Question

The acceleration acting on a falling object due to gravity varies inversely with the square of the object's distance from the center of Earth. At the surface of Earth, where x = 1 Earth radius, the acceleration is y = 9.8 m/s2

1. Use the multiply-multiply pattern of power functions to find the acceleration at 3 Earth radii from the center. Round to the nearest hundredth.

2. Find the particular equation expressing y as a function of x.

3. What is the acceleration due to Earth's gravity acting on someone standing on the Moon, 63 Earth radii away from Earth's center? Express your answer with 4 places after the decimal.

Answer 1

g = 9.8 *(Re/x)^2 m/s^2
where Re is the earth's radius,
will answer all you questions.

Note that x/Re is the number of Earth radii from the center.