How Do You Calculate an Astronaut's Weight Ratio from Moon to Earth?

[BuBbLeS01]

Homework Statement

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.

Homework Equations

Wmoon = mg
Wearth = mg

gmoon=
gearth= 9.81m/s^2

g= Gm/r^2

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.

 

[berkeman]

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}

 

[BuBbLeS01]

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

 

[BuBbLeS01]

I don't understand how to incorporate the ratios?

 

[dynamicsolo]

I don't understand how to incorporate the ratios?

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?

 

[BuBbLeS01]

F=Gm1m2/r^2

 

[dynamicsolo]

F=Gm1m2/r^2

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?

 

[Saladsamurai]

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
1 Earth radius=k*moon radius and so on...

Then make proper substitutions.

Casey