On the surface of the Moon an astronaut has a weight of Fg = 120 N. The radius of the Moon is Rm = 1.74 x 106 m, the gravitational constant is G = 6.67 x 10-11 N m2kg2 and the mass of the Moon is Mm = 7.35 x 1022 kg.

Solve numerically for the mass of the astronaut ma in kg

To solve numerically for the mass of the astronaut (ma) in kilograms, we can use the equation for gravitational force:

Fg = (G * Ma * ma) / R^2

Where:
- Fg is the weight of the astronaut on the Moon (120 N)
- G is the gravitational constant (6.67 x 10^(-11) N m^2/kg^2)
- Ma is the mass of the Moon (7.35 x 10^22 kg)
- ma is the mass of the astronaut (unknown)
- R is the radius of the Moon (1.74 x 10^6 m)

Rearranging the equation to solve for ma:

ma = (Fg * R^2) / (G * Ma)

Substituting the known values:

ma = (120 N * (1.74 x 10^6 m)^2) / ((6.67 x 10^(-11) N m^2/kg^2) * (7.35 x 10^22 kg))

Calculating the value:

ma ≈ 1.96 x 10^4 kg

Therefore, the mass of the astronaut is approximately 1.96 x 10^4 kilograms.

321

Well, you have the formula

F = GMm/r^2

So, plug in the numbers. What do you get?

Oh, OK. The astronaut's mass is thus

m = Fr^2/GM

Ok steve so I did 120(1.74x10^6)/(6.67x10^-11)(7.35x10^22)=2.300869565E19