<p><span class="math-container">$K_1$</span> is the semi-amplitude - half the difference between the maximum and minimum. For the curve you show, that is about 5 km/s.</p>
<p>In response to the additional questions:</p>
<p>When an equation is presented as
<span class="math-container">$$ a_{1,2} = f(x_{2,1})$$</span>
it means there are actually two equations:
<span class="math-container">$a_1 = f(x_2)$</span> and <span class="math-container">$a_2 = f(x_1)$</span>.</p>
<p>In the second piece of maths that <em>you</em> have written down, I would assume that <span class="math-container">$K_{12}$</span> and <span class="math-container">$v_{12}$</span> should actually be <span class="math-container">$K_{1,2}$</span> and <span class="math-container">$v_{1,2}$</span>.</p>
<p>What is <span class="math-container">$v_k$</span>? Well the equation you have written defines what <span class="math-container">$v_k$</span> is. It look like it is the speed of the secondary component around the centre of mass, but that depends on what <span class="math-container">$a_2$</span> means.</p>

CC BY-SA 4.0
2022-10-20T08:04:31.107Z
2022-10-21T10:43:37.087Z
2022-10-21T10:43:37.087Z
ProfRob
<p>How to determine the amplitude of RV curve <span class="math-container">$$K_1$$</span> for eccentric orbit when the anomaly is not known, please? Thank you very much</p>
<p><a href="https://i.sstatic.net/EFUHH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EFUHH.png" alt="enter image description here" /></a></p>
<p><strong>Edit:</strong></p>
<p>I thought that |RV_min-RV_max|/2 holds for circular orbits <span class="math-container">$e = 0$</span>.</p>
<p>I saw the following relations for <span class="math-container">$K_1$</span> and <span class="math-container">$K_2$</span> in the case of a triple star where the outer system has an eccentric orbit:</p>
<p><span class="math-container">$$K_1 = \frac{\sqrt[3]{\frac{(M_1+M_2) \sin^3 (i)}{1.036149\cdot 10^{-7} P(1-e^2)^{3/2}}}}{1+\frac{M_1}{M_2}}$$</span></p>
<p><span class="math-container">$$K_2 = K_1 \frac{M_1}{M_2}$$</span></p>
<p>I was searching for the original source and maybe found <a href="https://arxiv.org/pdf/0908.2624.pdf" rel="nofollow noreferrer">this (page 5)</a>, but I do not understand the meaning of <span class="math-container">$M_{1,2}$</span> and <span class="math-container">$K_{2,1}$</span>. Are these two equations? Does the first have <span class="math-container">$M_1$</span>, <span class="math-container">$K_2$</span>  and does the second use <span class="math-container">$M_2$</span> and <span class="math-container">$K_1$</span>?</p>
<p><a href="https://i.sstatic.net/38qsG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/38qsG.png" alt="enter image description here" /></a></p>
<p><span class="math-container">$$v_k = \frac{G(M_1+M_2+M_3)}{a_2}$$</span></p>
<p><span class="math-container">$$v_{12}=\frac{v_k M_3}{M_1+M_2+M_3}$$</span></p>
<p><span class="math-container">$$K_{12} = v_{12} \sin(i_2)$$</span>
<span class="math-container">$$K_{3} = v_{3} \sin(i_2)$$</span></p>
<p>Here I am not sure for what <span class="math-container">$v_k, v_{12}$</span>, and <span class="math-container">$K_{12}$</span> stands.</p>

<binary-star><radial-velocity>
How to determine the amplitude of RV curve for eccentric orbit?
Elena Greg
# How to determine the amplitude of RV curve for eccentric orbit?

(Asked by: username_0 on 2022-10-19)

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](https://i.sstatic.net/EFUHH.png)](https://i.sstatic.net/EFUHH.png)

**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)](https://arxiv.org/pdf/0908.2624.pdf), 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](https://i.sstatic.net/38qsG.png)](https://i.sstatic.net/38qsG.png)

$$v\_k = \frac{G(M\_1+M\_2+M\_3)}{a\_2}$$

$$v\_{12}=\frac{v\_k M\_3}{M\_1+M\_2+M\_3}$$

$$K\_{12} = v\_{12} \sin(i\_2)$$
$$K\_{3} = v\_{3} \sin(i\_2)$$

Here I am not sure for what $v\_k, v\_{12}$, and $K\_{12}$ stands.

**Tags:** binary-star, radial-velocity

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## 1 answers

### Answer by username_1 on 2022-10-20. Score: 4 | Accepted answer

$K\_1$ 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.


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