Once on the surface of Mars, the astronauts will have to adjust to the different

Question

Once on the surface of Mars, the astronauts will have to adjust to the different gravitational strength of another plates. Your weight is equalto to your mass (a measure of the amount of stuff in something) times the acceleration of gravity of the planet, g. As a formula, that's: W = m g So even through your mass (m) does not depend on where you are, your weight does? Use algebra to find the ratio of your weight on Mars (W_M) to your weight on Earth (W_E). Don't plugin any number for now. (You should notice that the mass of the astronsut cancels out, which is not surprising since it does not change!) The acceleration of gravity on a planet depends on its mass (M) and its size (R): g = GM/R^2 The constant G is Newton's gravitational constant, a number one can look up. But if we work in ratios, we don't have care about any constants. Use algebra to show that the ratio gM/gE does not depend on G. Calculate the ratio of an astronaut's weight on Mars to their weight on Earth, W_M/W_E. Mars has a mass of 6.4 times 10^23 kg, while Earth has a larger mass of 6.0 times 10^24kg. The ratio of the radius of Earth to the radius of Mars is R_E/R_M = 1.89.

Explanation / Answer

given that

W = m*g

and

g = G*M/R^2

W = G*m*M /R^2

Wm/We = mm*Re^2/me*Rm^2

Wm /We = 6.4*10^24*(1.89)^2 /6*10^24

Wm / We = 3.81

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