# Calculating Internal Energy Loss from Friction in Satellite Fall

• brunie

#### brunie

A 575 kg satellite is in a circular orbit at an altitude of 550 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 2.10 km/s. How much energy was transformed to internal energy by means of friction?

ok so

575kg at 550km
falls at 2100 m/s

so the internal energy lost should be the difference between the energy it had in orbit minus the energy it has when it crashes

so for final energy upon crash
Ek = 0.5 * 575 * 2100^2
= 1267875000

so whatever energies it has in orbit (gravitational, potenential, centripital ?) it loses the internal energy due to friction and then ends up with the Ek when it crashes

not too sure if I am attepting this properly, help would be appreciated

When in orbit, the satellite will have some gravitational PE and KE. (You'll need to figure those out!) That will be its initial total mechanical energy. When it reaches the ground it will have some final gravitational PE (figure that out) and some final KE (you are given the speed). The total mechanical energy upon landing (figure that out) will be equal to its initial mechanical energy less the amount of energy transformed to internal energy.

ok so for initial energy i can use the equation for total energy

-GMm/2(Re+h)
-(6.67x10^-11)(5.97x10^24)(575) / 2(6378100 + 550000)
-1.65 x 10^10

so this answer minus the final kinetic and final potential should b the energy loss

Ek = 0.5 * 575 * 2100^2
= 1.27 x 10^9

but I am not sure what equation to use for the final potential energy at crash
because if the satellite hits the Earth's surface wouldn't potential be zero?
also is it right to have the initial energy negative?

ok so for initial energy i can use the equation for total energy

-GMm/2(Re+h)
-(6.67x10^-11)(5.97x10^24)(575) / 2(6378100 + 550000)
-1.65 x 10^10
Realize that that equation for total energy is derived by adding PE plus KE. What's the formula for PE by itself? (Look it up if you need to.)

so this answer minus the final kinetic and final potential should b the energy loss

Ek = 0.5 * 575 * 2100^2
= 1.27 x 10^9

but I am not sure what equation to use for the final potential energy at crash
because if the satellite hits the Earth's surface wouldn't potential be zero?
No. The standard expressions for gravitational PE between objects (as used in arriving at the equation for total energy) have infinity as the PE = 0 reference. Read this: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/gravpe.html#c1"
also is it right to have the initial energy negative?
Sure.

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ok great, thank u for all ur help
it was really appreciated