As mentioned above, this is the spaceship from Mystery Science Theater 3000. The Satellite of Love (called the SOL for short) physically was several different models.
KTMA: The SOL was a funky looking space station. Originally the SOL was built by Joel, but that was quickly changed very early into the season. The SOL was large, made up literally of things laying around, and had no distinct shape. In fact, while I'm not sure I believe that the SOL was only seen in the opening during the KTMA days.
Comedy Central years: The SOL was redesigned by Trace Beaulieu for the first seasons on Comedy Central (then the Comedy Channel) apparently for the sole reason of reusing the "Demon Dog" joke in episode 102. The model of the SOL was 4 feet long. The SOL looked like a big dog bone with various hexes and pents covering the balls on either end. One of these hexes was the launch bay for the Deus Ex Machina (which helped Joel Robinson escape back to Earth). There was a satellite dish (presumably to receive the video feed from Deep 13) on the top most part of the mid section, close to the top left circular dome. There was also a spherical ball on the mid section of the SOL. Also, on the front of the SOL in between the "balls" was a big Gizmonic G. This was removed from the model when Joel Hodgson left in 1993. This model was auctioned off by Best Brains in 1999 for around $5,000 and the winner not only displayed the SOL at (I believe) DukCon in 2001, but had it refurbished by Trace Beaulieu himself.
Note: I've always thought that the "front" of the SOL was the part where the Gizmonic G was, and that the top most part of this is where the bridge of the SOL was. The door sequence was in the middle of the ship, and the top most left ball was where the theater was located.
MST3K: The Movie: There were two models of the SOL made for the 1996 feature film. A four foot model and a whopping eight foot model used in the opening fly-by scenes. The movie models were extremely well detained with little things (mostly model parts, with small toys being used for the eight foot sucker) and really made the SOL look like a full blown space ship. The spherical ball was finally given a purpose (with the manipulator arms). The lower decks of the SOL as well as Tom Servo's bedroom were seen for the first (and only) times. The same hexagon shape, junk covered walls theme was present in the film.
Sci-Fi years: The second model used in the MST movie was used for the SOL in seasons 7-10 of the show (while season 7 was a Comedy Central season it's grouped here for completeness). This model was extremely detailed and again, it looked way more like a real functioning space ship. This SOL was severely malfunctioning and in the progress of burning up in Earth's atmosphere in the 10th season episode "Soultaker" (1001) when it was repaired by Joel Robinson. This is when we learned that Dr. Clayton Forrester had sabotaged the SOL to self-destruct in 10 years (which is a bit of a inconsistency, since the SOL was said to have sat for 500 years between seasons 7 and 8. We can only assume that Dr. F's self-destruct mechanism failed and took 503 years to work properly). This SOL was destroyed during the last episode of the series (1013: Diabolik). Best Brains didn't auction this model after the series ended, presumably since it was partially destroyed during the reentry sequence in 1013.
Note: Very few of the props remain from the great eBay auction. The 4 & 8 foot models, the button panel from the SOL's bridge, and the remaining working bots were retained. Even the MST3K logo planet was sold for around $7,000. I find it strange that Best Brains, in it's double intent to make money and give the fans a piece of the show, would not sell this model unless it was (a): destroyed or (b): if it was saved in the unlikely event that the show is ever revived.