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A satellite moves in a low, nearly circular orbit of radius approximately equal to Earth's radius Re. Rockets fire briefly along its direction of motion so that its speed is instantaneously multiplied by sqrt(3/2). Find the farthest distance R from the Earth's centre that the satellite then reaches.

1. 4*Re
2. 3*Re
3. 2*Re
4. 2.5*Re

Correct answer: 3*Re

Solution

The boost happens at perigee. Using angular momentum (Re*v = R*vₐ) and energy conservation between perigee and apogee gives a quadratic for R/Re whose physically relevant root is 3.

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