Physics question

Question

A 65kg astronaut works in the International Space Station which orbits the Earth 370km above earth’s surface. What is the astronaut’s weight in the International Space Station? What is the astronaut’s weight on earths surface?

Answer 1

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 = M_earth = 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 = R_earth + 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 = R_earth. 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 = GM_earth/R_earth² = 9.8 m/s².