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Q & A: Escape Velocity of Earth

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Most recent answer: 10/22/2007
Q:
About how fast does a space craft have to be going to get into outer space? Does it continue at the speed? If yes, why? If no, why?
- Kitty
Wallace-Rose Hill Highschool, North Carlina
A:
The official name for this speed is called the "escape velocity". If a spacecraft is launched from a pad on the surface of the earth with this speed or greater, it will escape the Earth's gravitational field. The escape velocity can be calculated from the Earth's mass, its radius, and Newton's gravitational constant G: v_esc=sqrt(2*G*M/R). It is assumed for that formula that air resistance doesn't slow down the spacecraft (a very wrong assumption). For the Earth, this speed is 11200 meters per second, or about 25,000 miles per hour.

No, the spacecraft will not continue at that speed -- gravity will constantly pull the spacecraft towards the Earth and slow it down. If the spacecraft is launched going faster than v_esc, it will still continue at a slower speed long after it has climbed out of the Earth's gravitational field. If it is launched at v_esc, it will slow down and just barely not fall back, continuing farther out, but always more slowly. If the craft is launched at a speed slower than v_esc, it will fall back.

Air resistance is important. Dropping an object towards the earth from far away in space usually results in the object at least partially burning up due to the heat caused by friction in the atmosphere. By the same token, spacecraft shouldn't try to go through the atmosphere at that speed because they may burn up.

You could launch a spacecraft that slowly lifts itself up, always burning fuel. Then you could get into space without ever getting up to v_esc in speed. The biggest problem with this is that it takes more fuel on the entire trip to get into space in this manner. Hovering means burning lots of fuel while going nowhere. Going slowly just burns fuel that could otherwise help send the craft into space. And if fuel is burned higher up along the path of the spacecraft, more fuel would have to be burned lower just to lift that fuel up. It is more efficient to boost a lighter spacecraft up that's burned all of its fuel earlier. And even more efficient to drop the fuel tank once it's empty!

So actual spacecraft get launched as fast as possible without burning up.

Tom

(published on 10/22/2007)

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