On the ground, the gravitational force on a satellite is W. What is the gravitational force on the satellite when at a height R/50, where R is the radius of the Earth?
Correct answer: D. 0.96 W
- A. 1.04 W
- B. 1.02 W
- C. 0.98 W
- D. 0.96 W
- E. 2.13 W
Explanation
Because of equality F = - m. (G.M/r ²) = - m.g one draws G = G.M/r ² = [G.M/R ²] * [1 (1+z/R)]² =g○/(1+z/R) ² ► g (z) = g○/(1+z/R) ² ▬▬▬▬▬ > W/W○ = g/g○ = (1+z/R)⁻ ² = (1 + 1/50)^-2 = 0.961
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About Law of Universal Gravitation
Every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation, expressed as F = Gm₁m₂/r². Questions also involve the gravitational constant, vector direction, superposition of gravitational forces, and the distinction between gravitational force and gravitational field strength.
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