How is an object's size determined from other solar systems than our own? How are new large bodies being found in our solar system currently?
One method of finding planets orbiting stars is to analyze the transit effect. This is when a planet crosses the face of a star between the star and observer. This will block some of the light reaching the observer. By measuring this decrease in light from the star we can determine how much of the surface area of star is occluded.
The speed of a planet across the face of a star will let us calculate the orbital radius considering a circular orbit. The temperature of the star can be determined from its brightness and location on HR diagram and spectroscopic data. Combining this information lets us determine the size and of the planet.
Using space-based or ground-based telescopes and automated data collection and analysis methods large regions of the sky can be viewed for these transits. This method is highly accurate and will probably surpass the radial velocity method as most common method to discover new planets.
Another method for finding planets is known as the radial velocity method. When a planet orbits a star it is really the planet and star rotating about the center-of-mass of the system. Hence the star wobbles due to the bodies orbiting the star. It wobbles because usually the center-of-mass is inside the star and this results in the star rotating about an axis running thru the star but offset from the center. By doing a doppler analysis it can be determined whether the star is revolving or not and the period of revolution. The radial velocity method is the most effective method. The transit method is very limited by the viewing angle, the planet must pass between observer and star.
A good source to better learn about these methods is here.
The size of a planet is determined by
- The amount of gas & dust available to build it.
- The type of star it orbits.
- Its distance from the star.
- Whether or not the sort of resonances we see in Bode's Law come into play. We don't know for sure whether Bode's Law operates for all stars, some stars, or only our star.