Physics · Circular Motion & Momentum
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The orbital speed of satellite orbiting around the Earth is:
- A
√GM/Re
- B
√GMe/Re
- C
√GMe/R²
- D
√GMe/h
The correct formula to calculate the orbital speed (v) of a satellite orbiting the Earth is:
v = √(GMe/r)
where G is the gravitational constant, Me is the mass of the Earth, and r is the distance between the center of the Earth and the satellite.
To derive this formula, we can start with the centripetal force equation
F = m v² / r
G (Me * m) / r² = m v² / r
Solving for v, we get:
v = √(GMe/r)
(√GM/Re) only considers the mass of the Earth (M) and the radius of the satellite's orbit (R), but does not take into account the mass of the satellite (m). The correct formula for orbital speed should involve the mass of the satellite as well. Therefore, option A is incomplete and incorrect.
The correct formula to calculate the orbital speed (v) of a satellite orbiting the Earth is:
v = √(GMe/r)
where G is the gravitational constant, Me is the mass of the Earth, and r is the distance between the center of the Earth and the satellite.
To derive this formula, we can start with the centripetal force equation
F = m v² / r
G (Me * m) / r² = m v² / r
Solving for v, we get:
v = √(GMe/r)
(√GMe/R²) uses the correct mass of the Earth (Me), but the formula is incorrect. This formula calculates the acceleration due to gravity at a distance R from the center of the Earth, but it does not give the orbital speed of a satellite. Therefore, option C is incorrect.
(√GMe/h) uses h instead of R, which is incorrect. h is usually used to denote the altitude or height of the satellite above the Earth's surface, but the formula for orbital speed requires the distance from the center of the Earth (R). Therefore, option D is incorrect.
Tagged under Physics · Circular Motion & Momentum · 2009