Escape Velocity from the Earth

[toruk]

Does it have to be 25,000 mph? What if you traveled 10 miles per hour straight up and took a longer amount of time?

[lemur]

related question: what if you travelled 25,010mph and all nearby gravity-wells were moving away at x>10mph? Would you really continue indefinitely away from Earth or would spacetime eventually curve in such a way that you would end up in an Earth-bound trajectory?

 

To answer your immediate question, however, I think that if you could continue ascending at 10mph, you would eventually reach an altitude where escape-velocity was 10mph and you would escape gravity that way. The problem is that I don't know if you could maintain a clear anti-gravity direction since you could basically fall into orbit in any direction without necessarily noticing a change in altitude, I think.

[Mr Skeptic]

Escape velocity is more like how fast you have to jump to jump all the way to outer space (neglecting air friction). You'll slow down along the way. But you can go slower if you have a rocket, since you're no longer limited to being in freefall.

 

As for going 10 miles per hour, I don't think that would be possible due to the length of time it would take and the amount of rocket fuel required. Maybe with a space elevator?

[between3and26characterslon]

Does it have to be 25,000 mph? What if you traveled 10 miles per hour straight up and took a longer amount of time?

 

I think for the Earth it's more like 17,500 mph but that's not the speed you need to get into space or orbit. The escape velocity is just one definition of massive objects. The escape velocity of the Earth is the speed you need to be going at the surface, travelling radially away from the centre in order to come to rest at infinity. This is ignoring air resistance and remembering that once past the surface your vehicle is unpowered. From that you can work out what speed you need to break orbit at the height you are at which is basically what lemur said.

 

So at 10mph you could get into space but I don't think you would break orbit.

Edited December 11, 2010 by between3and26characterslon

[insane_alien]

I think for the Earth it's more like 17,500 mph but that's not the speed you need to get into space or orbit.

 

17500mph is the speed you need to achieve a circular low earth orbit. escape velocity is ~11.2km/s which is indeed 25000mph.

 

So at 10mph you could get into space but I don't think you would break orbit.

 

if you applied thrust to maintain 10mph you would escape once you got past the threshold where the escape velocity is 10mph. it would take a LONG LONG time to get there however, as that distance is 266.7AU away as shown by this calculation

 

http://www.wolframalpha.com/input/?i=2*G*%28Mass+of+earth%29%2F%28%2810mph%29^2%29

 

it would take 283.1 millenia at 10mph

 

http://www.wolframalpha.com/input/?i=%282*G*%28Mass+of+earth%29%2F%28%2810mph%29^2%29%29%2F10mph

[Janus]

17500mph is the speed you need to achieve a circular low earth orbit. escape velocity is ~11.2km/s which is indeed 25000mph.

 

 

 

if you applied thrust to maintain 10mph you would escape once you got past the threshold where the escape velocity is 10mph. it would take a LONG LONG time to get there however, as that distance is 266.7AU away as shown by this calculation

 

http://www.wolframalpha.com/input/?i=2*G*%28Mass+of+earth%29%2F%28%2810mph%29^2%29

 

it would take 283.1 millenia at 10mph

 

http://www.wolframalpha.com/input/?i=%282*G*%28Mass+of+earth%29%2F%28%2810mph%29^2%29%29%2F10mph

 

Well. in practical terms, you wouldn't have to go that far to escape the Earth. You only need to get to the edge of the gravitational sphere of influence. (the point where the Sun's gravity begins to dominate). For the Earth, this works out to to be ~925,000 km. It would still take 6.6 years to reach this distance at 10 mph.

[insane_alien]

Well. in practical terms, you wouldn't have to go that far to escape the Earth. You only need to get to the edge of the gravitational sphere of influence. (the point where the Sun's gravity begins to dominate). For the Earth, this works out to to be ~925,000 km. It would still take 6.6 years to reach this distance at 10 mph.

 

yes, this is true, but leaving the earths sphere of influence at such a low velocity would mean the objects orbit would not differ significantly from earths orbit. this means the earth would still have a strong influence which wouldn't result in a stable orbit around the sun. possibly resulting in the object crashing back to earth a few hundred years later.

[zapatos]

Escape velocity is more like how fast you have to jump to jump all the way to outer space (neglecting air friction). You'll slow down along the way. But you can go slower if you have a rocket, since you're no longer limited to being in freefall.

 

As for going 10 miles per hour, I don't think that would be possible due to the length of time it would take and the amount of rocket fuel required. Maybe with a space elevator?

Why is more fuel required? I would have thought it would be about the same. For example, I always thought that walking a mile or running a mile burned about the same number of calories since you are moving the same mass the same distance (ignoring thngs like efficiency of movement).

[Sisyphus]

Why is more fuel required? I would have thought it would be about the same. For example, I always thought that walking a mile or running a mile burned about the same number of calories since you are moving the same mass the same distance (ignoring thngs like efficiency of movement).

 

Because you're fighting the same gravity for hours or days instead of minutes. The analogy is more like walking or running against a treadmill for a distance of a mile. (That is, you're at the other end of a mile long treadmill, not that a mile of tread has passed under you.) It takes 1g of thrust just to hover, which is actually quite a bit. Your acceleration upwards is from the excess over that already considerable thrust.

[toruk]

Thanks for all the responses. I guess I am thinking more along the practical lines. At 10 mph I think it would take an enormous amount of fuel. But with the requirement for an enormous amount of fuel comes the requirement for even more energy. It seems to me there is some limit to how slowly you can achieve escape. How did you get 6.6 years?

[Sisyphus]

How did you get 6.6 years?

 

Wasn't my figure, but:

 

10mph is about 16 kmph.

There are 24*365= 8760 hours in a year.

16*8760 = 140160 km per year.

 

925000km / 140160 km per year = about 6.6 years.

[lemur]

yes, this is true, but leaving the earths sphere of influence at such a low velocity would mean the objects orbit would not differ significantly from earths orbit. this means the earth would still have a strong influence which wouldn't result in a stable orbit around the sun. possibly resulting in the object crashing back to earth a few hundred years later.

 

Couldn't the object escape Earth's gravity by entering into solar orbit in the opposite direction as Earth? In that case, wouldn't it fall into the sun from there (unless Venus or Mercury got in the way, of course)?

 

edit: if so, I wonder how long it would take to fall into the sun, assuming it didn't burn up first which it would.

Edited December 11, 2010 by lemur

[D H]

Earth's orbital velocity around the Sun is about 66,600 miles per hour. Your 10 mile/hour figure won't even begin to make a dent in that number. It is very, very hard to make a dent in that number. In fact, it is easier to make a vehicle launched from Earth escape the solar system than it would be to make that object hit the Sun. Even getting to Mercury is hard. That is why we have had so few missions to Mercury.

[lemur]

Earth's orbital velocity around the Sun is about 66,600 miles per hour. Your 10 mile/hour figure won't even begin to make a dent in that number. It is very, very hard to make a dent in that number. In fact, it is easier to make a vehicle launched from Earth escape the solar system than it would be to make that object hit the Sun. Even getting to Mercury is hard. That is why we have had so few missions to Mercury.

 

Why should it be hard to get to Venus, Mercury, or the sun? It's downhill. If you escape Earth orbit in the opposite direction so that your speed is slightly less than that of Earth, shouldn't you begin to fall toward the sun the same way a satellite that loses speed begins falling toward Earth?

[Sisyphus]

Why should it be hard to get to Venus, Mercury, or the sun? It's downhill. If you escape Earth orbit in the opposite direction so that your speed is slightly less than that of Earth, shouldn't you begin to fall toward the sun the same way a satellite that loses speed begins falling toward Earth?

 

No, you'll just have a slightly smaller and more eccentric orbit. You won't fall towards the sun unless you get rid of almost all of the velocity you started with (the Earth's orbital velocity), which is the same as adding the difference. (Delta V is delta V.)

[lemur]

No, you'll just have a slightly smaller and more eccentric orbit. You won't fall towards the sun unless you get rid of almost all of the velocity you started with (the Earth's orbital velocity), which is the same as adding the difference. (Delta V is delta V.)

What is the minimum speed to avoid orbital decay at Earth's distance from the sun, then? How do you calculate that, btw?

[Sisyphus]

What is the minimum speed to avoid orbital decay at Earth's distance from the sun, then? How do you calculate that, btw?

 

"Orbital decay" in the sense of satellites slowing down and crashing to Earth is caused by the tiny amount of friction with the upper atmosphere. In the absence of some outside force like that, orbits don't decay. In order to crash into the Sun, you would just have to get yourself into an orbit that intersects with the Sun's surface. Starting out from the Earth, that would mean a great deal of acceleration to get rid of almost all of the relative velocity you started with. So in other words, you would go from being in an almost circular orbit, to the apogee of a very eccentric ellipse.

 

EDIT: Here's a drawing:

 

 

The Earth (E) orbits the Sun (S) in a nearly circular orbit (blue), with a certain amount of perpendicular velocity. Increase that velocity at that same point, and you are in an elliptical orbit and starting at the perigee (red). If you increase it enough, the ellipse never closes, and you escape. Decrease it, and you're at the apogee (green.) Decrease it enough, and the orbit intersects with sun itself (orange). This is all starting from the same point and with velocity in the same direction, but of different magnitudes.

[lemur]

"Orbital decay" in the sense of satellites slowing down and crashing to Earth is caused by the tiny amount of friction with the upper atmosphere. In the absence of some outside force like that, orbits don't decay. In order to crash into the Sun, you would just have to get yourself into an orbit that intersects with the Sun's surface. Starting out from the Earth, that would mean a great deal of acceleration to get rid of almost all of the relative velocity you started with. So in other words, you would go from being in an almost circular orbit, to the apogee of a very eccentric ellipse.

 

So you'd have a hard time hitting the sun. Even if you aimed at it and gave a good bit of thrust in its direction, you'd still have a good chance of flying over it if you didn't use enough thrust. That's really interesting that it's so difficult to fall into a gravity-well. You would think it would be more effort to keep from falling in, but I guess that is a terrestrial-rooted subjective bias.

[D H]

Here is what what Sisyphus and I are talking about, in numbers:

• Earth's orbital velocity about the Sun is 29.79 km/s.
  
• Solar system escape velocity at 1 AU from the Sun is 42.12 km/s.
  
• An orbit with an apohelion of 1 AU and a perihelion of 0.005 AU will just intersect Earth's orbit and the Sun's surface.
  
• The orbital velocity for this orbit is 2.97 km/s at apohelion.
  

 

 

That means that only 12.34 km/s needs to be added to a vehicle launched from Earth to place it on a solar system escape trajectory while 26.81 km/s needs to be removed from a vehicle launched from Earth to place it on a Sun-intersecting trajectory. Given the nastiness of the rocket equation, it is a whole lot harder to place a vehicle on a Sun-intersecting trajectory than it is to make it escape the solar system.

[lemur]

That means that only 12.34 km/s needs to be added to a vehicle launched from Earth to place it on a solar system escape trajectory while 26.81 km/s needs to be removed from a vehicle launched from Earth to place it on a Sun-intersecting trajectory. Given the nastiness of the rocket equation, it is a whole lot harder to place a vehicle on a Sun-intersecting trajectory than it is to make it escape the solar system.

 

That's amazing. I would have expected the reverse, just because there are more planets beyond Earth's orbit than within it, and because those planets are further from Earth than Earth is from the sun. So much for intuitive gravitation. This does, however, aid my thinking about why electrons are prone to certain orbits/'levels and resist deviating from the level they're in. Apparently, any satellite changes the eccentricity of its orbit significantly before achieving a new consistent altitude. Could this be described as orbital elasticity?

[Janus]

That's amazing. I would have expected the reverse, just because there are more planets beyond Earth's orbit than within it, and because those planets are further from Earth than Earth is from the sun. So much for intuitive gravitation. This does, however, aid my thinking about why electrons are prone to certain orbits/'levels and resist deviating from the level they're in.

1. Electrons do not orbit the nucleus like planets orbit the Sun. This way of looking at atoms was discarded decades ago.

2. Electrons maintain discreet energy levels because there are no allowable energy levels in between'

 

Apparently, any satellite changes the eccentricity of its orbit significantly before achieving a new consistent altitude. Could this be described as orbital elasticity?

If you exert a force on a satellite such that it moves from a circular orbit to an elliptical one, it will stay in that elliptical one until something else acts on it to change that. It will not just adopt a new circular orbit on its own.

[Mr Skeptic]

Here is what what Sisyphus and I are talking about, in numbers:

• Earth's orbital velocity about the Sun is 29.79 km/s.
• Solar system escape velocity at 1 AU from the Sun is 42.12 km/s.
• An orbit with an apohelion of 1 AU and a perihelion of 0.005 AU will just intersect Earth's orbit and the Sun's surface.
• The orbital velocity for this orbit is 2.97 km/s at apohelion.

 

 

That means that only 12.34 km/s needs to be added to a vehicle launched from Earth to place it on a solar system escape trajectory while 26.81 km/s needs to be removed from a vehicle launched from Earth to place it on a Sun-intersecting trajectory. Given the nastiness of the rocket equation, it is a whole lot harder to place a vehicle on a Sun-intersecting trajectory than it is to make it escape the solar system.

 

And to add to the fun, if you want to make a soft landing when you get there then you need to get rid of all that velocity you gain by falling toward the sun, which would add yet more energy requirement.

[lemur]

1. Electrons do not orbit the nucleus like planets orbit the Sun. This way of looking at atoms was discarded decades ago.

People tell me this whenever I so much as suggest there is any similarity between the two types of systems. Despite this, I continue to see something very fundamental in the way an orbiting body remains in motion as a result of the satellite's inertia while simultaneously generating a more or less stabile trajectory. I see this as the basis for the volume of matter, though I continue to wonder why electrons wouldn't fall into the nucleus or continuously deteriorate in orbital level due to energy losses via radiation. To me it seems like electrons may orbit like planets, except that the electrons undergo a lot more external "trajectory-bumps," including as a result of same-charge repulsion from other nearby electrons. This could account for the "cloud-like" nature of electron orbits, no?

 

2. Electrons maintain discreet energy levels because there are no allowable energy levels in between'

Right, but there must be some reason why. I would guess that reason has something to do with complimentary orbital patterns that form as a result of inter-electron same-charge repulsion. They probably have certain margins of orbital-shape variation that can occur before they "snap" out of one orbital-level into another.

 

If you exert a force on a satellite such that it moves from a circular orbit to an elliptical one, it will stay in that elliptical one until something else acts on it to change that. It will not just adopt a new circular orbit on its own.

Right, but if there were lots of other satellites influencing its motion on a regular basis, it might tend toward certain kinds of patterns, no?

 

 

[Sisyphus]

lemur, orbitals and orbits are completely different things. If you must make an analogy to some classical situation, you'll be closer to the truth if you think of an electron as a standing wave instead of a little object zipping around. The orbital is just the shape of that standing wave.

 

The reason only certain energy levels are "allowed" is just a mathematical consequence of their wave nature, similar to how it's only possible to have certain patterns of peaks and troughs on a vibrating drum.

[Janus]

People tell me this whenever I so much as suggest there is any similarity between the two types of systems.

For good reason, because there isn't.

Despite this, I continue to see something very fundamental in the way an orbiting body remains in motion as a result of the satellite's inertia while simultaneously generating a more or less stabile trajectory.

You are basing this on an insufficient understanding of both orbital mechanics and the structure of the atom. This is known as GIGO.

 

I see this as the basis for the volume of matter, though I continue to wonder why electrons wouldn't fall into the nucleus or continuously deteriorate in orbital level due to energy losses via radiation. To me it seems like electrons may orbit like planets, except that the electrons undergo a lot more external "trajectory-bumps," including as a result of same-charge repulsion from other nearby electrons. This could account for the "cloud-like" nature of electron orbits, no?

No. Electron clouds are probability based. They just define where you are likely to find the electron. At a given instant, the electron might not even be in the area defined by the cloud.

 

Right, but there must be some reason why. I would guess that reason has something to do with complimentary orbital patterns that form as a result of inter-electron same-charge repulsion. They probably have certain margins of orbital-shape variation that can occur before they "snap" out of one orbital-level into another.

More GIGO. Forming an opinion from faulty premises.