# Gravitation: Orbits

### Problems on Orbits

Problem : What is the escape velocity from the earth? ( M e = 5.98×1024 kilograms, r e = 6.38×106 meters)

Problem : If a black hole contains a singularity (all the mass is concentrated at a point) with a mass 1000 times the mass of the sun, what is the radius beyond which light cannot escape? This is called the Schwartzchild radius. The mass of the sun is 1.99×1030 kilograms and the speed of light is 3×108 m/s.

Problem : We would expect a satellite orbiting the earth to be slowed down by friction with the atmosphere. We also know that velocity is inversely proportional to the radius of the orbit, so when the satellite slows down, it should spiral away from the earth. But it is observed that satellites spiral in towards the earth. How can we explain this paradox?

Problem : Suppose the viscous drag causes a 2000 kilogram satellite to increase its speed from 10000 m/s to 15000 m/s. If the satellite had an initial orbital radius of 6.6×103 kilometers, what is its new orbital radius? ( M e = 5.98×1024 kilograms).

Problem : At a height of 2×107 meters above the center of the earth, three satellites are ejected from a space shuttle. They are given tangential speeds of 5.47 kilometers/sec, 4.47 km/sec, and 3.47 km/sec respectively. Which one(s) will assume circular orbits? Which elliptical? The mass of the earth is 5.98×1024 kilograms.

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