# Accurate formula for calculating the mass of an exoplanet using the transit method

A friend and I did some work on exoplanets with the help of a research institute (IEEC in Spain) for a major high school project. What we did was to "redetect" the exoplanet XO-6b through the transit method. This is the scientific paper of the official discovery https://arxiv.org/pdf/1612.02776.pdf . With the data and information provided we could only extract the flux-time curve and with it calculate the radius of the planet. Once the radius was calculated, we wanted to go further and know more characteristics of the planet such as mass, period, distance to its star... What happened is that we needed the mass and we discovered that the most natural way to calculate it was through the method of radial velocities to which we did not have access. What we decided to do was to look in books and we found the following formula that approximated the mass of the planet:

$$M_P = \left(\frac{R_P}{R_\oplus}\right)^{2.06}M_\oplus$$

$$M_P = \left(\frac{162549\cdot10^3}{6370\cdot10^3}\right)^{2.06} \cdot 5,972\cdot10^{24}$$

$$M_P = 4,230\cdot10^{27} kg$$

$$M_P(M_J) = \frac{4,230\cdot10^{27}}{1,89\cdot10^{27}} = 2,48M_J$$

The problem with this formula is that it is imprecise and the result is not satisfactory as it is not within the range of the official finding which is M XO-6b = 1.9 ±0.5 MJ. Our result was 2.48 MJ (Masses of jupiter). Considering that our radius calculation already deviated a bit from the official one it is not a bad approximation but I would like to know if there is a more correct way to calculate the mass just knowing the radius and having the flux-time curve. With the mass we wanted to calculate other variables like the orbital period or the semi-major axis but the results deviated a lot.

• You are accepting answers to hastily. Give others a chance to add their own answers or indeed find the mistakes in mine. There's no rush. Feb 20 at 16:06
• @ProfRob Okay, thank you for the recommendation, I'm new here. Feb 20 at 16:07
• I don't know how you would want to derive the mass of the planet without the radial velocities of the star. And the paper you linked to clearly states that the radial velocities can not be reliably measured as the star rotates too fast for this (the spectral lines are too broad). They only can give an upper limit of $4.4 M_J$. The value of $1.9 M_J$ they mention is not much more than a guess. I also don't know why you need the mass of the planet for the orbital period or the semi-major axis. Both should only depend on the star's mass. Feb 20 at 16:32
• @WiseMode I have converted the inline image to MathJax. Please check that I have done so correctly and consider using MathJax in the future. Feb 20 at 16:41