How to determine the amplitude of RV curve $$K_1$$ for eccentric orbit when the anomaly is not known, please? Thank you very much

enter image description here


I thought that |RV_min-RV_max|/2 holds for circular orbits $e = 0$.

I saw the following relations for $K_1$ and $K_2$ in the case of a triple star where the outer system has an eccentric orbit:

$$K_1 = \frac{\sqrt[3]{\frac{(M_1+M_2) \sin^3 (i)}{1.036149\cdot 10^{-7} P(1-e^2)^{3/2}}}}{1+\frac{M_1}{M_2}}$$

$$K_2 = K_1 \frac{M_1}{M_2}$$

I was searching for the original source and maybe found this (page 5), but I do not understand the meaning of $M_{1,2}$ and $K_{2,1}$. Are these two equations? Does the first have $M_1$, $K_2$ and does the second use $M_2$ and $K_1$?

enter image description here

$$v_k = \frac{G(M_1+M_2+M_3)}{a_2}$$

$$v_{12}=\frac{v_k M_3}{M_1+M_2+M_3}$$

$$K_{12} = v_{12} \sin(i_2)$$ $$K_{3} = v_{3} \sin(i_2)$$

Here I am not sure for what $v_k, v_{12}$, and $K_{12}$ stands.


1 Answer 1


$K_1$ is the semi-amplitude - half the difference between the maximum and minimum. For the curve you show, that is about 5 km/s.

In response to the additional questions:

When an equation is presented as $$ a_{1,2} = f(x_{2,1})$$ it means there are actually two equations: $a_1 = f(x_2)$ and $a_2 = f(x_1)$.

In the second piece of maths that you have written down, I would assume that $K_{12}$ and $v_{12}$ should actually be $K_{1,2}$ and $v_{1,2}$.

What is $v_k$? Well the equation you have written defines what $v_k$ is. It look like it is the speed of the secondary component around the centre of mass, but that depends on what $a_2$ means.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .