<p>You don't need to collect data for one cycle in order to determine the period.</p>

<p>From Newtonian's physics, we know precisely how a trajectory of one particle orbitting around another one would be. Since the instantaneous velocity (v_inst) at any point on the trajectory is tangential to the point on the trajectory, we can decompose the v_inst into the radial velocity which we can match with the observation from, e.g., redshift. With assumption of constant v_inst and trajectory, we can determine the period from just a couple of observations (depending on how accurate the redshift can be measured, and the number of variables in the equation).</p>

CC BY-SA 4.0
2018-12-09T08:45:16.590Z
You need more than 2 measurements to estimate the parameters of an elliptical orbit.
ProfRob
CC BY-SA 4.0
2018-12-09T15:17:41.773Z
@RobJeffries How many measurements are required to extrapolate the parameters of an elliptical orbit?
BenjaminF
CC BY-SA 4.0
2019-02-12T16:58:03.077Z
I would say, as with any data, that the uncertainty decreases with more measurement. In this case it seems to me that we are reconstructing a sinusoidal curve.
Jack R. Woods
CC BY-SA 4.0
2018-12-08T17:18:44.550Z
2018-12-08T17:18:44.550Z
Kornpob Bhirombhakdi
<p>The radial velocity technique has apparently been used to discover exoplanets with extremely long orbital periods of ~10,000 days. For example, see this link:</p>

<p><a href="https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&amp;config=planets" rel="noreferrer">https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&amp;config=planets</a></p>

<p>If the period of a planet is ~10,000 days, then the period of the star must be the same. However, this would mean that observations would need to be made over ~30 years to get a complete picture of the radial velocity variation of the star, a time which is far too long. How then are radial velocity measurements used to discover such planets?</p>

<observational-astronomy><exoplanet><doppler-effect><radial-velocity>
How are exoplanets with 10,000 day periods discovered with the radial velocity method?
user4437416
# How are exoplanets with 10,000 day periods discovered with the radial velocity method?

(Asked by: username_0 on 2018-12-08)

The radial velocity technique has apparently been used to discover exoplanets with extremely long orbital periods of ~10,000 days. For example, see this link:

<https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=planets>

If the period of a planet is ~10,000 days, then the period of the star must be the same. However, this would mean that observations would need to be made over ~30 years to get a complete picture of the radial velocity variation of the star, a time which is far too long. How then are radial velocity measurements used to discover such planets?

**Tags:** observational-astronomy, exoplanet, doppler-effect, radial-velocity

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## 1 answers

### Answer by username_1 on 2018-12-08. Score: 1 | Accepted answer

You don't need to collect data for one cycle in order to determine the period.

From Newtonian's physics, we know precisely how a trajectory of one particle orbitting around another one would be. Since the instantaneous velocity (v\_inst) at any point on the trajectory is tangential to the point on the trajectory, we can decompose the v\_inst into the radial velocity which we can match with the observation from, e.g., redshift. With assumption of constant v\_inst and trajectory, we can determine the period from just a couple of observations (depending on how accurate the redshift can be measured, and the number of variables in the equation).

> **Comments:**
> **username_2**: You need more than 2 measurements to estimate the parameters of an elliptical orbit.  
> **username_3**: @RobJeffries How many measurements are required to extrapolate the parameters of an elliptical orbit?  
> **username_4**: I would say, as with any data, that the uncertainty decreases with more measurement. In this case it seems to me that we are reconstructing a sinusoidal curve.  

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