Without what could you never leave Earth?

If we put the question like that, we’d probably get a lot of different answers ranging from pragmatic (“a rocket”) to very human (“my dog”) to downright silly (“my beloved Star Trek DVD collection”). But from a physicist’s perspective, there’s only one right answer: escape velocity.

Escape velocity is the minimum speed needed for a free, non-propelled object to escape with a single impulse from the gravitational influence of a massive body, e.g. a planet, starting from the surface of said planet.
To put it more simply, it’s how fast e.g. a rocket would have to be in order to leave the Earth. You can find the physics formula on the Escape Velocity Mug. Here, G is the universal gravitational constant, M the mass of the body to be escaped from, and r the distance from the centre of mass of the body to the object.

For Earth, this velocity is almost 8 km per second!