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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 an astronaut weighs 196 pounds on the surface of the Earth, what will this astronaut weigh 300 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)

Respuesta :

the astronaut would weigh 1 pound above the Earth.

How to calculate the weight

Given that;

Gravitational force = Gm/r^2

M1 = 196 pounds

M2 = unknown

R1 = 4000 miles

R2 = 300 miles

We can deduce that;

[tex]\frac{m1}{r^21} = \frac{m2}{r^22}[/tex]

Let's substitute the values

[tex]\frac{196}{4000^2} = \frac{x}{300^2}[/tex]

[tex]\frac{196}{1.6 *10^7} = \frac{x}{9 *10^4}[/tex]

Cross multiply

196 × 9 ×10^4 = x × 1.6 ×10^7

1.76 × 10^7 = x × 1.6 ×10^7

Make 'x' the subject of formula

x = [tex]\frac{1.76* 10^7}{1.6*10^7}[/tex]

x = 1.1

x = 1 pound

Thus, the astronaut would weigh 1 pound above the Earth.

Learn more about gravitational force here:

https://brainly.com/question/11359658

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