Energy Required To Launch A Satellite Into Orbit
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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass m and radius r in a circular orbit at an altitude of 2r.
Energy required to launch a satellite into orbit. An artificial satellite is revolving in a circular orbit at height of 1 2 0 0 k m above the surface of the earth. However the total energy input required to put a satellite into an orbit of radius r around a planet of mass m and radius r is therefore the sum of the gravitational potential energy gmm 1 r 1 r and the kinetic energy of the satellite gmm r. This means that even though it takes nearly a million joules of energy to lift a 1 kg mass to an altitude of 100 km it takes over 30 million joules of extra energy to give it. Neglect the rotational ke due to the earth s rotation.
Satellites in a highly inclined orbit such as a polar orbit take more energy than a satellite that circles the. For most satellite launches the scheduled launch rocket is aimed straight up at first. Apollo moon landing and space shuttle programs and the russian soyuz program as well as the. The radius of the satellite around the center of the earth is r 17 2 r where r is the radius of the earth.
6 7 1 0 1 1 n m 2 k g 2 is. Examples of human spaceflight include the u s. A 5gmm 6r b 2gmm 3r c gmm 2r d gmm 2r. If the radius of the earth is 6 4 0 0 k m and mass is 6 1 0 2 4 kg the orbital velocity g 6.
Msatellite 3000 kg mearth 5 98 1024 kg rearth 6 37 106 m and g 6 67259 10 11 nm2 kg2. Find the energy required to launch a satellite from earth into the circular orbit at the specified radius r 17 2r. The amount of energy required to launch a satellite into orbit depends on the location of the launch site and how high and how inclined the orbit is. All satellites today get into orbit by riding on a rocket or by riding in the cargo bay of a space shuttle.
Yuri gagarin of the soviet union was the first human to conduct a spaceflight. The extra energy needed to make an object travel fast enough to stay in orbit is more than 30 times as much as the energy needed to lift it to an altitude of 100 km. Satellites in high earth orbit require the most energy to reach their destination.
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