The geostationary orbit is a unique circular orbit above the equator of a planet, for which the orbital period is equal to the rotation period of the planet. For Earth, the geostationary orbit is 4.22 x 104 km from the centre of the Earth. The Earth rotates in 23 hours and 56 minutes. a) A failed satellite, whose apogee distance is at Earth's geostationary orbit, has only half the required orbital speed of a geostationary satellite at apogee. Calculate the perigee distance of the orbit of this failed satellite. b) If another planet has twice the size of Earth and the same average density as Earth, while rotating in the same amount of time, calculate the radius of the geostationary orbit for this planet.

The geostationary orbit is a unique circular orbit above the equator of a planet, for which the orbital period is equal to the rotation period of the planet. For Earth, the geostationary orbit is 4.22 x 104 km from the centre of the Earth. The Earth rotates in 23 hours and 56 minutes. a) A failed satellite, whose apogee distance is at Earth's geostationary orbit, has only half the required orbital speed of a geostationary satellite at apogee. Calculate the perigee distance of the orbit of this failed satellite. b) If another planet has twice the size of Earth and the same average density as Earth, while rotating in the same amount of time, calculate the radius of the geostationary orbit for this planet.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

Problem 2. Satellite orbits.
The geostationary orbit is a unique circular orbit above the equator of a planet, for
which the orbital period is equal to the rotation period of the planet. For Earth, the
geostationary orbit is 4.22 x 104 km from the centre of the Earth. The Earth rotates
in 23 hours and 56 minutes.
a) A failed satellite, whose apogee distance is at Earth's geostationary orbit, has only
half the required orbital speed of a geostationary satellite at apogee. Calculate the
perigee distance of the orbit of this failed satellite.
b) If another planet has twice the size of Earth and the same average density as
Earth, while rotating in the same amount of time, calculate the radius of the
geostationary orbit for this planet.

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