Question
would force of gravity on an object on the surface of the Earth is 100 N, what one force be on the same object which at an altitude equal to __ a) one Earth radius? b) two earth radii? c) three Earth radii?
Solution
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Adley
Expert ยท Tutor for 3 years
Answer
Here's how to calculate the force of gravity at different altitudes:**Understanding the Concept**The force of gravity between two objects is inversely proportional to the square of the distance between their centers. Doubling the distance reduces the force to one-fourth. Tripling the distance reduces it to one-ninth, and so on.* **Formula:** F = G * (m1 * m2) / r^2 * F = Force of gravity * G = Gravitational constant (we don't need this for this problem) * m1 and m2 = masses of the two objects (Earth and the other object in this case) * r = distance between the centers of the two objectsSince the mass of the Earth and the object remain constant, we can simplify the problem by focusing on the changing distance.**Calculations*** **a) One Earth radius altitude:** * The object is now *two* Earth radii away from the Earth's center (one radius to the surface + one radius altitude). * Since the distance has doubled, the force is reduced to (1/2)^2 = 1/4 of its original value. * Force = 100 N * (1/4) = **25 N*** **b) Two Earth radii altitude:** * The object is now *three* Earth radii away from the Earth's center. * The distance has tripled, so the force is reduced to (1/3)^2 = 1/9 of its original value. * Force = 100 N * (1/9) = **11.11 N** (approximately)* **c) Three Earth radii altitude:** * The object is now *four* Earth radii away from the Earth's center. * The distance has quadrupled, so the force is reduced to (1/4)^2 = 1/16 of its original value. * Force = 100 N * (1/16) = **6.25 N**