MCQ
Which graph best represents the variation of radius $r$ of a circular orbit of a satellite against its time period $T$ ?
- A$1$
- B$2$
- C$3$
- ✓$4$
✓
Answer
Correct option: D.
$4$
d
(d)
(d)
Consider a satellite of mass $M$ revolving in a circular orbit around the earth, which is located at the center of its orbit. If a satellite is at height $h$ above earths surface the radius of the orbit $r = R _e$ th where $R _e$ is radius of earth. The gravitational force between $M _e$ and $M$ provides the centripetal force for circular motion
or $V ^2=\frac{ GM _e}{ R _e+ h } \quad V =\sqrt{\frac{ GM _e}{ R _e+ h }}$
Hence orbital velocity depends on height of the satellite above earth's surface. Time period if satellite is time taken to complete one revolution.
$T =\frac{2 \pi r }{ V }=2 \pi\left( R _{ e }+ h \right)$
$\sqrt{ Re _{ e }+ h } / GM _{ e }$
$T ^2=\frac{4 \pi^2\left( R _e+ h \right)^3}{ GM _e}$ where $r = R _{ e }+ h$
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