Physics Problem HELP PLEASE!?

anonymousanonymous
in Science & Mathematics

What is the speed period, and radial acceleration of a communications satellite in a circular orbit 2000km above the surface of the earth. The earth's radius is 6380 km and its mass is 5.98 x 10^24 kg. G = 6.67 x 10^-11 Nm^2kg^-2. At what height above the surface of the earth should the satellite be placed for the orbital speed to be 5000 m/s?

Comments

  • randy-prandy-p

    I'll bet you've been given some formulas relevant to satellites. What are they?

    You can derive them from Newton's law of gravity, so I'll start there. But as I say, I'll bet you already have this derivation or something like it in your notes.

    Centripetal acceleration of satellite = GM/r^2 = v^2/r

    So v^2 = GM/r

    v = sqrt(GM/r)

    "What is the speed period, and radial acceleration of a communications satellite in a circular orbit 2000km above the surface of the earth. The earth's radius is 6380 km and its mass is 5.98 x 10^24 kg. G = 6.67 x 10^-11 Nm^2kg^-2."

    There's G, M and r. r is the distance from the center of the earth in meters. You've been given the radius of the earth and the altitude above the surface in km. You'll have to figure out r from that.

    Plug them in. That's v.

    The length of one orbit is 2pi*r. Use that to figure out how long it takes to go that distance (the period) at the given speed.

    "At what height above the surface of the earth should the satellite be placed for the orbital speed to be 5000 m/s?"

    You have v, you have G, you have M. Solve for r.

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