Tough assignment question - help would be appreciated

[Mohammed17]

As a moon follows its 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


Ok so I know the equation that will be used is:

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

But I have nooooo idea where to start.

Do I do Fg of the moon = (0.11)(Fg)planet + (Fg)planet

...?

 

[fzero]

You're on the right track, but you need to distinguish between Fg((r)max) and Fg((r)min) in the equation that you wrote.

 

[Mohammed17]

Ok so it would be:

1/r^2 (max) = (0.11)/r^2 + 1/r^2

so it would be: 1/r^2 max = 1.11/r^2 min

cross multiplication would give me:

(1.11)r^2 max = r^2 min

Since we need the ratio of r^2 max to r^2 min
divide both sides by r^2 min.

1.11 r^2 max / r^2 min = 1

now divide both sides by 1.11
r^2 max / r^2 min = 1/1.11 = 0.90

Square root of (r^2 max / r^2 min) = Square root of (0.90)

Therefore:

(r)max / (r) min = 0.95

 

[Mohammed17]

Ok so it would be:

1/r^2 (max) = (0.11)/r^2 + 1/r^2

so it would be: 1/r^2 max = 1.11/r^2 min

cross multiplication would give me:

(1.11)r^2 max = r^2 min

Since we need the ratio of r^2 max to r^2 min
divide both sides by r^2 min.

1.11 r^2 max / r^2 min = 1

now divide both sides by 1.11
r^2 max / r^2 min = 1/1.11 = 0.90

Square root of (r^2 max / r^2 min) = Square root of (0.95)
(r) max / (r) min = 0.95

Is this correct?

May someone go over it. Is my logic correct? I guess since Fg is inversely proportional to radius, then if Fg is 11 % larger, the radius must be a portion smaller ?

 

[fzero]

Yes, if the gravitational force is larger, the distance is smaller by a factor involving an inverse square root.

 

[Mohammed17]

Yes, if the gravitational force is larger, the distance is smaller by a factor involving an inverse square root.

is my value correct though? 0.95 ?

 

[fzero]

What you wrote looks correct but the problem is asking for (r)max/(r)min.

 

[Mohammed17]

What you wrote looks correct but the problem is asking for (r)max/(r)min.

I did get (r) max / (r) min. IT was equal to 0.95. I just forgot to show that i square rooted both sides in the above posts. I fixed that though.