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I am trying to solve for $R$ as this is the radius of a RR Lyrae type of variable star from the formula: $$P^{-1}\frac{dP}{dT}=1.5R^{-1} \frac{dP}{dT}$$ $P$ is the star's brightness variability period and of course here we are to be taking the derivative of the period with respect to time.

Here are my questions: The period IS a rate of change, so isn't the value I get from my data for the period the derivative already? As such could I just replace the $P^{-1}\frac{dP}{dT}$ with that value? But then how do I take the derivative of the $R^{-1}\frac{dP}{dT}$? Surely I don't just replace this with the period value as well; that would result in turning this into a simple algebraic equation. Do I need to take an integral to solve for $R$, and if so can someone show me how that is done in this instance? I am using a spreadsheet to sort my data and eventually determine the period of several of these types of stars, so is there a different value I need to put in for $P$ and then let $T$ be the overall length of time for imaging (for instance, suppose I imaged a star for $2$ weeks; would $T$ be $14$ days)?

Thanks to all who are working on this!
-Melanie and Dave

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  • $\begingroup$ What's $T$, temperature or time? $\endgroup$ – Nosrati Aug 1 '18 at 17:03
  • $\begingroup$ T is time, the unit I believe is in days $\endgroup$ – MPGDS APU Aug 3 '18 at 1:05
  • $\begingroup$ I presume there's a typo in your equation: shouldn't it be $dR/dT$ on the right hand side? $\endgroup$ – Intelligenti pauca Jan 25 '19 at 20:29
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Your equation (I corrected a typo) $$P^{-1}\frac{dP}{dT}=1.5R^{-1} \frac{dR}{dT}$$ can be rewritten as $$\frac{d}{dT}\ln P=\frac{d}{dT}(1.5\ln R),$$ that is: $$\ln P=\ln R^{1.5}+\text{constant},$$ and finally: $$P=k\cdot R^{1.5},$$ where $k$ is a constant, to be determined from initial conditions.

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