A planet exerts a gravitational force of magnitude 7 ×10^22 N on a star. If the planet were four

Name: Problem 15, Chapter 3: Matter & Interactions
Uploaded: 2022-04-08T18:22:43-08:00
Duration: 59 s
Channel: Lucas Finney
Description: A planet exerts a gravitational force of magnitude 7 ×10^22 N on a star. If the planet were four times closer to the star (that is, if the distance between the star and the planet were 1 / 4 what it is now ), what would be the magnitude of the force on the star due to the planet?

step 1 For this problem, we are told that a planet exerts a gravitational force of magnitude 7 times 10

Question

A planet exerts a gravitational force of magnitude $7 \times$ $10^{22} \mathrm{N}$ on a star. If the planet were four times closer to the star (that is, if the distance between the star and the planet were $1 / 4$ what it is now $),$ what would be the magnitude of the force on the star due to the planet?

   A planet exerts a gravitational force of magnitude $7 \times$ $10^{22} \mathrm{N}$ on a star. If the planet were four times closer to the star (that is, if the distance between the star and the planet were $1 / 4$ what it is now $),$ what would be the magnitude of the force on the star due to the planet?

Matter & Interactions

Ruth W. Chabay,… 4th Edition

Chapter 3, Problem 15

Instant Answer

Solved by Expert Lucas Finney

04/08/2022

Step 1

Step 1: The gravitational force between two objects is given by the formula: \[F = G \frac{m_1 m_2}{r^2}\] where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance Show more…

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A planet exerts a gravitational force of magnitude $7 \times$ $10^{22} \mathrm{N}$ on a star. If the planet were four times closer to the star (that is, if the distance between the star and the planet were $1 / 4$ what it is now $),$ what would be the magnitude of the force on the star due to the planet?

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Key Concepts

Inverse Square Law

The inverse square law states that the strength of a force, such as gravity, decreases with the square of the distance from the source. This means that if the distance is reduced by a factor, the force increases by the square of that factor, making it essential for predicting how gravitational forces change with distance.

Newton's Law of Universal Gravitation

This fundamental law explains that every two masses in the universe attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. It forms the basis for understanding gravitational interactions in astrophysics and orbital mechanics.

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