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## Homework Statement

Determine how much energy is needed to move a satellite of mass 500kg to an orbit of height equal to earth's radius.

## Homework Equations

Gravitational Potential:

[tex]V = \frac{-GMm}{R}[/tex]

Where M is the mass of Earth (6*10^24kg), m is the mass of the satellite (500kg) and R is the distance from the center of earth.

## The Attempt at a Solution

The energy I need is equal to the difference between orbital and surface potential.

Surface Potential:

[tex]V = \frac{-6.67*10^-11*6*10

^{24}*500}{6300}[/tex]

I obtain a value of about -3.17*10^12.

Orbital Potential:

[[tex]V = \frac{-6.67*10^(-11)*6*10^(24)*500}{2*6300}[/tex]

I obtain a value of about -1.59*10^12.

I now subtract the two values: (-3.17*10^12)-(-1.59*10^12) to obtain -1.58*10^11 J or

-158,000MJ... The problem is that my textbook gives as an answer -16,000MJ. Disregarding the difference between 1.58 and 1.6, which is surely due to my approximations, why am I getting a result ten times bigger?

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