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The path followed by satellites in orbit can either be circular or elliptical. A satellite (or space shuttle for that matter) in low Earth orbit can be orbiting at some distance up to 620 miles (1000 km) above the Earth’s surface.

Luna 1, launched in 1959, was the first man-made object to achieve escape velocity from the Earth.

A satellite traveling in low Earth orbit is moving at around 5 miles per second. Interestingly, that around the same speed that any object has to travel to escape Earth’s gravity. This is called escape velocity.

Escape velocity is sometimes misunderstood to be the speed a powered vehicle, such as a rocket, must reach to leave Earth and travel through outer space. The calculated  escape velocity above is commonly the escape velocity at a planet’s surface, and it actually decreases with altitude. Escape velocity is actually the speed above which an object will depart on a ballistic trajectory, i.e. fired from a cannon as in the picture below, and never fall back to the surface nor assume a closed orbit. Such an object is said to “escape” the gravity of the planet.

Isaac Newton's analysis of escape velocity. Projectiles A and B fall back to earth. Projectile C achieves a circular orbit, D an elliptical one. Projectile E escapes.

A vehicle with a propulsion system can continue to gain energy and travel away from the planet, in any direction, at a speed lower than escape velocity so long as it is under power. If the vehicle’s speed is below its current escape velocity and the propulsion is removed, the vehicle will assume a closed orbit or fall back to the surface. If its speed is at or above the escape velocity and the propulsion is removed, it has enough kinetic energy to “escape” and will neither orbit nor fall back to the surface.

Learn more, and do the calculations yourself, here and here.