# How to determine the amplitude of RV curve for eccentric orbit?

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

Edit:

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 $$K_1$$?

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

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

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

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

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