<p>To use the Doppler shift, you need to know by how much the light is blue/red-shifted. </p>

<p>Suppose you have a light curve where the wavelength varies between <span class="math-container">$\lambda_1$</span> and <span class="math-container">$\lambda_2$</span>. Using these wavelengths, the Doppler shift will give you an interval of radial velocities. This gives you a value for <code>K</code> that you can plug into your last equation to derive <span class="math-container">$M_p$</span>. </p>

CC BY-SA 4.0
2020-02-25T13:59:26.453Z
2020-02-25T13:59:26.453Z
usernumber
<p>An astronomer, T observed the spectrum of a distant star X. The spectral lines were observed to have tiny blueshifts and redshifts regularly with a period of 1.27 years. T concluded that the star is wobbling slightly due to a planet orbiting it. Let the estimated mass of the planet when                                                     </p>

<p>(a) eccentricity of the orbit e = 0 be k*10^23 kg<br>
(b) and for e = 0.6 be x*10^22 kg.<br>
Assume that there is only one major planet and the axis of rotation of the system is perpendicular to the line of sight.</p>

<p>Mass of Star = 23.86163 x 10^30 kg 
Time Period = 463.55 days 
Shift in wavelength = 1.7627 x 10^-5 nm</p>

<p>You have to find out 'k' and 'x'                       </p>

<p>I studied about the Doppler Spectroscopy method.
I know that the relation
<span class="math-container">$$
K = \left(\dfrac{2\pi G}{P_{orb}}\right) ^{1/3}\dfrac{M_p}{(M_{*}+M_p)^{2/3}}\dfrac{1}{\sqrt{1-e^2}}
$$</span>
holds where K = radial velocity half amplitude.
How can I use the doppler shift given into this?
Thanks.</p>

CC BY-SA 4.0
2019-01-05T19:49:43.080Z
Why do you think that the shift goes into that relation?
Alchimista
<exoplanet><mass><spectroscopy><doppler-effect><radial-velocity>
Doppler Spectroscopy - Finding mass of an exoplanet
Kunal Gupta
# Doppler Spectroscopy - Finding mass of an exoplanet

(Asked by: username_0 on 2019-01-05)

An astronomer, T observed the spectrum of a distant star X. The spectral lines were observed to have tiny blueshifts and redshifts regularly with a period of 1.27 years. T concluded that the star is wobbling slightly due to a planet orbiting it. Let the estimated mass of the planet when

(a) eccentricity of the orbit e = 0 be k\*10^23 kg  
(b) and for e = 0.6 be x\*10^22 kg.  
Assume that there is only one major planet and the axis of rotation of the system is perpendicular to the line of sight.

Mass of Star = 23.86163 x 10^30 kg
Time Period = 463.55 days
Shift in wavelength = 1.7627 x 10^-5 nm

You have to find out 'k' and 'x'

I studied about the Doppler Spectroscopy method.
I know that the relation
$$
K = \left(\dfrac{2\pi G}{P\_{orb}}\right) ^{1/3}\dfrac{M\_p}{(M\_{\*}+M\_p)^{2/3}}\dfrac{1}{\sqrt{1-e^2}}
$$
holds where K = radial velocity half amplitude.
How can I use the doppler shift given into this?
Thanks.

**Tags:** exoplanet, mass, spectroscopy, doppler-effect, radial-velocity
> **Comments:**
> **username_1**: Why do you think that the shift goes into that relation?  

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## 1 answers

### Answer by username_2 on 2020-02-25. Score: 1

To use the Doppler shift, you need to know by how much the light is blue/red-shifted.

Suppose you have a light curve where the wavelength varies between $\lambda\_1$ and $\lambda\_2$. Using these wavelengths, the Doppler shift will give you an interval of radial velocities. This gives you a value for `K` that you can plug into your last equation to derive $M\_p$.


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