Initially a satellite of 100 kg is in a circular orbit of radius . This satellite can be moved to a circular orbit of radius by supplying of energy. The value of is______.

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Solution

Q.
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 10^{6} J$ of energy. The value of $α$ is______.

$($ Take Radius of Earth $R_{E} = 6 \times 10^{6} m and 𝑔 = 10 m / s^{2})$ [2026]

1 100

2 500

3 1000

4 150

Ans.
(3)

Energy of a satellite in a circular orbit is given as

$E = \frac{- G M_{E} m}{2 r}; r = radius of circular orbit$

$Required energy to be supplied = Δ E = E_{f} - E_{i}$

$Δ E = (\frac{- G M_{E} m}{2 (3 R_{E})}) - (\frac{- G M_{E} m}{2 (1.5 R_{E})})$

$= \frac{G M_{E} m}{6 R_{E}}$

$Now, g = \frac{G M_{E}}{R_{E}^{2}} \Rightarrow \frac{G M_{E}}{R_{E}} = g R_{E}$

$∴$ $Δ E = \frac{1}{6} g m R_{E}$

$= \frac{1}{6} \times 10 \times 100 \times 6 \times 10^{6}$

$= 1000 \times 10^{6}$

$α = 1000$

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