Some satellites are located in what is called a geosynchronous orbit around the Earth, in which they maintain their position over a particular location on the Earth as the Earth spins on its axis. For instance, one such satellite might be directly above Quito, Ecuador at all times. For this exercise, take the mass of the Earth to be 5.97 x 1024 kg, and we will also assume that the Earth takes exactl 24 hours to rotate once on its axis. (a) How far from the center of the Earth is such a satellite, assuming it is over a particular point on the equator at all times? m (b) What is the speed of this satellite, in its circular orbit around the Earth? Neglect the fact that the Earth itself is moving, too!

Some satellites are located in what is called a geosynchronous orbit around the Earth, in which they maintain their position over a particular location on the Earth as the Earth spins on its axis. For instance, one such satellite might be directly above Quito, Ecuador at all times. For this exercise, take the mass of the Earth to be 5.97 x 1024 kg, and we will also assume that the Earth takes exactl 24 hours to rotate once on its axis. (a) How far from the center of the Earth is such a satellite, assuming it is over a particular point on the equator at all times? m (b) What is the speed of this satellite, in its circular orbit around the Earth? Neglect the fact that the Earth itself is moving, too!

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 46P: A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits...

See similar textbooks

Similar questions

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are sueful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for Earth in Appendis D.
A satellite of mass 1250 kg is to be placed in a circular orbit at a height h=210 km above the Earth’s surface, where g=9.2 m/s2. (a) What is the weight of the satellite at this altitude? (b) With what tangential speed must it be inserted into its orbit? The Earth’s radius is R= 6370 km.
You wish to put a 1000.0 kg satellite into a circular orbit above the earth's surface with a period of 300.0min. The mass and radius of the earth is 5.972x10²⁴ kg and 6371km, respectively. What speed, distance from the earth's surface, and radial acceleration will it have?
If the satellite has a mass of 4800 kg and a radius of 4.1 m , what is the required steady force of each rocket if the satellite is to reach 39 rpm in 4.5 min ?
A 216.2 kg satellite is geosynchronous orbit around the Earth stays over the same spot and takes 24 hours to make one revolution. Given the following data, determine the satellite’s height above the surface of the Earth. G = 6.67 x 10-11 Nm2/kg2, mass of Earth = 5.98 x 1024 kg, radius of Earth = 6.38 x 106 m.
A geosynchronous orbit is one where the period of the rotation of the thing you’re orbiting is equal to your orbital period. If the period for the Earth is 1 day, and it has a mass of 5.972 x 10^24 kg, what is the semimajor axis for a geosynchronous orbit?
Suppose an artificial satellite has been put into circular orbit about the Earth, at a distance from the center of the Earth equal to 1/4 the distance from the Earth's center to the Moon's center. In terms of the Moon's period Tm, what will be the period of the satellite?
A satellite is in an elliptical orbit, with a perigee of 2.0 earth radii and an apogee of 6.6 earth radii. If its velocity is 2.10 km/s at apogee, what is its velocity at perigee? Provide your answer in km/s. Hint: Make use of the conservation of angular momentum. A. 6.2 km/s B. 6.9 km/s C. 8.0 km/s D. 8.8 km/s
A proposed space station includes living quarters in circular ring 47.5 m in diameter. At what angle speed should the ring rotate so the occupants feel that they have the same weight as they do on earth?
A space station is constructed in the shape of a wheel 20 m in diameter, with essentially all of its 5.2×105 kg mass at the rim. Once the station is completed, it is set rotating at a rate that requires an object at the rim to have radial acceleration g , thereby simulating Earth's surface gravity. This is accomplished using two small rockets, each with 130 N thrust, that are mounted on the rim of the station. How long will it take to reach the desired spin rate, and how many revolutions will the station make in this time?
Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can dig a long tunnel from one side of the Earth straight through the center and exit the other end, any object falling into the tunnel will appear at the other end (i.e. the opposite side of the Earth) in just 2530 s (42.2 min). Call that time t. Let t be a function of G, M, and R, where G = 6.67 x 10^-11 m3 kg−1 s−2 is the Universal Gravitational Constant, M = 5.98 x 10^24 kg, and R = 6400 km. (a) From dimensional analysis alone find the expression for t, up to a numerical constant c.(b) Determine the value of c by using the above values in the expression found in part (a).
Two identical uniform spheres A and B, with mass M=M= 1.00 [kg], are placed 0.500 [m] away from another spherical mass C with mass m=m= 0.300 [kg] as shown: If mass C is released from rest, what is its net acceleration? Assume that only the gravitational forces from spheres A and B act on C. State also the direction if it is upward or downward.