For the purpose of oceanography and meteorology, Pakistan has launched a Remote Sensing Satellite System (RSSS) at an altitude of 7 x 10^5 m above the ground station.At the time of launch, the orbital velocity of the artificial satellite was calculated as(Note: The value of gravitational constant, mass and radius of Earth are 6.67 x 10" Nm³/kg.5.9 x 10 kg and 6.3 × 10º m respectively.)
Correct answer: D. 7.4 x 10^3 m/s.
- A. 5.6 x 10^7 m/s.
- B. 6.2 x 10^7 m/s.
- C. 6.8 x 10^3 m/s.
- D. 7.4 x 10^3 m/s.
Explanation
To find the orbital velocity, we use the formula v = √(GM/(R+h)), where G is the gravitational constant (6.67 x 10-11 Nm²/kg²), M is the mass of Earth (5.9 x 1024 kg), R is the radius of Earth (6.3 x 106 m), and h is the altitude of the satellite (7 x 105 m). Calculating this gives an orbital velocity of approximately 7.4 x 103 m/s. The other options are either too high or incorrect based on the calculations.
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Satellite motion uses gravitational force as the centripetal force required for circular orbit, giving relationships among orbital radius, period and orbital velocity. Questions cover geostationary conditions and weightlessness, while distinguishing orbital velocity, escape velocity and the satellite's tangential speed.
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