An

earth satellite of mass 200 kg lost energy slowly through atmospheric

resistance and fell from an orbit of radius 8.0 x 106 m to 7.8 x 106 m.

Calculate the changes in the potential, kinetic and total energies of

the satellite during this transition period.

Answers: ( -2.57E8 J, 1.28E8 J, -1.28E8 J ) where E denotes x10

Solution:

a)

b)

Assuming the orbits are in circular motion as it decays from to

equation can be assumed to be valid to approximate this motion

Thus,

c)

since

check:

This answer can also be verified from the formula relationship on page Newton's Mountain Projectile Orbits which is not intended to be memorized.

Using the simulation:

using R = 8.0X10^6 , v = 7072.8 m/s for circular motion orbit, you can get for satellite m = 1kg, KE = 2.501X10^7 J, PE = -5.002X10^7 J and TE = -2.501X10^7 J |

using R = 7.8X10^6 , v = 7162.9 m/s for circular motion orbit, you can get for satellite m = 1kg, KE = 2.565X10^7 J, PE = -5.131X10^7 J and TE = -2.565X10^7 J |

Thus,

?KE = 200(2.565X10^7 - 2.501X10^7) = 1.28X10^8 J

?PE = 200(-5.131X10^7 - (-5.002X10^7)) = -2.58X10^8 J

?TE = 1.28X10^8 + (-2.58X10^8) = 1.30X10^8 J

where the slight difference is due to carry over error from the significant figures of the computer model.

reference:

http://commons.wikimedia.org/wiki/File:R_%3D_geo_Re_2012-10-08_1809.png#.7B.7Bint:filedesc.7D.7D