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we know that satelites turn around a star in ellipse path (or parabola/hyperbola)

I wanted to know where does the energy go when a satelite comes closer to a Star

we have angular momentum for the satelite itself and another angular momentum for spin of satelite

and we know that angular momentum = Constant

because f(r) = k , f([tex]\theta[/tex])=0

but if we calculate the velocity of satelite at diffrent distances we realize that angular momentum will give one answer which says that some Energy goes somewhere but where?

changes to spin ? ( Iw

^{2}/2 )

but angular momentum of spin must be constant too ?

Thanks