Gravitational acceleration on Mars is 3.72 m/s^2, whereas gravitational acceleration on Earth (sea level) is 9.81 m/s^2, meaning Mars's gravity has only about 37.9% the strength of earth's gravity.
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To determine a person's weight on the surface of any planet, use Newton's 2nd law:
F = ma (force...or "weight" in this case equals mass times acceleration)
Let's rewrite this:
W = mg (where W represents the force (which is weight) and g represents gravitational acceleration)
You can assume the person's mass is the same, regardless of the planet he or she is on. So rearrange the equation, solving for mass.
m = W / g
Now, you can write an equation for mass, weight, and acceleration on mars...
m = W_mars / g_mars
...and one for mass, weight and acceleration on earth...
m = W_earth / g_earth
Since the mass is constant, set the two equations equal to each other and solve for the desired weight.
W_mars/ g_mars = W_earth / g_earth
The process is the same for comparing earth weight to moon weight. Simply replace the marsian values with lunar values and solve. It's just algebra.

Acceleration due to gravity on the moon is 1.6 m/s^2.
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"The Moon" is the moon's name. Other "moons" are called moons because with respect to their planets, they are in positions relatively similar to our moon's position with respect to the earth.