# Integrating radial velocity with respect to time

I'm a highschool student who is writing a research paper about plotting Period-Luminosity graph of the Cepheid variables by deriving distance through independent method such as trigonometric parallax and Baade-Wesselink method: $$∆R = R(t) - R(t_0) = -p \int_{t_0}^t v(t)dt$$

While trying to understand and use the Baade-Wesselink method, I faced some difficulties in terms of calculating linear radius variation. According to some papers, I need to integrate radial velocity with respect to time to get the linear radius variation from $t_0$ to $t$, where $t = t_0$ $+$ its period.

I got the linear radial velocity from the SIMBAD database. For example, for the V* AQ Pup (one of classical Cepheids), its radial velocity is 56.9km/s. Then how do I integrate this value from $t_0$ to $t$? Does this mean [56.9t]^t_t0 and after all $56.9t_1 - 56.9t_0$?

And also, may I ask how can I get the value of $t_0$ and $t$? Does this mean "proper motion" in here?

• The radial velocity given in SIMBAD is averaged with respect to t to give the overall radial velocity of the star with respect to the Sun, this removes the radial velocity impact of the star's pulsation. What you need is raw radial velocity data for the star covering an entire pulsation period. – James Screech Aug 9 '16 at 11:46
• @JamesScreech Can you suggest any database that gives the most updated raw radial velocity data? The one I found is this, crocus.physics.mcmaster.ca/Cepheid, but I found it that some of them are quite outdated. Also, may I ask which program you recommend best for integrating the radial velocity? The one I'm going to use is the Logger pro. Thank you. – 7_G.S.N Aug 9 '16 at 15:13
• Sorry I cannot help with either – James Screech Aug 10 '16 at 7:20