Quote:
Originally Posted by Kingswood
I have read through the above, and I follow most of it (particularly the worked example) except for the derivation of the constants C and A. On the third page it discusses the derivation of these constants. However, this derivation is unclear. One problem is the use of a constant m that doesn't seem to be defined anywhere. [Snip!]
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Welcome to BAUTForum,
Kingswood!
The constant
m refers to the mass of the equatorial ring.
Quote:
Originally Posted by Kingswood
On page 5, the figures given for C and A gave a result for the expression ((C-A)/C) roughly equal to 0.003293 (which for some reason is converted to 1/304). [Snip!]
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The 304 refers to the number of days in the free or Eulerian precession. The Earth is not rigid, however, so what is observed is a seemingly random wobble with a period of about 430 days called the Chandler Wobble.
Quote:
Originally Posted by Kingswood
What I would like to do is derive a general formula for use in a spreadsheet that gives rough estimates for the rate of precession for any terrestrial planet. The tricky part is these constants (C and A) which I lack the knowledge to derive from first principles.
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That's OK; no one derives them from first principles because to do so would require detailed knowledge of the distribution of the Earth's mass. We have to content ourselves with measurements of these moments by other means.
Quote:
Originally Posted by Kingswood
Ideally I would like to derive these from oblateness, equatorial radius and density because I have these figures on hand. Thanks in advance for any advice.
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I've gone looking for these quantities in two of my references, but I can only find J
2 and J
4 for the planets. Now J
2*M*R
2 is (C-A), where M is the mass and R is the equatorial radius. But I can't find C and/or A for anything other than the Earth and Moon. I would suggest Googling for +"moment of inertia" +Mars, etc. for each of the planets you're interested in.
Edited to add: I prefer the moments A, B, and C to be dimensionless constants, but others take them to have dimension kg*m
2, and I have followed that convention above.