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Exercise [17.07]
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Joined: 26 Mar 2010, 04:39
Posts: 109
Here is my solution for exercise 17.7 in PDF format.

It's quite interesting that we can determine the relative densities of the sun and moon just by measuring the relative strengths of their tidal effects (which should be possible to work out by comparing the height of ocean high tides when the sun and moon are pulling in the same and opposite directions) .

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File comment: Exercise 17.7 Exercise17.7.pdf [39.14 KiB]
30 May 2010, 04:42 Joined: 26 Mar 2010, 04:39
Posts: 109
I looked up the actual values for the lunar and solar tidal acceleration values as well as the densities of the sun and moon and discovered that Penrose has made an error.

In fact the tidal acceleration due to the moon is around 0.00000011 times the acceleration due to gravity at the earth's surface while the tidal acceleration due to the sun is around 0.000000052 times (both measured along the axis joining the centres of mass). This tells us that the tidal acceleration due to the moon is roughly 2.11 times that of the sun rather than 5 times as claimed in the book.

When adjusted to use this value, the calculation should tell us that the moon is roughly 2.11 times as dense as the sun. I looked up these values and found:

Density of sun = 1.4 g / cm3
Density of moon = 3.346 g / cm3

This gives that the density of the moon is about 2.39 times that of the sun, which I guess agrees close enough with the result of 2.11 times that we approximated.

30 May 2010, 07:28 Page 1 of 1 [ 2 posts ]