College

We appreciate your visit to The gravitational force F between an object and the Earth is inversely proportional to the square of the distance from the object to the center. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The gravitational force, F between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If anastronautweighs 206 pounds on the surface of the Earth, what will this astronaut welgh 100 miles above the Earth? Assume that the radius of the Earth is 4000 miles(Round off your answer to the nearest pound.)

The gravitational force F between an object and the Earth is inversely proportional to the square of the distance from the object to the center

Answer :

To the nearest pound, the weight of the astronaut 100 miles above earth is 196 pounds

How to get the weight

We have to solve for the weight using this proportion

[tex]\frac{w_2}{w_1} = \frac{R^2}{(R+h)^2}[/tex]

such that w₁ = weight of the astronaut obn earth surface = 206

w₂ = weight above earth

R = 4000

h = 100

We have to put the values on the formula

[tex]\frac{w_2}{206} = \frac{4000^2}{(4000+100)^2}[/tex]

[tex]\frac{w_2}{206} = \frac{16000000}{(16810000)}[/tex]

when we solve the equation above we have

206 * 16000000 = w₂ * 16810000

3296000000 / 16810000 = w₂

w₂ = 196.07

To the nearest pound, the weight of the astronaut 100 miles above earth is 196 pounds

Thanks for taking the time to read The gravitational force F between an object and the Earth is inversely proportional to the square of the distance from the object to the center. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada