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Physics / Classical Mechanics 0 / Chapter 8 / Problem 8.34

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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Suppose that we decide to send a spacecraft to Neptune,

Chapter 8, Problem 8.34

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QUESTION:

Suppose that we decide to send a spacecraft to Neptune, using the simple transfer described in Example 8.6 (page 318). The craft starts in a circular orbit close to the earth (radius 1 AU or astronomical unit) and is to end up in a circular orbit near Neptune (radius about 30 AU). Use Kepler's third law to show that the transfer will take about 31 years. (In practice we can do a lot better than this by arranging that the craft gets a gravitational boost as it passes Jupiter.)

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QUESTION:

Suppose that we decide to send a spacecraft to Neptune, using the simple transfer described in Example 8.6 (page 318). The craft starts in a circular orbit close to the earth (radius 1 AU or astronomical unit) and is to end up in a circular orbit near Neptune (radius about 30 AU). Use Kepler's third law to show that the transfer will take about 31 years. (In practice we can do a lot better than this by arranging that the craft gets a gravitational boost as it passes Jupiter.)

ANSWER:

Step 1 of 3

From the Kepler’s third law, the period is given by,

Here, is the universal gravitational constant and is the mass of the sun .

The orbits of Earth and Neptune are shown as follows.

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