How would people prove that dark matter exists, and how would it change are understanding of the known universe.

Answer 1

In an active galaxy, where stars and dust are orbiting around a supermassive black hole of that galaxy, obeys the laws of centripetal, centrifugal and other circular mechanics. The velocity of a star close to black hole and velocity of the star at edge of the galaxy has a calculated proportion due to inverse square distance law. But the velocity of these edge stars are weird on every galaxy, where these kind of difference in velocity happens when there is an extra mass between supermassive black hole and the star. And also these mass effects the gravitational lensing being an extra mass in a galaxy.

By understanding these dark matter, we may unlock the mystery of universe and by understanding it's quantum states we can understand much about invisible forces and many more.

Hope that helps.