The space shuttle typically travels in a circular orbit at an altitude of 500 km

Question

The space shuttle typically travels in a circular orbit at an altitude of 500 km above the Earth's surface. The Earth itself has a radius of about 6400 km. The shuttle can travel in a circular orbit, at constant speed, without any need for the rocket engine to be on, if it travels at just the right speed (a) Given that the value of g is 8.50 m/s2 at an altitude of 500 km, determine the value of the shuttle's speed in this circular orbit. (Use three significant figures.) 16.1 X 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 (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 8.50 m/s2 O The value of g is not even close to 8.50 m/s2 at the height of the space shuttle's orbit-we just made up a number so you could do a calculation. The value of g, 500 km above the Earth's surface, is almost zero. The astronauts feel weightless because they, and the shuttle, are in free fall while they are orbiting the Earth The astronauts aren't weightless! That's just another NASA conspiracy theory The astronauts only feel weightless during liftoff, not in orbit. At 500 km above the Earth's surface, the Earth and the Moon exert equal and opposite gravitational forces on the astronauts, making them feel weightless. None of these answers is right. The astronauts certainly can't be in free fall-they're not getting any closer to the Earth o Additional Materials Section 5.5: Uniform Circular Motion Section 5-6: Solving Problems Involving Uniform Circular Motion eBook Submit Answer Save Progress

Explanation / Answer

given radius of earth R = 6400 km
height of the shuttle, h = 500 km from the surface of the earth

a. given acceleration due to gracity at the orbit of the shuttle , g = 8.5 m/s/s
   let shuttle speed be v
   then
   v^2/(R + h) = g
   v^2 = g(R + h) = 8.5(6400 + 500)*10^3
   v = 7658.328 m/s

b. let numebr of orbits made in 24 hours be n
   then 2*pi*(R + h)*n = v*24*60*60
   n = 7658.328*24*60*60/2*pi*(R + h)
   n = 15.262 orbits in 24 hours

c. as the value of g = 8.5 m/s/s
   also, in the frame of reference of the shuttle, the outward centrifugal force ( due to non inertial frame of reference) cancels this out and hence the astronauts feel weightlessnes
   so the astronauts feel weightless because they and the shuttle are in free fall when they are orbiting the earth

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