An artificial satellite in the presence of frictional forces will move into an orbit closer to the earth and may have increased kinetic energy. Explain this.

Explanation

`E` (total Energy)`=1/2mv^(2)+(-(GMm)/r)`
where `m` is the mass of the satellite `M=`mass of the earth and `r=` radius of the orbit. Being the dynamics of circlar motion,
`(GMm)/(r_(2))=(mv^(2))/r`
or `v^(2)=(GM)/r`
Hence `E=(-1)/2(GM)/r m=-1/2 mv^(2)=-k` (kinetic energy)
`E_(i)` (initial energy) `=-1/2(GM)/(r_(0))`
`E_(f)` (final energy) `=-1/2(GM)/r` By the principle of conservation of energy
`E_(i)=E_(f)+W`( work done by frictional force)
`implies-1/2(GM)/(r_(0))=1/2(GM)/r+W`
or `1/2 GM(1/r-1/(r_(0)))=W ` (a positive quantity)
`:. 1/rgt1/(r_(0))` or `rltr_(0)`
Also, `K_(0)=-K+W`
or `K-K_(0)=W` (a positive quantity)
`:. KltK_(0)`