Explain the astrometric method that astronomers use to search for other planetary systems that orbit a star.

Transit Method

Explanation:

Most of the planets revolving around the other stars are found using transit method. Since stars are very bright and bigger in comparison to any planet revolving around them. Observing them directly is not possible. In transit method astronomers look for opportunities when these planets transit across the stars as seen from Earth. Because of this transit the brightness of the star will appear to dip. With the help of the duration of the dip and frequency of the dip astronomers find out the size and orbital period of such planets.

Some of the exoplanets are found using wobble method and direct imaging as well.

0.11 m/s and 0.28 m/s should be correct