Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1340001     The gravitational force by a star on a planet.     1340001
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Question

 

A planet of mass kg is at a location m. A star of mass kg is at a location m. What is the gravitational force by the star on the planet?

 



Solution

 

Begin by drawing a picture, showing the star and planet, and their positions.


Figure: A star and planet.

To calculate the gravitational force on the planet, we need the relative position of the planet (i.e. the position of the planet relative to the star). This is the position vector from the star to the planet.


Figure: The relative position vector of the planet.

The gravitational force on the planet is given by Newton's Law of Gravitation.

where is the relative position of the planet. The relative position of the planet in this case is

Note that the relative position vector points to the right and downward which matches the picture, giving us confidence that our calculation is correct. Find the magnitude of and its unit vector.

Now, substitute the given quantities and solve for the gravitational force on the planet.

Note that the gravitational force points to the left and upward. This is the direction from the planet toward the star, which is consistent with the fact that gravitational force is attractive. A picture of the gravitational force on the planet is shown below. Note that the direction of the gravitational force on the planet is to the left and upward, which is consistent with our calculation.


Figure: The gravitational force by the star on the planet.