Cheap camera for night shots?

So I really like taking photos and I especially like shots at night (the stars and sky specifically), I have a budget of $300 currently, and I'm stuck with an iPhone 5. I'm a high school student and my parents won't allow me to get a job because of school. Christmas is relatively soon so my budget might boost up around $100-$150, but otherwise I'm suck. I originally planed to get a gopro Hero 3 black, but the night shots are not great on that. I doubt that this product exists, but I really need a camera that can shoot night shots AND preferably is able to do star trails and timelapses, It needs to be fairly cheap, $500 and below. Is there any camera that suits these requirements? Thank ya!

Added (1). 1) I own a tripod already
2) I know several people who do professional photography, I'm taking a photography class in school, and I have done plenty of research online from blogs and other free sources

First, what do you know about night photography?

Second, you don't enough money for a controllable camera to do night shooting. Best cameras for night long (time) exposures are dslr cameras starting at about $500… These aren't cheap.

Your next best bet is a bridge camera at probably $300.

Then there's the tripod, thought of that?

Then some education in how to do night photography… What about that?

None of this stuff is "cheap".

You know I like contributor Jim A. Very much but he and others don't believe you can take a good picture unless you have a $500-$600 DSLR. Well I'm here to tell you there are lots of cameras that can fill your bill.
I would suggest the Canon Powershot SX series cameras. The current model is the Canon Powershot SX50 IS. You might check Canon's website to see if it has all the features your are looking for. THEN you might do as I did. I tried the SX50 IS and found it hard to hold steady with the zoom lens racked out all the way. So I found an earlier model where the lens was not nearly as long, that was refurbished at about half the price, which fit my budget fine for this purchase.
I also like the Fuji SL300 that sells at about $200.00 NEW!
Even though these cameras are called "bridge" cameras they perform very well, especially with the resolution set to maximum pixels. When you get your new camera be sure to make a11x14 print of one of your first shots and I'm sure you will be pleased. 4x6 prints won't tell you a thing as to the quality of the camera.