David D. answered 04/23/21
Science and Math Tutor with a PhD in Physics
Weight is just a measure of how strong Gravity is pulling on something. The equation for the force due to gravity is F = Gm1m2/r2 where G = 6.67 x 10-11 Nm2/kg, m1 and m2 are the masses of the two objects and r is the distance between them. We want to know the force of gravity due to the earth so m1 = Mearth = 5.972 x 1024 kg. The distance is measured from the center of the earth to the person. The first problem, the astronaut is 370 km above the earth so r = Rearth + 370 km = 6378 km +370 km = 6748 km. Plugging in all these values into the force equation we have F = ((6.67 x 10-11 Nm2/kg)*(5.972 x 1024 kg)(65 kg)/(6748000 meters)2 = (8.75 N/kg)(65 kg) = 568.6 N. Note that 8.75 N/kg is an acceleration (F=ma or F/m = a). The astronaut's weight on earth uses the same formula but r = Rearth. We now have F = ((6.67 x 10-11 Nm2/kg)*(5.972 x 1024 kg)(65 kg)/(6378000 meters)2 = (9.8 N/kg)(65 kg) = 637 N. For any object on earth, the simple equation for weight is W = mg where g is 9.8 m/s2 (or 9.8 N/kg). In the equation for force we see how little g is derived. g = GMearth/Rearth2 = 9.8 m/s2.