# Help me understand this equation

1. Apr 4, 2006

### tony873004

**** Edit, appearently, Latex is not working right now. Here's my best effort to duplicate this post without Latex: ***

In the following journal paper:
http://articles.adsabs.harvard.edu/...e=PDF_HIGH&amp;type=PRINTER&amp;filetype=.pdf

the top of page 424 contains this formula
a(t)=af-delta a exp(-t/tau)

which if I'm not mistaken is the same as
a(t)=af-delta a e(-t/tau)

It gives an object's semi-major axis at time t for an object that is migrating from the orbit where it formed, to where it is in the current epoch.

tau is the timescale of the migration
and ai can be computed by
af-delta a

It would make sense to me that a(0) should equal ai, and a(tau) should equal af.

My first assumption is correct. a(0) does equal ai since e0=1.

But my second assumption can only work if e-1 = 0, which it does not.

Does anyone care to guess what I'm doing wrong?

*** The Latex version for when TEX starts working again ***
In the following journal paper:
http://articles.adsabs.harvard.edu/...e=PDF_HIGH&amp;type=PRINTER&amp;filetype=.pdf

the top of page 424 contains this formula
$$a(t)=a_{f}-\delta a exp(-t/\tau)$$

which if I'm not mistaken is the same as
$$a(t)=a_{f}-\delta a e^{(-t/\tau)}$$

It gives an object's semi-major axis at time t for an object that is migrating from the orbit where it formed, to where it is in the current epoch.

$$\tau$$ is the timescale of the migration
and ai can be computed by
$$a_{f}-\delta a$$

It would make sense to me that a(0) should equal ai, and $$a(\tau)$$ should equal af.

My first assumption is correct. a(0) does equal ai since e0=1.

But my second assumption can only work if e-1 = 0, which it does not.

Does anyone care to guess what I'm doing wrong?

Last edited: Apr 4, 2006
2. Apr 5, 2006

### tony873004

I figured it out. As long as I posted the question here, I might as well post the answer too incase anybody was curious. I e-mailed the author of the paper and she responded:

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