<p>So I've been given the velocity curve, parallax and apparent magnitude of a star in a binary system with what is potentially a black hole. I've calculated from the apparent magnitude and parallax that the star is a type F5V, which puts the mass at about 1.4 Solar Masses. The velocity curve has an inclination of 90, and oscillates back and forth between +/- 75km/s. There is no data on the companion of this star, just the fact that it <em>could</em> be a black hole. I'm supposed to estimate the mass by numerically approximating a polynomial.
So far I've used this equation</p>

<p><span class="math-container">$\frac{M^{3}}{(m+M)^{2}} = \frac{Pv^{2}}{2\pi G}$</span></p>

<p>where M is the mass of the thing I don't know, m is the mass of the known companion (1.4 solar masses) P is the period (5.59 days) and v is of course the velocity (75km/s)</p>

<p>I got lazy and wrote <span class="math-container">$\frac{Pv^{2}}{2\pi G}$</span> as <span class="math-container">$k$</span> and arrived at</p>

<p><span class="math-container">$M^{3} - kM^{2} - km^{2} = 0$</span></p>

<p>Using python's optimize library I found the mass of this unkown partner to be about 0.018 solar masses. My question here is where did I go wrong, and if I didn't go wrong anywhere is that a realistic mass for a super small black hole / other very small, dense and invisible object? </p>

CC BY-SA 4.0
2019-03-09T23:18:54.350Z
Yeah I'm sorry I meant 90 degrees, in that the radial velocity times the sine of the inclination can be ignored as it's 1. I'll make the edit in the original question.
TheNerdyCoder
CC BY-SA 4.0
2019-03-10T07:37:46.230Z
That final equation is also wrong. $(m+M)^2 \neq m^2 + M^2$
PM 2Ring
<black-hole><mass><binary-star><kepler>
Mass of a potential black hole in a binary system
TheNerdyCoder
# Mass of a potential black hole in a binary system

(Asked by: username_0 on 2019-03-09)

So I've been given the velocity curve, parallax and apparent magnitude of a star in a binary system with what is potentially a black hole. I've calculated from the apparent magnitude and parallax that the star is a type F5V, which puts the mass at about 1.4 Solar Masses. The velocity curve has an inclination of 90, and oscillates back and forth between +/- 75km/s. There is no data on the companion of this star, just the fact that it *could* be a black hole. I'm supposed to estimate the mass by numerically approximating a polynomial.
So far I've used this equation

$\frac{M^{3}}{(m+M)^{2}} = \frac{Pv^{2}}{2\pi G}$

where M is the mass of the thing I don't know, m is the mass of the known companion (1.4 solar masses) P is the period (5.59 days) and v is of course the velocity (75km/s)

I got lazy and wrote $\frac{Pv^{2}}{2\pi G}$ as $k$ and arrived at

$M^{3} - kM^{2} - km^{2} = 0$

Using python's optimize library I found the mass of this unkown partner to be about 0.018 solar masses. My question here is where did I go wrong, and if I didn't go wrong anywhere is that a realistic mass for a super small black hole / other very small, dense and invisible object?

**Tags:** black-hole, mass, binary-star, kepler

> **Comments:**
> **username_0**: Yeah I'm sorry I meant 90 degrees, in that the radial velocity times the sine of the inclination can be ignored as it's 1. I'll make the edit in the original question.  
> **username_1**: That final equation is also wrong. $(m+M)^2 \neq m^2 + M^2$  

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## 0 answers

