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A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 × 10^6 m above the surface of earth. If earth's radius is 6.38 × 10^6 m and g = 9.8 m/s^2, then the orbital speed of the satellite is:

1. 8.56 km s^−1
2. 9.13 km s^−1
3. 6.67 km s^−1
4. 7.76 km s^−1

Correct answer: 7.76 km s^−1

Solution

The orbital speed of a satellite is given by v = √(gR), where R is the distance from the center of the Earth to the satellite. Here, R = Earth's radius + height of the satellite = 6.38 × 10^6 m + 0.25 × 10^6 m = 6.63 × 10^6 m. Substituting, v = √(9.8 × 6.63 × 10^6) ≈ 7.76 km/s.

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