Show the nature of the following graph for a satellite orbiting the earth.
(a) `K E` vs orbitial radius `R` (b) `PE` vs orbital radius `r` (c ) `TE` vs orbital radius `R`.

Explanation

Orbital velocity `v_(0) = sqrt((GM)/(R ))`
`:. K.E. = (1)/(2) m v_(0)^(2) = (1)/(2)m(GM)/(R )`
or `K.E. prop (1)/(R )`
i.e., K.E. decreases exponentially.
`P.E. = -(GmM)/(R )`
`P.E. prop - (1)/(R )`

Total energy = K.E. + P.E.
i.e. `T.E. = (GmM)/(2R) - (GmM)/(R )`
T.E. `= -(GmM)/(R )`
The graph is shown in figure.