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

(a) Radius of the orbit of the shuttle, R= Re+h= 6400+500 km = 6.9*106 m

The force of gravitation at R can be equated as (value of g is taken at height R from earth)

GMem/R2 = mg

Me=gR2/G

Now at any moment Since it is has a constant velocity net force on it will be zero, i.e,

GMem/R2 = mv2/R

v=sqrt(g*R) {putting the value of Me from above}

v=7658.32 m/s

(b) let us say that the shuttle makes n orbits in time 24 hrs= 24*3600 seconds

total distance traveled=n*2*3.14*R

since velocity is constant,

distance = velocity*time

n*2*3.14*6.9*106= 7658.32*24*3600

n=15.26 orbits

(c) option b is correct

the shuttle is in free fall but it cannot fall due to its huge orbital velocity hence it 'falls' around the earth.

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