How did Hubble determine the universe was expanding?

Answer 1

The basic idea is that the farther away a galaxy is from us, the faster it moves away from us. You can get a rough comparison of distances to galaxies from their brightness and apparent diameter; and you can measure the speed by which they move away from us using the Doppler effect.

The above is the standard talk. Following is the non-standard talk. It is easier to see larger things, especially in the distance. So, the larger stars are seen in the distance (maybe). In any event, light leaving a star may be likened to mass leaving the Earth. That is, the higher (further away from the star or from the Earth) an "object" goes, the more kinetic energy it loses to gravitational potential energy. When the "object" is light, it does not slow down. Nevertheless, it loses energy -- it reddens. So star light from far-away stars is reddened because it moves against the gravitational potential of the star. Nearer, stars have less reddening (less climbing out of a gravitational well). Note, speed is not mentioned! If the star were not moving relative to our Sun or if the star were moving away from our Sun -- in both conditions -- you would see a red shift. Hmm, more work has to be done. But you can easily see the problem of blindly believing Hubble, for there are two reasons that could explain redness.

Answer 2

Hubble did not determine that the universe is expanding.

Hubble determined that the light of all distant galaxies is red-shifted, and
the farther they are from us, the more red-shifted their light is.

The simplest explanation for this fact is that the distant galaxies are moving away from us,
and the farther from us they already are, the faster they're moving away.

And the most widely accepted explanation for THAT is that the universe is expanding.