Problem C: Gravity at the ISS (5 Points)

The International Space Station (ISS) orbits the Earth at an altitude of around 410 km. The ISS does not fall towards the Earth, and the astronauts & objects are floating weightlessly. On Earth's surface, objects fall with a gravitational acceleration of approximately 9.81 m/s².

(a) Show that the following equation gives the percentage P of how much the grav. acceleration decreases between the surface of Earth (R: Earth's radius, 6371 km) and an object at altitude 2:

2 P(2)=1-(1+)

(b) What is P(2) for the altitude of the ISS, and why are objects weightless nevertheless? (c) At what distance does the grav. acceleration become only 1% of that on Earth's surface?