<p>All of the orbital elements can be derived by direct imaging, so long as you observe long enough to see a fair fraction of the orbit.</p>

<p>Kepler's third law then gives the total mass of the system and the relative orbits may give the mass ratio and hence individual masses (though this would be quite uncertain if the mass ratio was large).</p>

<p>Absolute masses could also come from dynamical measurements (i.e. velocities), but you can get these if the system is at a known distance. Again, because the star wouldn't move very much, this would likely lead to a highly uncertain planetary mass.</p>

<p>The planet mass might instead be estimated from its luminosity, an estimate of its age, and a cooling model. The radius can be estimated from its temperature and luminosity.</p>

CC BY-SA 4.0
2020-01-04T22:23:16.087Z
Yeah I mean only with direct imaging, not using radial velocities nor astrometry or spectroscopy
Carlos Vázquez Monzón
CC BY-SA 4.0
2020-01-05T00:07:43.983Z
@antispinwards True. Though the degeneracy would not affect any mass estimate.
ProfRob
CC BY-SA 4.0
2020-01-05T09:20:46.373Z
@uhoh that we're talking about exoplanets?
ProfRob
CC BY-SA 4.0
2020-01-05T11:47:06.773Z
Ah! yes that's what I missed.
uhoh
CC BY-SA 4.0
2020-01-05T16:12:16.670Z
Could you please specify how do you estimate the radius of a planet from its temperature and luminosity?
Carlos Vázquez Monzón
CC BY-SA 4.0
2020-01-05T16:48:07.480Z
@CarlosVázquezMonzón $L \simeq 4\pi R^2 \sigma T^4$
ProfRob
CC BY-SA 4.0
2020-01-06T00:25:14.097Z
Does the same formula for stars also holds for reflected light then?
Carlos Vázquez Monzón
CC BY-SA 4.0
2020-01-06T08:04:08.447Z
@CarlosVázquezMonzón directly imaged planets are not seen in scattered light. At least, not currently.
ProfRob
CC BY-SA 4.0
2020-01-04T21:23:10.240Z
2020-01-04T21:23:10.240Z
ProfRob
<p>I wonder which orbital elements of a exoplanet can be found <strong>only</strong> applying direct imaging. I know that the angular separation combined with parallax can give us the semi-major axis, but what about the other elements? Is it possible? And what about the mass or the radius of the planet (given known mass and radius of the star)?</p>

<exoplanet><orbital-elements>
Derivation of the orbital parameters of a exoplanet discovered by direct imaging
Carlos Vázquez Monzón
# Derivation of the orbital parameters of a exoplanet discovered by direct imaging

(Asked by: username_0 on 2020-01-04)

I wonder which orbital elements of a exoplanet can be found **only** applying direct imaging. I know that the angular separation combined with parallax can give us the semi-major axis, but what about the other elements? Is it possible? And what about the mass or the radius of the planet (given known mass and radius of the star)?

**Tags:** exoplanet, orbital-elements

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## 1 answers

### Answer by username_1 on 2020-01-04. Score: 3 | Accepted answer

All of the orbital elements can be derived by direct imaging, so long as you observe long enough to see a fair fraction of the orbit.

Kepler's third law then gives the total mass of the system and the relative orbits may give the mass ratio and hence individual masses (though this would be quite uncertain if the mass ratio was large).

Absolute masses could also come from dynamical measurements (i.e. velocities), but you can get these if the system is at a known distance. Again, because the star wouldn't move very much, this would likely lead to a highly uncertain planetary mass.

The planet mass might instead be estimated from its luminosity, an estimate of its age, and a cooling model. The radius can be estimated from its temperature and luminosity.

> **Comments:**
> **username_0**: Yeah I mean only with direct imaging, not using radial velocities nor astrometry or spectroscopy  
> **username_1**: @antispinwards True. Though the degeneracy would not affect any mass estimate.  
> **username_1**: @uhoh that we're talking about exoplanets?  
> **username_2**: Ah! yes that's what I missed.  
> **username_0**: Could you please specify how do you estimate the radius of a planet from its temperature and luminosity?  
> **username_1**: @CarlosVázquezMonzón $L \simeq 4\pi R^2 \sigma T^4$  
> **username_0**: Does the same formula for stars also holds for reflected light then?  
> **username_1**: @CarlosVázquezMonzón directly imaged planets are not seen in scattered light. At least, not currently.  

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