Gravitational Force Problem - Help

[SpacemanRich]

Homework Statement

As a moon follows it's orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. Find the ratio r_max / r_min, where r_max is the moon's maximum distance from the center of the planet and r_min is the minimum distance.

Homework Equations

Newton's law of Gravitation F = G m₁m₂ / r²

The Attempt at a Solution

I found the ratio to be, r_max / r_min = 0.949 to 3 significant digits.
My textbook says the ratio is 1.05. I think the text if wrong. Can someone try this problem and let me know what you get.
Thanks,
R.

 

[SammyS]

Homework Statement

As a moon follows it's orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. Find the ratio r_max / r_min, where r_max is the moon's maximum distance from the center of the planet and r_min is the minimum distance.

Homework Equations

Newton's law of Gravitation F = G m₁m₂ / r²

The Attempt at a Solution

I found the ratio to be, r_max / r_min = 0.949 to 3 significant digits.
My textbook says the ratio is 1.05. I think the text if wrong. Can someone try this problem and let me know what you get.
Thanks,
R.

If r_max / r_min < 1, then r_max < r_min .

Does that make any sense?

Where is the gravitational force greater, at r_min or at r_max?

 

[berkeman]

Homework Statement

As a moon follows it's orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. Find the ratio r_max / r_min, where r_max is the moon's maximum distance from the center of the planet and r_min is the minimum distance.

Homework Equations

Newton's law of Gravitation F = G m₁m₂ / r²

The Attempt at a Solution

I found the ratio to be, r_max / r_min = 0.949 to 3 significant digits.
My textbook says the ratio is 1.05. I think the text if wrong. Can someone try this problem and let me know what you get.
Thanks,
R.

At first I thought you were right, but there is an ambiguity in the notation. Is r_max the radius where the force is max, or is it the maximum radius? You get the two different answers depending on how you define the subscripts of the radius variable...

 

[kreil]

Hint

$$F_{max} = \frac{Gm_1m_2}{r_{min}^2}$$

 

[SpacemanRich]

If r_max / r_min < 1, then r_max < r_min .

Does that make any sense?

Where is the gravitational force greater, at r_min or at r_max?

The gravitational force is greatest at r_min.
The confusion was over whether r_min meant the point where the moon is closest to the planet, or if it meant the variable r of the Gravitational formula for F_min. From the responses I got, I was not the only one confused by the wording of the problem.

 

[SpacemanRich]

At first I thought you were right, but there is an ambiguity in the notation. Is r_max the radius where the force is max, or is it the maximum radius? You get the two different answers depending on how you define the subscripts of the radius variable...

I'm glad I was not the only one confused by the wording of the problem. The hint given by kreil clarified it, and the problem works out fine then. Thanks for your input.

 

[SpacemanRich]

Hint

$$F_{max} = \frac{Gm_1m_2}{r_{min}^2}$$

That makes it perfectly clear what I was missing when reading the problem. Now the problem works as expected.

Thanks for opening my eyes..

Regards,
Rich