A satellite is to revolve round the earth in a circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period ? Take g at the surface = 9.8 m/ $s^{2}$ and radius of the earth = 6400km.

7.08 km/s, 118 minutes

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11.08 km/s, 18 minutes

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8.08 km/s, 111 minutes

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4.08 km/s, 11 minutes

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Solution

The correct option is A
7.08 km/s, 118 minutes

Suppose, the speed of the satellite is v.The acceleration of the satellite is $\frac{v^{2}}{r}$ , where r is the radius of the orbit.The force on the satellite is $\frac{G M m}{r^{2}}$ with usual symbols.Using Newton's second law,

$\frac{G M m}{r^{2}} = m \frac{v^{2}}{r}$

or, $v^{2} = \frac{G M}{r} = \frac{g R^{2}}{r} = \frac{(9.8 m / s^{2}) (6400 k m)^{2}}{(8000 k m)}$

giving v = 7.08 km/s.

The time period is $\frac{2 π r}{v} = \frac{2 π (8000 k m)}{(7.08 k m / s)} \approx 118$ minutes.

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A satellite is to revolve round the earth in a circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period ? Take g at the surface = 9.8 m/s2 and radius of the earth = 6400km.

A satellite is to revolve round the earth in a circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period ? Take g at the surface = 9.8 m/ $s^{2}$ and radius of the earth = 6400km.