Chapter 2: Problem 24

What would be the gravitational force on you if you were at a point in space a distance $R$ (the Earth's radius) above the Earth's surface?

Short Answer

Expert verified

Answer: The gravitational force on the person would be $24.5 m1 N$, where m1 is their mass in kilograms.

Step by step solution

Write down Newton's Law of Universal Gravitation

The gravitational force F between two objects with masses m1 and m2, separated by a distance d, can be calculated using the equation: $$F = G\frac{m1 * m2}{d^2}$$ where G is the gravitational constant $(6.674\times10^{-11} Nm^2/kg^2)$.

Determine the variables in the equation

In this exercise, we are calculating the gravitational force on you (m1) from Earth (m2) when you are at a distance R above Earth's surface. So, m1 = Your mass (kg) m2 = Earth's mass $(5.972\times10^{24} kg)$ d = Distance between your center and the center of Earth $$d = R_{Earth} + R$$ R = Earth's radius $(6.371\times10^6 m)$.

Calculate the distance

The distance between your center and the center of Earth, when you are above Earth's surface at a distance R, is given by: $$d = R_{Earth} + R$$ $$d = 6.371\times10^6 + 6.371\times10^6$$ $$d = 12.742\times10^6 m$$

Calculate the gravitational force

Now, using Newton's Law of Universal Gravitation, let's calculate the gravitational force on you when you are at a distance d from the center of Earth: $$F = G\frac{m1 * m2}{d^2}$$ $$F = \frac{6.674\times10^{11} * m1 * 5.972\times10^{24}}{(12.742\times10^6)^2}$$ $$F =\frac{6.674\times10^{11} * m1 * 5.972\times10^{24}}{1.624\times 10^{14}}$$ $$F = 24.5 m1 N$$ The gravitational force on you if you were at a point in space a distance R (Earth's radius) above Earth's surface is $24.5 m1 N$, where m1 is your mass in kilograms.

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What would be the gravitational force on you if you were at a point in space a distance \(R\) (the Earth's radius) above the Earth's surface?

Short Answer

Step by step solution

Write down Newton's Law of Universal Gravitation

Determine the variables in the equation

Calculate the distance

Calculate the gravitational force

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