Which mathematical formulas are used in the search for extraterrestrial planets?

[Gliese123]

Hello there!
I'm currently working on an essay regarding astrophysics. The level of this essay is of high school standards but I do like math and physics so advanced calculations doesn't frighten me.

Anyway so the essay's is about the astrophysics behind our search for extraterrestrial planets and I'm keen to conclude this. However, I seem to get stuck at the math part since I don't know what kind of formulas I should use for this. For instance the transit method or the Doppler method and more. To get this essay as complete as possible, I would like to demonstrate my own examples in this by having mathematical formulas and calculations for my "own solar system"

Are there any persons here who are familiar with the very physics behind extraterrestrial methods? Not the literal part but the mathematical part. If you know any about anything then you're the best!

 

[mfb]

You might be interested in the Kepler laws and the Doppler effect.
Transits are simple geometry - if the luminosity of the star goes down by 0.01%, the planetary disk has 0.01% of the star's visible area, which corresponds to 1% of its radius, for example.

 

[Gliese123]

You might be interested in the Kepler laws and the Doppler effect.
Transits are simple geometry - if the luminosity of the star goes down by 0.01%, the planetary disk has 0.01% of the star's visible area, which corresponds to 1% of its radius, for example.

Thank you! Well I've looked over the Kepler laws a bit.. But it seems to be many ways of finding planets.

 

[mfb]

There are many ways, but most of them measure the orbital period in some way and calculate the orbital radius based on the period and the estimated stellar mass.
Astrometry (not successful yet, but Gaia should change this), direct imaging (rare) and microlensing (rare) are the only examples, I think. They can get a direct measurement related to the distance.

 

[bossman27]

If you want to get a bit more technical, read up on single-lined spectroscopic binaries. Incase you aren't already aware, single lined just means that only one object in the system is visible to us (as opposed to double lined, where we can see two distinct spectra). Of course, as mfb has already alluded to, it is usually the case that a star-planet system is a single-lined spectroscopic binary.

Here is a link to some excellent material from J. B. Tatum's Celestial Mechanics notes: http://www.astro.uvic.ca/~tatum/celmechs.html
Double and single lined spectroscopic binary systems are covered in chapter 18, though chapter 17 on visual binary stars introduces the important orbital elements as they pertain to binaries.

Of particular interest for star-planet(s) systems is the mass function when M>>m. (see section 18.4) It is also well worth mentioning, however, that Tatum is largely skeptical of concluding that the unseen object is a planet without additional supporting evidence. His reasons for this stance are particularly interesting and noteworthy, especially if you're writing a paper on methods used in planetary searches.

 

[Gliese123]

If you want to get a bit more technical, read up on single-lined spectroscopic binaries. Incase you aren't already aware, single lined just means that only one object in the system is visible to us (as opposed to double lined, where we can see two distinct spectra). Of course, as mfb has already alluded to, it is usually the case that a star-planet system is a single-lined spectroscopic binary.

Here is a link to some excellent material from J. B. Tatum's Celestial Mechanics notes: http://www.astro.uvic.ca/~tatum/celmechs.html
Double and single lined spectroscopic binary systems are covered in chapter 18, though chapter 17 on visual binary stars introduces the important orbital elements as they pertain to binaries.

Of particular interest for star-planet(s) systems is the mass function when M>>m. (see section 18.4) It is also well worth mentioning, however, that Tatum is largely skeptical of concluding that the unseen object is a planet without additional supporting evidence. His reasons for this stance are particularly interesting and noteworthy, especially if you're writing a paper on methods used in planetary searches.

Great facts and Great link! Thanks a lot :D