Vostok 1 launched from a point near the Aral Sea, at 06:07 UT and flew northeast at first over the top of the Earth and down into night time over the Pacific Ocean, before emerging into sunlight again over the Southern Atlantic and heading back up again across the whole African continent and the Middle East, to land at 07:55 UT, just north of the Caspian Sea. You can explore Yuri's route around the world further with our First Orbit App. The orbit of one body about another under the influence of gravity, like a spacecraft orbiting the Earth, or the Earth orbiting the Sun, can be defined by six numbers, known as Keplerian or Classical Orbital Elements (COEs).
For more information on the mathematics of orbits please click here. To find out how to see the International Space Station pass overhead please visit NASA's ISS viewing site here or this wonderful Astroviewer site.