# How is exoplanet mass found by astrometry?

1. Feb 23, 2005

### physkid

Questions in the title. Any help is appreciated :)

2. Feb 23, 2005

### marcus

how much do you know already?

do you understand how the mass of the star is told by its spectrum (the H-R diagram)?

if you know the mass of the star then a lower bound on the mass of the planet can be deduced by how much the star is made to wobble by the planet

how much of this do you know, or have already thought through?

3. Feb 23, 2005

### physkid

Ahh right i get it. Knowing star mass gives you planet radius from keplers third and then elliptic orbits with reduced mass formula should give an estimate of planet mass? is that correct?

4. Feb 23, 2005

### marcus

i dont want to tell you what you already know

suppose you observe a main sequence star and you tell by its color that it is the same mass as the sun

and you see a doppler shift that tells you that the star is going away from you for 6 months and coming at you for six months----it is wobbling slightly on a one year cycle.

then you know by Kepler that it has a planet that is 1AU away from it.

and if the dopplershift record looks sinusoidal you know the orbit is roughly circular (this is a detail)

and you know by Kepler that the planet speed is 30 km/second

now from the size of the dopplershift you deduce the wobble speed of the star------say that it is at least 30 meters per second

THE RATIO OF THE SPEEDS IS at most 1000 THEREFORE the ratio of the masses is at most 1000
this sais that the mass of the planet is at least 1/1000 of the mass of the star

maybe you already thought thru that and your question means that you are digging deeper for some further refinement or alternative, please
elaborate

5. Feb 23, 2005

### physkid

I know how they get the mass from radial velocity measurements but astrometry is supposed to be more accurate as the orbital inclination is not a prevailant factor.

I was just not sure how they actually get the mass. I mean do they measure the amplitude of the wobble and determine a orbital radius for the star in which case it would be easy to gain a planetary mass from a two body elliptical orbit model, or is it done some other way?

6. Feb 23, 2005

### marcus

the reason for the inequality instead of simple equality is that the orbit plane may be tilted to our line of sight
so the to and fro speed of the star may be greater than what we measure by doppler (in which case the planet is more massive than we calculate using the doppler speed)

[edit: I wrote this before I saw your answer. obviously you do not need so much explanation]

BTW, I see you are new to PF, welcome. Probably your questions and other posts will be an asset to the board (judging from this one case)

Last edited: Feb 23, 2005
7. Feb 23, 2005

### marcus

Ah! good for you physkid. you really mean astrometry!

yes, with accurate astrometry one can see the star wobble back and forth in the sky, so one can do the same kind of analysis

and also I guess you can combine doppler with this

You ask how is the mass of the star determined.
Unless the star belongs to a binary system I think the usual way is using the main sequence-----basically by looking at the spectrum (more massive stars are hotter)

Now I do not understand your problem. If one sees a star making a little circle or oval in the sky, and one knows its mass, then is it not easy to use Kepler laws and deduce the orbit and mass of the planet?

8. Feb 23, 2005

### physkid

could you just substitute reduced mass in instead of using the star mass as in the doppler case?

9. Feb 23, 2005

### marcus

physkid, I hope you get some other people to answer
there are a bunch here
me, I dont care if you use the combined mass of star and planet, or if you use the star mass alone----the estimates of star mass are themselves so uncertain and the planet mass (if it is only around 1/1000 of primary as in Jupiter case) is sotospeak in the noise.
I hope you start other questionthreads and get chronos phobos labguy garth turbo nereid (I am forgetting some) selfadjoint ohwilleke and others to answer.
I guess I will sign off and hope someone else can supply details about deducing exoplanet specs.

Last edited: Feb 24, 2005
10. Feb 23, 2005

### Chronos

There are a number of approaches currently in use in detecting extrasolar planets. The field has become quite interesting in recent years. Try here for an overview:
http://cfa-www.harvard.edu/planets/searches.html [Broken]

Last edited by a moderator: May 1, 2017
11. Feb 23, 2005

### Labguy

There is astrometry mentioned and the "easy" cases where the planets happen to transit the star or protostar. The doppler measure is limited and can only give the lower limit of a planets mass even if the star's mass is easily determined. From: http://sse.jpl.nasa.gov/news/display.cfm?News_ID=9416 [Broken]

Last edited by a moderator: May 1, 2017