**** Edit, appearently, Latex is not working right now. Here's my best effort to duplicate this post without Latex: ***(adsbygoogle = window.adsbygoogle || []).push({});

In the following journal paper:

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1995AJ....110..420M&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf [Broken]

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 a_{i}can be computed by

a_{f}-delta a

It would make sense to me that a(0) should equal a_{i}, and a(tau) should equal a_{f}.

My first assumption is correct. a(0) does equal a_{i}since e^{0}=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/cgi-bin/nph-iarticle_query?1995AJ....110..420M&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf [Broken]

the top of page 424 contains this formula

[tex]a(t)=a_{f}-\delta a exp(-t/\tau)[/tex]

which if I'm not mistaken is the same as

[tex]a(t)=a_{f}-\delta a e^{(-t/\tau)}[/tex]

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.

[tex]\tau[/tex] is the timescale of the migration

and a_{i}can be computed by

[tex]a_{f}-\delta a[/tex]

It would make sense to me that a(0) should equal a_{i}, and [tex]a(\tau)[/tex] should equal a_{f}.

My first assumption is correct. a(0) does equal a_{i}since e^{0}=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?

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# Help me understand this equation

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