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The gravitational force between a 105 kg person and the 5.97 times 10²⁴ kg earth is 1,030 N. Calculate the distance from the person to the center of the earth?

User Pavlin
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Final answer:

To calculate the distance from the person to the center of the Earth, you can use Newton's law of universal gravitation.

Step-by-step explanation:

To calculate the distance from the person to the center of the Earth, we can use Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N*m^2/kg^2), m1 is the mass of the person, m2 is the mass of the Earth, and r is the distance from the person to the center of the Earth.

Using the given information, we can rearrange the equation to solve for r:

r = sqrt((G * m2) / F)

Plugging in the values, we get:

r = sqrt((6.674 × 10^-11 N*m^2/kg^2 * 5.97 × 10^24 kg) / 1030 N)

r ≈ 6385 km

User Atikot
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