why cant a flying object just leave the atmosphere at a slower speed? why does it need to achieve ‘escape velocity’? if a rocket goes straight up at 100kmph without stopping, it should escape the atmosphere eventually right?

Question

why cant a flying object just leave the atmosphere at a slower speed? why does it need to achieve ‘escape velocity’? if a rocket goes straight up at 100kmph without stopping, it should escape the atmosphere eventually right?

In: Physics

Answer 1

Suppose you’re in a spaceship near to a planet. Let’s assume for a moment that the planet is very very tiny so we’re never at risk of crashing into it, and that it has no atmosphere. Let’s also assume that our rocket has run out of fuel. If our rocket’s initial speed is low enough, we will remain in orbit around the planet – specifically we will trace out an ellipse around it. If the speed is high enough, we will keep getting further and further from the planet – specifically we will trace out the shape of a hyperbola. Somewhere in the middle there is a speed, depending only on our initial distance from the planet (EDIT: and the mass of the planet), which marks the boundary between those two outcomes. This is the escape velocity.

Now in real life there are a few complications. Depending on the direction we’re travelling, we might collide with the planet. This is possible regardless of how fast we’re going. If we’re close enough to the planet that its atmosphere causes substantial drag, then things get a lot more complicated and whether or not we can escape its gravity depends on the density and viscosity of the atmosphere, the path we take through it, and how streamlined our rocket is. And if we still have fuel left and are using the engine to accelerate, this also complicates things. So “escape velocity” is not really a very relevant concept when we’re talking about a rocket that is on the ground on a planet with a thick atmosphere.

But if we’re already far out in space with no atmosphere around us, we’re orbiting a body and we want to leave it and travel to a different body, it’s a very useful concept. The “cost” of maneuvers out in space is often measured in terms of “delta v”, i.e. the amount by which our engine needs to change our speed. The difference between our current speed and the escape velocity is the delta v we need to escape the orbit of the body.