Moon to Earth Gravitational Force Problem

[ddn87]

Homework Statement

Compare the gravitational force on a 9 kg
mass at the surface of the Earth (with radius 6.4 × 10^6 m and mass 6 × 10^24 kg) with
that on the surface of the Moon (with mass 1 /81.3 ME and radius 0.27 RE ). What is the force on the Earth?
Answer in units of N.

Homework Equations

I need to use this equation... F(from 1 to 2)= G(m1m2/r^2) r(from 1- 2)

The Attempt at a Solution

I know that G is a constant which equals 6.67 x 10^-11. I believe and m1 and m2 are the masses of Earth and the object respectivly. I believe the r^2 is the radius of Earth squared. I am just not sure where r(from1-2) is i know that it is a vector. please help !

 

[Seannation]

Since you're being asked to compare forces, m1 will in both cases be the 9kg block and m2 will either be the Earth or the moon.

For the r value, consider the mass of the Earth and moon to be concentrated at the centre. Consider the 9kg mass to be at the surface. The variable r is the distance between these points, i.e. the radii of each planet.

 

[ddn87]

I believe what you are trying to say is that R is the sum of the two radii?

 

[ddn87]

then dividing by two?

 

[Seannation]

No, not at all. The two radii given are for the Earth and the moon, respectively (the moon radius is expressed in terms of a ratio of the earth's). Since the question is asking you to compare two forces -- one on the Earth and one on the moon -- you need to do two calculations: one for the 9kg mass on the surface of the earth, and one for the 9kg mass on the moon. When you're doing the calculation for the earth, you use the value for Earth's radius for your r, and when you're doing the moon you use the moon's radius for r.

Hope this helps.

 

[ddn87]

Im beginning to understand this concept a little more... so when I add Earth and the moon's Radii I get the total radius which is in the m1m2/ r^2 part of the problem... the r(from 1-2) is the radius from the 9 kg object to the center of the earth?

 

[Seannation]

As far as I understand the question, the Earth and the moon's radii should not be added together at all. As I said in my last post, you've to do two calculations and compare them.

For the Earth calculation, m1 is 9kg (the mass), and m2 is 6*10^24kg (the earth), and r is 6.4*10^6 (distance between the centre of the Earth and the surface of the earth, where the 9kg mass is). For the moon calculation, m1 is again 9kg, m2 is 7.38*10^22 (mass of the Earth divided by 81.3, as the question states), and r is 1728000 (0.27 times the Earth's radius, as the question states).

I've done the calculation for Earth and got a force of something like 90N, which matches up well when we consider Earth has an acceleration due to gravity of ~10ms^-2.

 

[Tzim]

Yeah at both equations you put r when r is always the distance between the object and the centre of the planet(earth or moon)
so F1=G*Me*M1/r1 when r1 is the distance between the object on the surface of the Earth from the centre of the earth
F2=G*Mm*M1/r2 when r2 is the distance between the object on the surface of th moon from the centre of the moon

 

[ddn87]

THANKS ill try this out

 

[Tzim]

Sorry mistake in the above equations when i have r1 is r1^2 and when i have r2 is r2^2.but the other are correct.thats the idea