Which equation (s) are used to detect the presence of dark matter in galaxies? A) Doppler shift equation B) Kepler's 3rd Law C) Wien's Law D) A and B

Answer: D) A and B (Doppler shift equation and Kepler's 3rd Law)

Explanation:

According to Kepler's 3rd Law of Planetary motion "The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit".

So, this law establishes a relation between the orbital period of a body orbiting a greater body in space with the size of its orbit. This leads to the fact that a small body can be caught by the gravitational attraction of a massive body and the time it takes to the smaller body to orbit the massive body is proportional to the size of its orbit.

On the other hand, the Doppler shift equation is related to the Doppler effect and refers to the change in a wave perceived frequency (or wavelength=color) when the emitter of the waves, and the observer move relative to each other. From there, it is deduced that the farther the galaxy is, the more redshifted it is in its spectrum proving the expansion of the universe.

Now, this equation can be applied in order to analyze the velocity of the stars within a galaxy (as Vera Rubin did), and then galaxy rotation curves can be obtained. However, in this type of diagram it is observed a characteristic behavior in the rotation speed of the stars within the galaxies, which differs from the rules of the orbital movement postulated by Kepler.

This means that in these galaxy rotation curves it has been observed that the rotation speed of stars is "constant", regardless of the distance to the center of the galaxy. This discrepancy is used to detect the existence of dark matter in galaxies and the universe.