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stevenspray
2007-Nov-03, 10:17 AM
He everyone!

I was wondering what the minimun velocity is whereby one can escape Earth's gravity. Does one HAVE to accelerate to overcome the gravitational pull?

Let's say,hypothetically, you have a machine that will enable you to traverse into outer space from the surface of the Earth at a constant velocity. Would you be able to do this at a speed of 1m/sec?

Another thing I was wondering about; what exactly keeps the moon in a relative stable orbit around Earth? What keeps celestial bodies from crashing into each other, overcoming the attractive force of gravity?

antoniseb
2007-Nov-03, 12:00 PM
Hi stevenspray,

Escape velocity refers to a speed you'd need to be going at the surface of an object (such as the Earth) to be able to coast the rest of the way and escape. No allowance is given for wind resistance or anything like that.

If you had a machine that was able to keep you moving away from the Earth at a constant velocity, even 1 mm/sec would be enough to eventually escape.

Concerning what keeps the Moon in a stable orbit, I suggest looking it up on wiki or something. Look up clestial mechanics, because they will explain it more clearly than I can do off the cuff. The short answer is that the force of gravity on the Moon from the Earth is exactly equaled by the force on the Moon from the acceleration of gravity curving its path around the Earth.

Jeff Root
2007-Nov-03, 03:01 PM
Escape speed is the speed needed to escape without any further
impulse. That is, if you have that speed, you will coast away from
Earth without ever falling back. The farther you are from Earth,
the less speed needed to escape. just above Earth's atmosphere,
escape speed is 11.2 kilometers per second (7 miles per second).

Escape speed fom the Sun, at the distance Earth is from the Sun,
is 42.1 kilometers per second (26.2 miles per second).

Most interestingly, the escape speed does not depend on the
direction you are headed: Whether you head directly away from
Earth's center or tangental to an orbit, the speed is the same.

Here is a little bit of info about orbits: Orbital Speed (http://www.freemars.org/jeff/speed/index.htm)

-- Jeff, in Minneapolis

Tucson_Tim
2007-Nov-03, 03:23 PM
Let's say,hypothetically, you have a machine that will enable you to traverse into outer space from the surface of the Earth at a constant velocity. Would you be able to do this at a speed of 1m/sec?

Yes. Just as Antoniseb said. But your machine would have to continue to apply the force.

Fortunate
2007-Nov-03, 04:46 PM
Could we just think in terms of work? You need to do enough work to overcome the potential energy bound up in the gravitational attraction between the vehicle and the Earth. You can do the necessary work quickly, attain escape velocity early, and your effort is sufficient, or you can keep plugging away a bit at a time. Just like mowing the lawn.

MaDeR
2007-Nov-03, 07:32 PM
Another thing I was wondering about; what exactly keeps the moon in a relative stable orbit around Earth? What keeps celestial bodies from crashing into each other, overcoming the attractive force of gravity?
Velocity. Moon falls to Earth all time. But moon zips also with somewhat big velocity in one direction. Because of Earth gravity, this direction is skewed (so in effect Moon goes 'round), but not THAT skewed to hit Earth.

This is very simple link that explains it nicely...
http://spaceplace.nasa.gov/en/kids/orbits1.shtml

Fortunate
2007-Nov-03, 08:58 PM
Another thing I was wondering about; what exactly keeps the moon in a relative stable orbit around Earth? What keeps celestial bodies from crashing into each other, overcoming the attractive force of gravity?

The link supplied by MaDeR is a very good one.

Or try this:
An object tends to move in a straight line at a constant speed unless some force acts on it. A force will cause the object to accelerate in the direction of the force because of Newton's second law of motion (F = ma). Uniform circular motion is produced by a force with a constant magnitude but a direction that keeps changing so that it always points towards the center of the circle. Sound familiar? That perfectly describes the Earth's gravitational pull on the moon. The force necessary to produce circular motion is called "centripetal force" (petere in Latin means "to seek". Centripetal force makes the object want to move towards the center of the circle, but its efforts to do so keep getting foiled by its own momentum, which tries to keep it moving in a straight line).

We often think of acceleration as "speeding up" or "slowing down", but acceleration is any change in velocity. Remember that velocity is a vector with both a magnitude and a direction. Sometimes an acceleration only changes the velocity's direction but not its magnitude. That is the situation with uniform circular motion. The pull of the Earth is just strong enough to keep the moon in orbit but not strong enough to make the moon move closer to the Earth.

Noclevername
2007-Nov-03, 09:43 PM
Actually the Moon is slowly moving away from us because the Earth's rotation is "dragging" it along into a higher speed. It's getting harder and harder to hold on.

Tucson_Tim
2007-Nov-03, 09:46 PM
Actually the Moon is slowly moving away from us because the Earth's rotation is "dragging" it along into a higher speed. It's getting harder and harder to hold on.

Isn't that because the Earth's rotation is slowing, progressing towards tidal lock, and momentum must be conserved.

Noclevername
2007-Nov-03, 09:48 PM
Isn't that because the Earth's rotation is slowing, progressing towards tidal lock, and momentum must be conserved.

It's slowing. In about 200 million years or so we'll have a 25 hour day. The Moon gains speed (energy), we lose it. Stop, theif!

RapidEye
2007-Nov-03, 11:31 PM
Would you be able to do this at a speed of 1m/sec?
You can't go vertical at a constant rate of 1m/sec without using acceleration to overcome earth's gravity.

Tucson_Tim
2007-Nov-03, 11:45 PM
You can't go vertical at a constant rate of 1m/sec without using acceleration to overcome earth's gravity.

I think this is true. Even though the speed is a constant 1 m/sec, the velocity vector is constanly changing.

MEATHEAD
2007-Nov-04, 01:33 AM
The real question is how much force is required to achieve escape velocity.

ASEI
2007-Nov-04, 01:41 AM
You can have all sorts of scenarios involving all sorts of force profiles vs time to reach escape velocity. All that's needed for it to finally be escape velocity is for your kinetic + gravitational potential energy > 0. This means that you aren't in an elliptical or circular orbit, you've transitioned into a hyperbolic orbit that will take you away from Earth and never return you.

You can do it in an instant with an infinite dirac-delta of force. You can do it over a few minutes with a million lb thrust rocket burn. Or you can do it over the course of a few weeks by (somehow) moving at a constant rate of 1m/sec away until you are far enough away from the Earth that your escape speed is 1 m/sec.

If you were a hundred million LY from earth (well, assuming you're looking only at you and earth, and not the other bodies out there) and moving with zero relative velocity, then you haven't escaped.

If you were 1m from earth and moving at 20 km/sec, then you have escaped and are no longer in a closed orbit.

If your
kinetic (expressed positive) + gravitational potential (expressed negative) < 0 - elliptical orbit
kinetic + gravitational potential energy = 0 - parabolic orbit (boundary case of hyperbolic orbits)
kinetic + gravitational potential energy > 0 - hyperbolic escape orbit

Your gravitational potential energy is a function of where your vehicle is in the system (how far away it is from a spherical mass, in most relevant cases)
Your kinetic energy is a function of how fast you're going.

KE = m_vehicle*magnitude(velocity)^2
PE = -G*M_EARTH*m_vehicle/radius from earth to vehicle

escape velocity = sqrt(G*M_EARTH/radius from earth)

stevenspray
2007-Nov-04, 11:16 AM
Thanks for all the input guys, appreciate it!

grant hutchison
2007-Nov-04, 09:44 PM
I think this is true. Even though the speed is a constant 1 m/sec, the velocity vector is constanly changing.I'm not clear what you're thinking of here, to make the velocity vector change. Is it the rotation of the Earth? How about if we take off from the north (or south) pole?

Grant Hutchison