There are a few different ways that astronomers can work out the size of a solar system. One method is to use the transit method. This method involves observing a star as a planet passes in front of it, causing a slight dimming of the star's light. By measuring the amount of time it takes for the planet to transit the star, and knowing the distance to the star, astronomers can calculate the planet's size.

Another method for determining the size of a solar system is to use the radial velocity method. This method involves measuring the slight changes in a star's radial velocity (the speed at which the star is moving towards or away from Earth) as a planet orbits it. By measuring these changes in velocity, and knowing the mass of the star, astronomers can calculate the mass of the planet. From the planet's mass and radius, astronomers can then determine its size.

Finally, astronomers can also use the astrometric method to determine the size of a solar system. This method involves measuring the slight changes in a star's position as a planet orbits it. By measuring these changes in position, and knowing the distance to the star, astronomers can calculate the planet's distance from the star. From the planet's distance from the star and its mass, astronomers can then determine its size.

By using a combination of these methods, astronomers can determine the size of solar systems with a high degree of accuracy. This information is important for understanding the formation and evolution of solar systems, and for comparing them to other solar systems in the universe.