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Geodesic Deviation

by Arcon
Tags: deviation, geodesic
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Arcon
#1
Jan24-04, 04:05 AM
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Can someone take a look at

http://wps.aw.com/wps/media/objects/...ments/Ch21.pdf

and tell me how they go from Eq. (7) to Eq. (8)? I've tried this and keep getting additional terms.
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lethe
#2
Jan24-04, 11:19 AM
lethe's Avatar
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Originally posted by Arcon
Can someone take a look at

http://wps.aw.com/wps/media/objects/...ments/Ch21.pdf

and tell me how they go from Eq. (7) to Eq. (8)? I've tried this and keep getting additional terms.
i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.
Arcon
#3
Jan24-04, 11:24 AM
P: n/a
Originally posted by lethe
i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.
I fingered it out

One has to drop not only the term &chi*&chi but the term which is the product of &chi and a derivative of &chi. That was what I was missing.

Arcon
#4
Jan24-04, 11:59 AM
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Geodesic Deviation

Thank you

I believe that I've fingered it out

One has to drop not only the term χ*χ but the term which is the product of χ and a derivative of χ. That was what I was missing.

Again - thanks for the response

Arcon
Arcon
#5
Jan25-04, 12:55 PM
P: n/a
Originally posted by lethe
i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.
Seems that this small detail (drop term with χdχdT) has always tripped me up in that derivation. I guess I was just blind to it. But now that I know it then the derivation is simple.

Just to make sure I understood the approximation can you check this for me?

http://www.geocities.com/physics_wor..._deviation.htm

I commented on the terms to drop right after Eq. (14) and right after Eq. (15)

Thanks

I don't know how I missed this before but the equation of geodesic deviation clearly shows that tidal forces are velocity dependant!

Arcon


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