Determining the orbital radius of extrasolar planets

[aggieg]

Homework Statement

Basically I don't understand how you do this - the course I'm doing keeps mentioning the orbital radius of extrasolar planets but doesn't tell you HOW to find it?
Can anyone please help - in plain English, please, I'm not a natural scientist!

Homework Equations

The Attempt at a Solution

 

[Delphi51]

We have a formula relating the period of the orbit to its radius. It is easy to observe the period, so the radius can then be calculated. The longer answer is that the formula has the mass of the star in it and that mass is not easy to observe. I think some guessing is involved but I don't really know. Stars are very interesting and a lot is known about how they work, so perhaps there is a way to guess the mass fairly well from observations of the star's characteristics.

 

[aggieg]

We have a formula relating the period of the orbit to its radius. It is easy to observe the period, so the radius can then be calculated. The longer answer is that the formula has the mass of the star in it and that mass is not easy to observe. I think some guessing is involved but I don't really know. Stars are very interesting and a lot is known about how they work, so perhaps there is a way to guess the mass fairly well from observations of the star's characteristics.

Hi Delphi
Yes, it's actually the formula I'm trying to find
Best wishes
AggieG

 

[Delphi51]

There is a lovely way to find the satellite formula for circular motion. You begin by saying Fc = Fg
meaning that the centripetal force required to hold the planet in circular motion is provided by the gravitational force between planet and star. Then fill in the detailed formulas for Fg and Fc (choosing the one with the period T in it rather than the one with velocity).

 

[rwisz]

Determining the orbital radius of extrasolar planets is a complex process that involves multiple factors and techniques. In general terms, the orbital radius of a planet is the distance between the planet and its host star. This distance can vary greatly depending on the size and mass of the planet, as well as the characteristics of its host star.

To determine the orbital radius of an extrasolar planet, scientists use a variety of methods such as radial velocity, astrometry, and transit photometry. These techniques involve measuring the motion and position of the planet in relation to its host star and using mathematical equations to calculate the orbital radius.

One common method is the radial velocity method, which involves measuring the tiny wobbles in a star's motion caused by the gravitational pull of an orbiting planet. By analyzing these wobbles, scientists can calculate the orbital radius of the planet.

Another method is astrometry, which involves tracking the precise position of a star over time and using this data to determine the presence and characteristics of any orbiting planets.

The transit photometry method involves measuring the slight dip in a star's brightness as a planet passes in front of it. By analyzing the duration and frequency of these dips, scientists can calculate the orbital radius of the planet.

Overall, determining the orbital radius of extrasolar planets is a challenging but important task in the field of exoplanet research. It requires a combination of observational data, mathematical equations, and advanced techniques to accurately calculate this crucial parameter.