Why do disk stars bob up and down as they orbit the galaxy?

When the stars get a little bit farther from the disk, the other stars that are still in the disk will pull them toward it as a consequence of the gravity between them.

Explanation:

Galaxies have different structures due to parameters as the orbit of the stars around the center of the galaxy or the metallicity¹ of the stars (which serves to find the age of the stars). For example, in the case of the Milky Way, it has:

The Halo

The Bulge

The Thick Disk

The Thin Disk

The Halo has old stars with low metallicities and random orbits, while the bulge has stars with the same random motions like the one in the Halo.

The Thick Disk has stars with orbits oriented in the same direction but with  metallicities a little bit higher than the one from the Halo but lower than the stars in the Thin Disk.

The stars that are in the thin disk have orbits oriented in the same direction and are the ones with the higher metallicity levels, which means that they are the most younger in the galaxy.

In general the stars in the disk of the galaxy (thick disk and thin disk) goes up and down as they orbit the center of the galaxy, the reason for this is that when they get a little bit farther from the disk, the stars that are still in the disk pull them back toward it as a consequence of the gravity between them.

Remember the equation of the Universal gravitation law:

 (1)

Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of two objects and R is the distance between them.

Notice how equation 1 expresses that the force of gravity is inversely proportional to the square of the distance between the two objects, which means that the force of gravity will decrease as the square of the distance increase.

Key terms:

¹Metallicity: the abundance of heavier elements against the presence of Helium or Hydrogen.

b.

explanation:

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