Question

The International Space Station typically travels in a circular orbit at an altitude of 400 km above the Earth's surface. The Earth itself has a radius of about 6400 km. Assume that the space station travels in a circular orbit at constant speed (this is a perfectly reasonable assumption).

A. Given that the value of g is 8.68m/s28.68m/s2at an altitude of 400 km, determine the value of the space station's speed in its circular orbit. _______ m/s

B. At this speed, how many orbits does the shuttle make in 24.0 hours? Use three significant figures. Partial orbits are fine—an answer like 7.34 orbits would be perfectly acceptable. _______ orbits

C. It is well known that astronauts who are on the space shuttle experience weightlessness. How can that be, if the value of g is 8.68  m/s28.68m/s2?

Answer 1

Answer 2

A) mg = mv² / r ( in circular orbit)

cancel the mass on both sides

g = v² / r

v = sqrt ( rg)

v = sqrt ((6400 + 400) * 1000 * 8.68)

v = 7.6e3 m/s

-----------------------------------------------------------------

B) time taken to complete one orbit

t = 2 * pi * 6800000 / 7.6e3

t = 1.5616 hr

so, in 24 hours , it will complete

N = 15.36 orbits

( In reality, ISS completes 16 orbits per day, so our answer is pretty accurate)

------------------------------------------------------

C) This is an interesting question...........no matter how far we are above earth surface, gravity will be there ( that's called micro gravity) ........... now at an altitude of 400 km , the astronauts ( with ISS) are in free fall around the earth and we know that any object in free fall will feel weightless as there is no contact force and the only force is gravity and we will not feel the effect of gravity if there is no opposing force .......that is the reason we feel weightlessness in orbit.