Detecting Multiple Planets Around a Star

[cepheid]

In the Doppler shift or radial velocity method for detecting exoplanets, it is assumed that the orbital period of the star's planetary companion is equal to the period of the star's detected wobble. I'm assuming that this fact comes straight from the solution to the two-body problem.

My question is, what if a star has multiple planets in orbit around it? Say, for example, we were viewing our solar system from afar. Would we be able to detect anything other than Jupiter? I guess this is an n-body problem, although it seems that the typical thing to do is to assume that the interaction between each planet and the parent star is much greater than the interactions among planets, which can be ignored. So, I guess that this is like 8 independent two-body problems, each of which gives a solution that is a good (zeroth-order? first-order?) solution for that planet's orbit.

What's confusing me is that the solution to each two-body problem would have you believe that the parent star wobbles with a period equal to the orbital period of the second object. So, how could the sun wobble "around" the barycentre on 8 different timescales? What does the wobble look like if there are multiple planets, and how are we supposed to know that they are there?

 

[Nik_2213]

IIRC, the way it is done is to look for 'residuals': The Doppler wobble from the first planetary candidate gives an approximate orbit. Further observations improve the estimate. Later observations show that the first planet is running a bit faster then a bit slower than its predicted motion. Back-calculating these 'residuals' give an estimate for a second planet. Further measurements improve the estimate until new, cyclic 'residuals' appear...

 

[Nabeshin]

Looks something like this:
http://innumerableworlds.files.wordpress.com/2009/04/sunwobble.jpg?w=460&h=431

 

[cepheid]

Interesting! Thanks Nik_2213 and Nabesin for the verbal and visual help, respectively.

 

[pmacias]

I can provide some clarification on this topic. First, it is important to note that the Doppler shift or radial velocity method is just one of several techniques used to detect exoplanets. Other methods include the transit method, direct imaging, and gravitational microlensing.

In the Doppler shift method, the assumption that the orbital period of the star's planetary companion is equal to the period of the star's detected wobble is based on the two-body problem solution. This is a simplified assumption and may not accurately represent the complex dynamics of a multi-planet system.

In reality, a star with multiple planets will exhibit a more complex wobble pattern, with each planet contributing to the overall motion of the star. This can make it more challenging to accurately detect and characterize each individual planet.

However, with advanced techniques and technology, it is possible to detect multiple planets around a star. For example, the use of high-resolution spectroscopy can help distinguish between the different signals from each planet and provide more detailed information about their orbits.

Additionally, the presence of multiple planets can also affect each other's orbits, causing slight variations in their respective periods and wobble patterns. These effects, known as transit timing variations and radial velocity variations, can provide clues to the presence of multiple planets in a system.

In summary, while the Doppler shift method may make simplified assumptions about the dynamics of a multi-planet system, there are other techniques and advanced technologies that can help detect and characterize these systems. It is an ongoing and exciting area of research in the field of exoplanet detection and study.