What is the shape of our solar system?
In early 1605 Johannes Kepler discovered that planets moved in a elliptical orbit. So this still doesn't explain the real shape of our solar system, this is just how the planets orbit the sun. If we look at how Termination shock works we can see how the solar system is contained in a shell like structure.
This is a model of our heliosphere. The heliosphere is a bubble of solar wind around the solar system. As the solar systems moves through the galaxy, it gives the heliosphere a tail, the heliotail.
The real shape of the solar system is like a bullet. Voyager 1 and 2 were used to discover and prove the shape of the heliosphere, Voyager 1 was launched on September 5, 1977, and is the farthest Earth spacecraft from Earth. Voyager 2 was launched 16 days before Voyager 1, but on a trajectory that took longer to reach Saturn and Jupiter. It was launched to study Neptune and Uranus and Voyager 1 was launched to go out of the solar system and study things that have once only been theories. The bullet shape of the solar system is caused by the speed of the solar system moving through the galaxy. The heliosphere is going so fast it drags a tail of solar wind behind the heliosphere called the heliotail. The termination shock is the boundary of the suns influence and heat. This allows the solar system to stay together and look like a bullet.