# Ratio of wight on moon-earth

1. Sep 30, 2007

### BuBbLeS01

1. The problem statement, all variables and given/known data
Suppose that the ratio of the Moon's mass to the Earth's mass is given by 1.200E-2 and that the ratio of the Moon's radius to the Earth's radius is given by 2.740E-1. Calculate the ratio of an astronaut's Moon-weight to Earth-weight.

2. Relevant equations
Wmoon = mg
Wearth = mg

gmoon=
gearth= 9.81m/s^2

g= Gm/r^2

3. The attempt at a solution
Okay this seems like a very simple problem but the fact that they are giving me ratios in the problem for the mass and radius I am confused as to how to go about solving this.

2. Sep 30, 2007

### Staff: Mentor

You are on the right track. Write the force equations for the astronaut's weight for the Earth and the Moon, using subscripts to keep the mass of the Earth and moon identified, as well as the mass of the astronaut and the radii of the Earth and the moon. Once you have those two equations written out with the subscripts keeping everything straight, you will see how to use the ratios to help you get the answer.

Here, I'll help with the equation for the weight force of the astronaut on the Earth:

$$F_e = \frac{G m_e m_a}{{r_e}^2}$$

3. Sep 30, 2007

### BuBbLeS01

Hmm...I am not seeing it...
Fe = GMeMa/Re^2
Fm = GMmMa/Rm^2
Do I have it set up right?

4. Sep 30, 2007

### BuBbLeS01

I don't understand how to incorporate the ratios?

5. Sep 30, 2007

### dynamicsolo

You are asked for the ratio of the astronaut's weight on the Moon compared to that on the Earth. What would that ratio be in terms of Fe and Fm? What would your expression on the right-hand side reduce to? Do you have the data required to calculate that value?

6. Sep 30, 2007

### BuBbLeS01

F=Gm1m2/r^2

7. Sep 30, 2007

### dynamicsolo

Well, yes... but you already wrote down forces Fe and Fm. What are those? How do they relate to weights? What ratio do you need to work out?

8. Sep 30, 2007

The important thing here is to note that the question is very specifically asking for the ratio of an astronaut's Moon-weight to Earth-weight.
...RATIO.

So the left-hand side should be a ratio, more specifically $$\frac{w_{moon}}{w_Earth}}$$

Now rewrite the everything in terms of the Moon...that is