Chung Homework_1 solutions

Thus all we really need is keplers third law

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Unformatted text preview: we immediately have the period. Thus, all we really need is Kepler’s Third Law, rearranged to solve for the radius at which a geosynchronous satellite must orbit. Problem 13) No, it is not possible to put a satellite in orbit over the North Pole, as the North Pole is stationary while the earth rotates. Since the satellite must also be orbiting the earth as well, there is no possible orbital path for the satellite to take while remaining over a fixed spot like the North Pole. Problem 14) To find the difference in gravitational potential energy, one must calculate the energy at both the apogee and perigee. Using the Gravitational Potential Energy Equation (12-8) we can solve: Problem 15) The amount of energy required to get a spacecraft from the Earth to the Moon is greater than the energy required to get the same spacecraft from the Moon to the Earth because as we learned in section 12-5, the escape velocity for the earth is much greater than the escape velocity for the moon, irrespective of mass being launched. Thus, it requires more energy to leave the Earth. Problem 16) The escape speed of the earth would increase, as we can see from the escape velocity equation (12-11) We can see that reducing the radius would increase the escape velocity required to pull away from Earth’s new gravitational field. Problem 17) Again, using the escape velocity equation (12-11), but replacing the relevant variables to reflect that we are now using Mars data: Problem 18) The question is basically asking what the radius needs to be for the escape velocity to equal that of light speed. This is also known as the Schwarzchild Radius....
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