physics

posted by .

Compute the orbital radius of an earth satellite that has an equatorial orbit and always remains above a fixed point P on the earth's surface. Communication satellites have such "geosynchronous" orbits (see figure). These satellites are used to relay radio and television signals around the world.

  • physics -

    How do you determine the altitude at which a satellite must fly in order to complete one orbit in the same time period that it takes the earth to make one complete rotation?

    The force exerted by the earth on the satellite derives from

    ...................................................F = GMm/r^2

    where G = the universal gravitational constant, M = the mass of the earth, m = the mass of the satellite and r = the radius of the satellite from the center of the earth.

    GM = µ = 1.407974x10^16 = the earth's gravitational constant.

    The centripetal force required to hold the satellite in orbit derives from F = mV^2/r.

    Since the two forces must be equal, mV^2/r = µm/r^2 or V^2 = µ/r.

    The circumference of the orbit is C = 2Pir.

    A geosycnchronous orbit is one with a period equal to the earth's rotational period, which, contrary to popular belief, requires 23hr-56min-4.09sec. to rotate 360º, not 24 hours. Therefore, the time to complete one orbit is 23.93446944 hours or 86,164 seconds

    Squaring both sides, 4Pi^2r^2 = 86164^2

    But V^2 = µ/r

    Therefore, 4Pi^2r^2/(µ/r) = 86164^2 or r^3 = 86164^2µ/4Pi^2

    Thus, r^3 = 86164^2(1.407974x10^16)/4Pi^2 = 2.647808686x10^24

    Therefore, r = 138,344,596 feet. = 26,201.6 miles.

    Subtracting the earth's radius of 3963 miles, the altitude for a geosynchronous satellite is ~22,238 miles.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    at what height above the earth's surface in a circular orbit have to travel in order to have an orbital period half that of a geosynchronous satellite's period?
  2. Physics

    Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above the earth's surface, while that for satellite B is at a height of 720 km. Find the orbital speed for each satellite.
  3. Physics

    A satellite with an orbital period of exactly 24.0 h is always positioned over the same spot on Earth. This is known as a geosynchronous orbit. Television, communication, and weather satellites use geosynchronous orbits. At what distance …
  4. physics

    Two Earth satellites, A and B, each of mass m = 960 kg, are launched into circular orbits around the Earth's center. Satellite A orbits at an altitude of 4500 km, and satellite B orbits at an altitude of 13600 km. a) What are the potential …
  5. Physics

    If an artificial earth satellite is in an orbit around the earth’s equator with a period of exactly 1 day, how does its motion look to an observer on the rotating earth if it orbits in the same direction as the earth turns?
  6. Physics

    Some communication satellites are put into a circular geosynchronous orbit in which the satellite remains above a certain position on the earth's equator as it orbits. Such a satellite would always be in the same position in the sky …
  7. physics 1

    Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 418 km above the earth’s surface, while that for satellite B is at a height of 731 km. Find the orbital speed for (a) satellite A …
  8. physics

    Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 418 km above the earth’s surface, while that for satellite B is at a height of 731 km. Find the orbital speed for (a) satellite A …
  9. physics

    A geosynchronous Earth satellite is one that has an orbital period equal to the rotational period of the Earth. Such orbits are useful for communication and weather observation because the satellite remains above the same point on …
  10. physics

    Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 427 km above the earth’s surface, while that for satellite B is at a height of 873 km. Find the orbital speed for (a) satellite A …

More Similar Questions