = -6.049 E9 J

initial kinetic = 2.153 E 7 J (using Earth's rotational period of 463.9 s to find Earth's v)
now here's where I am not sure
for initial potential energy do you use the total radius or just the radius of the earth?

Since it is sitting on the surface of the Earth, doesn't it make sense to use the Earth's radius?
 

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