Precalc HW (NO IDEA HOW TO SOLVE)

Low Earth orbiting satellites orbit between 200 and 500 miles above Earth. In order to keep the satellites at a constant distance from Earth, they must maintain a speed of 17,000 miles per hour. Assume Earth's radius is 3960 miles.

a. Find the angular velocity needed to maintain a LEO satellite at 200 miles above earth.

b. How far above Earth is a LEO with a angular velocity of 4 radians per hour?

c. Describe the angular velocity of any LEO satellite

I posted another topic, but no one replied. THX <3!

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  1. The key relationship is
    linear velocity = angular velocity x radius,

    a) since the satellite is 200 miles above the earth, the radius would be 4160 miles.

    lin. vel = ang vel. x radius
    17000 = av(4160)
    4.07 = av

    so the angular velocity would be 4.07 radians/hour
    (remember that 2pi, or 6.28 radians is one rotation, which makes this 234ยบ per hour)

    b) this seems to be the reverse question of a). Notice we got appr 4 radians per hour as the answer to the angular velocity, so the satellite would have to be about 200 miles above the earth.

    Check my calculations, this seems rather odd.

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