Final answer:
Astronomers determine the size of an asteroid without resolving it by measuring its distance from Earth, analyzing its rotation period, and observing its brightness using a known reflectivity.
Step-by-step explanation:
There are several indirect ways astronomers determine the size of an asteroid without resolving it. One way is by measuring the asteroid's distance from Earth. By using trigonometry and the parallax effect, astronomers can calculate the distance to the asteroid and then estimate its size. Another way is by analyzing the asteroid's rotation period. By observing changes in the asteroid's brightness over time, astronomers can determine how long it takes for the asteroid to complete one rotation, which provides information about its size. Additionally, astronomers can observe the asteroid's brightness and use a known reflectivity to estimate its size. By measuring the amount of light reflected by the asteroid, they can calculate its size based on its reflectivity.