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 2.700E-1. Calculate the ratio of an astronaut's Moon-weight to Earth-weight.

Now it seems like this problem really shouldn't be too difficult. However, I'm not sure of how to solve it given ratios instead of the actual masses and radius's.

Wm/We = gm/ge = (GMm/rm^2)/(GMe/re^2) or Mm(re^2)/Me(rm^2).

Right. But w/o knowing the actual mass of the earth and moon, only the ratio, how can I do this?

Lindsay, you are given Mm/Me, and rm/re

Wm/We= Mm/Me * (re/rm)^2

Ohhh I see now! Sorry, I just wasn't understanding before.

Thanks. :)

To solve this problem, we can use the concept of proportional relationships. Let's denote the ratio of the Moon's mass to the Earth's mass as "m" and the ratio of the Moon's radius to the Earth's radius as "r". We are given that m = 1.200E-2 and r = 2.700E-1.

To find the ratio of an astronaut's Moon-weight to Earth-weight, let's first assume that an astronaut's weight on Earth is denoted as "WE" and the astronaut's weight on the Moon is denoted as "WM".

1. Recall that weight is proportional to mass. So, weight is directly proportional to mass. Mathematically, this relationship can be represented as:
Weight ∝ Mass

2. Now, let's consider the weight of an object on the Moon compared to its weight on Earth. The weight on Earth can be denoted as WE and the weight on the Moon can be denoted as WM. According to the proportional relationship between weight and mass, the ratio of WM to WE will be equal to the ratio of the Moon's mass to the Earth's mass.

WM / WE = m [Equation 1]

3. Similarly, let's consider the radius of the Moon compared to the radius of the Earth. According to the proportional relationship between weight and radius, the ratio of WM to WE will be equal to the ratio of the square of the Moon's radius to the square of the Earth's radius.

WM / WE = (r^2) [Equation 2]

4. We now have two equations:
WM / WE = m [Equation 1]
WM / WE = (r^2) [Equation 2]

5. Since the two ratios, WM/WE, are equal, we can set them equal to each other:

m = (r^2)

6. Now, to find the ratio of an astronaut's Moon-weight to Earth-weight, we can substitute the values of m and r into the equation:

WM / WE = m = (r^2) = (2.700E-1)^2

7. Calculate (2.700E-1)^2 using a calculator:

(2.700E-1)^2 = 0.0729

8. Therefore, the ratio of an astronaut's Moon-weight to Earth-weight is approximately 0.0729.

In summary, we can find the ratio of an astronaut's Moon-weight to Earth-weight by comparing the ratios of the Moon's mass to the Earth's mass and the Moon's radius to the Earth's radius. Using these ratios, and applying the proportional relationships between weight and mass/radius, we can calculate the desired ratio.