Escape velocity a necessity?

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Escape velocity a necessity?

Postby HAL Jr » Mon Jul 27, 2009 7:18 pm

To exit the Earth's atmosphere we have been taught that you need to be travelling at 7 miles a second,but why is that a necessity? Why could not a ship achieve the appropriate altitude at a much lower speed and simply push thru the envelope? What would happen and why?
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Re: Escape velocity a necessity?

Postby admin » Tue Jul 28, 2009 8:35 am

If you are traveling upward at 7 miles per second or more, then you have enough velocity to reach orbit (neglecting friction and air resistance) even if you cut your engines. You could creep into orbit at a much slower speed by using continuous thrust, but it would be ruinously wasteful of fuel.

The equations are as follows, neglecting air resistance and friction and also ignoring the fact that as you move away from the center of the earth, the Earth's gravitational pull gradually decreases. 9.8 meters per second squared is the downward acceleration of gravity, v your veloctiy as a function of time, c your initial velocity, and h your height.

a = -9.8

v = c - 9.8 t

h = ct - 4.9 t^2
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Re: Escape velocity a necessity?

Postby slaven41 » Tue Jul 28, 2009 10:00 am

The 7 miles/sec number is the number necessary to escape earth's gravitational "well". Think of it this way. If you throw an object up in the air, the faster you throw it, the higher it goes before coming back. 7 miles/sec is how fast you have to throw it so that it never comes back.

Now you can also escape earth the way you describe: never actually getting up to 7 miles/sec but firing the rocket continuously over a much longer time. But as admin pointed out, you're better off doing it all at once.

Of course the 7 miles/sec number is from the surface of the earth. In general, it's given by (if I can figure out how to make the image feature work)
Image
where G is the universal gravitational constant (6.67 x 10^-11), M is the mass of the planet (or other round celestial object) in kg, and R is the initial distance from the center of the planet, in meters. (The resulting speed will be in meters per second, not miles per second.)

So if you have a space elevator and can launch your rocket from a much larger R, the speed you need to attain is smaller. Which is good, because the amount of fuel you need goes up exponentially with the amount of speed (delta v) you need.

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Re: Escape velocity a necessity?

Postby HAL Jr » Tue Jul 28, 2009 10:10 am

Oh god,funny figures-runs!

Err imagine I'm a 10 year old asking the same question cos when it comes to numbers i'm dyslexic!
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Re: Escape velocity a necessity?

Postby Brightonian » Tue Jul 28, 2009 10:56 am

Didn't Jules Verne calculate the correct escape velocity in De la Terre a la Lune? Except he had a projectile fired from a giant cannon rather than using rocket power.
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Re: Escape velocity a necessity?

Postby admin » Wed Jul 29, 2009 8:06 am

The calculation was well known in Verne's day, and I think he got the escape velocity right. He also realized that the acceleration of a cannon would kill the passengers, so he had nested cannons, where the outer cannon fires an inner cannon, which fires another inner cannon, which fires the passenger capsule. The capsule is designed to crash land on the moon, and the passengers, before they die, plan to communicate with earth by forming giant letters, visible from earth, out of blocks of stone. As matters develop, the capsule doesn't land, but whips around the moon and returns safely to earth, where it crashes into the ocean. The passengers survive the crash -- now that's impossible.
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Re: Escape velocity a necessity?

Postby admin » Wed Jul 29, 2009 8:07 am

Answer for Hal, Jr.'s hypothetical ten year old.

If you throw a rock upwards at 7 miles per second, it will never come down. Any slower, and it will come down eventually.
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Re: Escape velocity a necessity?

Postby HAL Jr » Wed Jul 29, 2009 11:59 am

Yes Rick,but why?
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Re: Escape velocity a necessity?

Postby admin » Thu Jul 30, 2009 7:37 am

When you throw something up, it moves upward more and more slowly, gets to the top, and starts back down. The harder you throw it up, the higher it goes, and the longer it takes to come back down. If the gravitational pull of the earth didn't depend on the height, it would always come back down eventually, but as it goes higher and higher, the pull of the earth gradually decreases. (I think I neglected that part in my earlier explanation, which means that my earlier explanation was wrong.) If it is going fast enough when it gets high enough, then the decreased pull of the earth isn't enough to bring it back down, and it just keeps going up. Near the surface of the earth, seven miles per second is the speed at which that happens.

You asked why you couldn't go slower and still get into space. You could, but that would require continuous thrust, which would use up fuel at a frightful rate. Since the rocket has to lift its own fuel, it is better to use up a lot of that fuel while still fairly close to the ground. You also save weight by throwing away the used-up fuel tanks. That's why we have multi-stage rockets.

We haven't discussed going into orbit, yet. That requires thrust not only upward, but also sideways. This is why rockets are launched near the equator. The sideways spin of the earth helps the rocket go into orbit.

An object in orbit is moving sideways fast enough so that as the earth pulls it down, the rocket moves sideways so that the earth is no longer in the way. When the rocket moves sideways, the earth is pulling from a slightly different direction, and the rocket is moving in a slightly different direction, and the same thing continuously happens -- the sideways motion keeps it from moving down.

Which reminds me of Arthur Dent, who can fly by trying to fall down and being so clumsy that he misses the earth. Or of that great scientific discovery "If you push something hard enough, it will fall over".

Next lesson: Why is a mouse that spins?
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Re: Escape velocity a necessity?

Postby HAL Jr » Thu Jul 30, 2009 9:08 am

So its a simple case of overcoming the pull of the earth's gravity. And that takes a LOT of energy or to be travelling very fast.
Now whats this about a mouse spinning? I think you worded that slightly wrong.
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Re: Escape velocity a necessity?

Postby admin » Thu Jul 30, 2009 3:04 pm

"Why is a mouse that spins?" is a nonsense riddle, at least a hundred years old. It's been quoted by both Doctor Who and Star Trek TNG. I'll wait to see if anyone here knows the answer.
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Re: Escape velocity a necessity?

Postby Brightonian » Thu Jul 30, 2009 4:21 pm

If anyone does know the answer, maybe they also know why a raven is like a writing-desk?
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Re: Escape velocity a necessity?

Postby HAL Jr » Fri Jul 31, 2009 8:09 am

A mouse called Why,that spins around?
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Re: Escape velocity a necessity?

Postby admin » Fri Jul 31, 2009 10:04 am

A raven is like a writing desk because the notes they produce are not the best notes.

But Lewis Carroll proposed the riddle without intending there to be an answer. The answer came much later.
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Re: Escape velocity a necessity?

Postby HAL Jr » Sat Aug 01, 2009 12:07 pm

Why is a mouse that spins
Or
Binky is a mouse that spins?
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