Free telescopes? Yes
Hi! Knowledge is power so I want to share with you a lot of it: ( http://users.gloria-project.eu/#/welcome )
This is a Spanish project at IAC (Astrophysics institute of Canary Islands) that let users work with a pretty good telescope freely. I am not going to lie, it is hard to make it work, last summer from the 300 nights I reserved the telescope (you have to go very fast when they open new slots, come one, come one, reserve), I just observed well in 56.
In that 56 I did the light curve of the asteroid 1992MC (cool name!). Basically The light curve let us calculate the rotational period of an asteroid, its composition (this is what I am trying to research now) and its shape. Here a better explanation (http://spaceguard.iasf-roma.inaf.it/NScience/neo/neo-how/mea-lightc.htm).
I recommed also the free software FotoDiff to create the graph at the top from stil images taken with the telescope!