# What is the apparent weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle moving at constant velocity if the radius of moon is 1.74*10^6 m and the mass of the...

What is the apparent weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle moving at constant velocity if the radius of moon is 1.74*10^6 m and the mass of the moon is 7.35*10^22 kg

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### 1 Answer

The weight of an object with mass m kg as measured on any body with mass M is the gravitational force of attraction with which the object is pulled towards the body. This is given by the relation F = `(G*M*m)/r^2` where G is a universal constant equal to `6.673*10^-11` ` m^3/(kg*s^2)` and r is the distance between the center of gravity of the two objects.

The apparent weight of the an astronaut with a mass 75 kg at a distance 4200 km from the center of the moon is equal to `W_m = 6.673*10^-11*7.35*10^22*75/(1.74*10^6)^2 = 1.2149859*10^-20 N`