- #1
max0005
- 52
- 0
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*1024*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?
Last edited: