The critical velocity of a satellite revolving around the Earth is 10 km/s at a height where gh = 8 m/s2. Calculate the height of the satellite from the surface of the Earth. (R = 6.4 × 106 m)
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Given: vc = 10 km/s = 10 × 103 m/s,
gh = 8 m/s3, R = 6.4 × 106 m
To find: Height of the satellite (h)
Formula: vc = \(\sqrt{g_h(R+h)}\)
Calculation: From formula,
10 × 103 = \(\sqrt{8\times(R+h)}\)
Squaring both the sides, we get,
100 × 106 = 8(R + h)
∴ 8(R + h) = 100 × 106
∴ R + h = \(\frac{100}{8}\) × 106
∴ h = 12.5 × 106 – R
= 12.5 × 106 – 6.4 × 106
= 6.1 × 106m
∴ h = 6100 km
The height of the satellite from the surface of the Earth is 6100 km.
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