Work done by a force changing the distance of a satellite's orbit

AI Thread Summary
To change a satellite's orbit from a radius of 1.81 × 10^7 m to 8.01 × 10^6 m, a net external force must perform work on the satellite. The initial and final orbital speeds were calculated using the formula v = sqrt(G * M_e / r), resulting in speeds of 4695.74 m/s and 7058.74 m/s, respectively. The work done was computed using the Work-Kinetic Energy Theorem, yielding a value of approximately 7.68 × 10^10 J. However, there is a concern about whether other forms of energy, besides kinetic energy, should be considered in this calculation. The discussion emphasizes the importance of accounting for all energy types when determining the work required for orbital changes.
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Homework Statement



A 5530-kg satellite is in a circular Earth orbit that has a radius of 1.81 × 10^7 m. A net external force must act on the satellite to make it change to a circular orbit that has a radius of 8.01 × 10^6 m. What work must the net external force do?

Homework Equations



Orbital Speed:
v = sqrt( G * M_e / r )
where G is the gravitational constant and M_e is Earth's mass

Work-Kinetic Energy Theorem:
W = K_f - K_i = .5*m*v_f^2 - .5*m*v_i^2

The Attempt at a Solution



v_i = sqrt( 6.674e-11 * 5.98e24kg / 1.81e7m )
v_i = 4695.74m/s

v_f = sqrt( 6.674e-11 * 5.98e24kg / 8.01e6m )
v_f = 7058.74m/s

W = .5*m*v_f^2 - .5*m*v_i^2
W = .5*5530kg*7058.74m/s^2 - .5*5530kg*4695.74m/s^2
W = 7.68002e10J
 
Last edited:
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Work = change in energy.
 
Simon Bridge said:
Work = change in energy.

I incorrectly found the work to be the difference between the initial and final kinetic energies above.
 
Are there other forms of energy present?
 
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