The orbits of synchronous satellites have been chosen so that viewed from the Earth they appear to be stationary. You are given the Earth’s radius R, the Earth’s mass M, and its angular velocity ω around its own axis. We assume that the rocket’s acceleration takes place in a very short time so that the gravitational effect during the ejection can be ignored. (a) Find the radius of the synchronous circular orbit. (b) The rocket is supposed to be launched at the equator of the Earth in parallel with the direction of the rotation of the Earth. It uses an intermediate semi-elliptical transfer orbit which just touches both circles: the equator of the Earth and the synchronous circular orbit. When it hits the synchronous orbit, the second short launch happens to increase its velocity for the synchronous orbiting. Calculate the total velocity impulse. (c) Given that the final mass to be placed in orbit is m, and the ejection velocity of the rocket is u, find the necessary initial mass
The orbits of synchronous satellites have been chosen so that viewed from the Earth they appear to be stationary. You are given the Earth’s radius R, the Earth’s mass M, and its angular velocity ω around its own axis. We assume that the rocket’s acceleration takes place in a very short time so that the gravitational effect during the ejection can be ignored. (a) Find the radius of the synchronous circular orbit. (b) The rocket is supposed to be launched at the equator of the Earth in parallel with the direction of the rotation of the Earth. It uses an intermediate semi-elliptical transfer orbit which just touches both circles: the equator of the Earth and the synchronous circular orbit. When it hits the synchronous orbit, the second short launch happens to increase its velocity for the synchronous orbiting. Calculate the total velocity impulse. (c) Given that the final mass to be placed in orbit is m, and the ejection velocity of the rocket is u, find the necessary initial mass
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The orbits of synchronous satellites have been chosen so that viewed from the Earth they appear to be stationary. You are given the Earth’s radius R, the Earth’s mass M, and its angular velocity ω around its own axis. We assume that the rocket’s acceleration takes place in a very short time so that the gravitational effect during the ejection can be ignored. (a) Find the radius of the synchronous circular orbit.
(b) The rocket is supposed to be launched at the equator of the Earth in parallel with the direction of the rotation of the Earth. It uses an intermediate semi-elliptical transfer orbit which just touches both circles: the equator of the Earth and the synchronous circular orbit. When it hits the synchronous orbit, the second short launch happens to increase its velocity for the synchronous orbiting. Calculate the total velocity impulse.
(c) Given that the final mass to be placed in orbit is m, and the ejection velocity of the rocket is u, find the necessary initial mass
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