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Chapter 14: Problem 27

A reconnaissance spacecraft circles the Moon at very low altitude. Calculate (a) its speed and \((b)\) its period of revolution. Take needed data for the Moon from Appendix C.

Short Answer

Expert verified
The spacecraft's speed and period of revolution around the moon can be calculated using the laws of circular motion in combination with the gravitational force. The exact numerical values would depend on the values for the moon's mass, the moon's radius and the gravitational constant given in Appendix C.

Step by step solution

01

Calculation for speed

The speed, \(v\), of an object moving in a circle of radius \(r\) under the influence of a gravitational body of mass \(m\) is given by the equation \(v = \sqrt{G \cdot \frac{m}{r}}\) where G is the gravitational constant. From Appendix C, get the required values for r (radius of the moon plus altitude of spacecraft which is very low in this case so it can be approximated to the moon's radius), m (mass of moon), and G (gravitational constant). Plug these values into the equation to get the speed.
02

Calculation for period of revolution

The period of revolution, \(T\), around a gravitational body of mass \(m\) in a circle of radius \(r\) is given by the equation \(T = \frac{2\pi r}{v}\). With the already calculated speed, \(v\), and the radius, \(r\), plugged into this equation, the student can find the period of revolution.

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