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August 4th, 2018, 02:48 PM   #1
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a = f(n), da/dt = f(dn/dt)

Let $a^3 = \frac{10096.676}{n^2}$. I know $a$, $n$ and $dn/dt$.

Is there any way to calculate $da/dt$?
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August 4th, 2018, 03:50 PM   #2
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Differentiate implicitly

$$3a^2\frac{da}{dt}=-\frac{20193.352}{n^3}\frac{dn}{dt}$$

and solve for $\frac{da}{dt}$.
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August 5th, 2018, 02:29 AM   #3
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Do you mean
$$\frac{da}{dt}=-\frac{\frac{20193.352}{n^3}\frac{dn}{dt}}{3a^2}$$ ?

The result seems good and the dimensional analysis is good (it's an astronomy problem). I should be reasonably sure that the formula I wrote in my program is correct.
Thanks a lot!
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Last edited by Cristiano; August 5th, 2018 at 02:33 AM.
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August 5th, 2018, 04:07 AM   #4
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That's it and you're welcome.
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