Talk:Escape velocity

From Wikipedia, the free encyclopedia

	Portal This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
B	This article has been rated as B-Class on the assessment scale.
High	This article is on a subject of High importance within physics.
Help with this template This article has been rated but has no comments. If appropriate, please review the article and leave comments here to identify the strengths and weaknesses of the article and what work it will need.

Could someone write the escape velocities into units of mach as well as km/s? Thanks. -- Astudent 04:52 Apr 30, 2003 (UTC)

Umm, you do realize that mach pretty explicitly refers to a speed in an atmosphere, and when you're in an atmosphere, atmospheric drag is going to completely skew the escape velocities anyway, right? -- John Owens 06:13 Apr 30, 2003 (UTC)

First, the standard escape velocity value of 11.2 km/s is at the surface of the earth were the speed of sound is easily defined and well understood. Hence giving the Mach number of the escape velocity is a valid request. (At much higher altitudes, were the atmosphere is rarified, clearly the definition of the Mach number breaks down.) Second, to the layman, the speed of sound is just the speed of sound in air at approximately sea level in "standard" atmospheric conditions. The layman doesn't understand that it varies with temperature (among other things). So while you are technically correct, it would be helpful to the layperson if the escape velocity were related to the only "fast" speed they understand: the speed of sound at sea level. Since the speed of sound at sea level is 1225 km/hr, then the "Mach number" of the escape velocity at sea level would be (40320 km/hr)/(1225 km/hr) = 33. So the Mach number of the escape veloctiy is 33 at the surface of the earth (though, as the article points out, this is impossible to reach due to air drag and hence atmospheric heating). But there you go for whoever asked.Jrdx 01:40, 16 December 2006 (UTC)

This makes no sense....

(One complication is that virtually all astronomical objects rotate. The frame of reference must not rotate for that statement to be correct. Moreover, the gravitational slingshot effect sometimes involves transfer of energy to the projectile from the slingshot body that depends on the spatial relationship between projectile and body. The body loses some angular momentum -- possibly rotational as well as orbital -- adding kinetic energy to the projectile. Therefore, the complete gravitational field of the slingshot body must be included in the overall field, which then can no longer be approximatively treated as symmetric. Moreover, not only do escape velocities vary from place to place, they vary with time in such cases. Even moreso, they may sometimes depend on direction.)

Again, this makes no sense.....

(For reasons given above, computers may often have to be used to compute solar-system escape velocities to some desired precision.)

(One complication is that virtually all astronomical objects rotate.

Planets and stuff spin.

The frame of reference must not rotate for that statement to be correct.

Refers to "so that "velocity" is a misnomer; it is a scalar quantity and would more accurately be called "escape speed"". If you have a rotating frame of reference, then it will be a vector quantity rather than scalar, and it would be appropriate to call it a "velocity" after all. E.g., in computing the escape velocity for the solar system from a point on the Earth, or in its near vicinity, you would get different escape speeds depending on where in the Earth's gravitational field the object was, even if you calculate the velocity relative to the Sun's position rather than the Earth's.

Moreover, the gravitational slingshot effect sometimes involves transfer of energy to the projectile from the slingshot body that depends on the spatial relationship between projectile and body.

The Voyager spacecraft didn't have enough fuel to get out of the solar system under their own thrust; because they were given trajectories that gave them a significant boost from the slingshot effect at Jupiter & Saturn, that speed became greater than the escape velocity in that direction. If they'd just been given that much speed in a random direction, they would almost certainly still be orbiting the Sun.

The body loses some angular momentum -- possibly rotational as well as orbital -- adding kinetic energy to the projectile.

In the slingshot effect, some of the larger body's (call it a planet) momentum is transferred to the spacecraft. Because the planet has such greater mass, it's not measurable how much the planet is slowed down (or sped up, if you approach from the other direction). Mechanically, a slingshot can be considered much the same as a totally elastic collision between the planet and spacecraft; it's just that long-range gravity is the medium of the interaction, instead of close-up electromagnetic forces (Van der Waals, I think?). There can also be a minor component of acceleration from the tidal effects, which will affect the planet's rotation.

Therefore, the complete gravitational field of the slingshot body must be included in the overall field, which then can no longer be approximatively treated as symmetric. Moreover, not only do escape velocities vary from place to place, they vary with time in such cases. Even moreso, they may sometimes depend on direction.)

So for calculating an escape velocity from the Sun, you need to consider "lumps" in the gravitational field, such as moving planets, which will alter the speed needed to escape the system in different directions.

(For reasons given above, computers may often have to be used to compute solar-system escape velocities to some desired precision.)

I hope that from the above, it should be obvious (and not even in the way mathematicians say "it's obvious") why a computer would be helpful.

--John Owens 22:32, 2004 Feb 1 (UTC)

I'm pretty sure that there's a difference between escape velocity and the minimum velocity needed to escape a body at any particular time if you use slingshots and other dynamic effects like fuzzy orbits. They're not the same thing.WolfKeeper 00:53, 12 September 2007 (UTC)

This thing has way, way too many parenthetical remarks. If the information is important, just work it into the body of the article. --24.156.119.50 16:14, 28 Mar 2004 (UTC)

I'm inclined to agree. I just added a section; now maybe I'll go back and do a bit of rearranging of the earlier sections. Michael Hardy 22:40, 6 Sep 2004 (UTC)

I figure this article would really benefit from a brief table showing the escape velocities of major astronomical bodies (earth, luna, sun, mars, saturn, maybe our galaxy). -- Finlay McWalter | Talk 22:47, 25 Jul 2004 (UTC)

The notes say that this article needs to cite its sources - however, the vast majority of its discussion is mathematical development from first principles, and any normal undergraduate physics textbook is a "source" as such. It's kind of like asking for a citation for 2+2=4. Newton computed this without a source at all. Perhaps his Principia Mathematica should be cited as the source? With a note that it's best understood in the original Latin?

Jamey Fletcher 70.154.151.196 20:21, 24 December 2006 (UTC)

1 These two sentences need work
2 speed vs velocity
3 Definition
4 Newer results
5 formula in section 2
6 Direction of rotation
7 Escape velocity 50 km above the surface of Venus
8 Multiple sources
9 Gravity well
10 The rocket misconception again
11 Rockets vs. Escape Velocity
12 Constant propulsion problem
13 Derivations Section
14 Misconceptions
15 Wrong image

[edit] These two sentences need work

Someone added these two sentences in the first paragraph:

It is a theoretical quantity, because it assumes that an object is fired into space like a bullet. Instead propulsion is almost always used during the first part of the flight, and to "escape", at no time the escape velocity need to be attained.

Right at the beginning it says this is about objects that are not being propelled, so "the first part of the flight" during which propulsion is used is simply not relevant; this topic does not apply to it, but only to the later part where there is no propulsion. Moreover, it does not make sense to say "propulsion is almost always used", since a comet passing by the Earth that is not pulled into an orbit around the Earth escapes without propulsion, simply because it is always moving at a speed higher than the escape speed at whatever distance from Earth it's at. Moreover, there is no assumption about "being fired like a bullet", since the assumption, stated right in the first sentence, is that this whole thing applies only when there is no "propulsion". The last clause is ungrammatical; it says:

to "escape", at no time the escape velocity need to be attained.

What does that mean? Does it mean an object under propulsion can be lifted to an infinite height? If so, it's not relevant; this is only about objects not under propulsion. More precisely, it is about objects on which no forces act except the conservative gravitational field. How other objects behave, i.e., objects on which other, possibly non-conservative forces act, is simply not part of this topic. This topic treats only objects that are not propelled.

And what is meant by the words "It is a theoretical quantity"? I might have thought it means that in reality gravitational forces other than the Earth act on an object. But after the word "because" it then appears that something else was intended. Michael Hardy 14:43, 7 Sep 2004 (UTC)

Note that the escape velocity from the surface of Earth is not a speed that a spacecraft sent to outer space actually attains: while being propelled the height increases and the corresponding escape velocity decreases.

But if the spacecraft is not going to orbit Earth, but is being sent to photograph Uranus close-up, doesn't it actually go a lot faster than the escape speed at the surface? I seem to recall that the Apollo spacecraft going to the moon moved at something like 10 miles per second during the early part of the trip. Michael Hardy 22:45, 7 Sep 2004 (UTC)

I don't think so, [1] says 10.4 km/s (Earth Fixed Velocity).--Patrick 08:52, 8 Sep 2004 (UTC)

Urhixidur, please explain why this would not be correct:

(Considering the kinetic energies it may seem strange that a speed of 12 km/s (by itself corresponding to 72 MJ/kg) can increase the kinetic energy of the spacecraft from 450 to 900 MJ/kg, but the gain is at the expense of the Earth's kinetic energy, the launch will slightly slow down Earth.)

--Patrick 16:56, 8 Sep 2004 (UTC)

There is no mention of where the vehicle's energy is coming from, and it need not come from the Earth. Consider the Earth and the prepped vehicle as two distinct bodies, co-orbiting the Sun and in contact with each other. Assume the vehicle is at the Earth's far side from the Sun. The vehicle suddenly acquires the requisite extra 12 km/s of forward motion, possibly by ejecting part of its own mass at extremely high velocity in the opposite direction (I chose the vehicle's position so that the ejecta would not blast the Earth's surface and cause complications; here we assume the vehicle and its ejecta both "miss" the Earth itself). The vehicle will indeed eventually leave the solar system (its ejecta will do the same much faster, in all likelihood). In what way has this affected the Earth's momentum or energy? None whatsoever.

There is the matter of the gravitational influence of the vehicle on the Earth and vice-versa, but this can be neglected here. In fact, if you insist on not neglecting it, you'll notice that the vehicle, since it leaves *ahead* of Earth, will lose some of its energy to the Earth's benefit through gravitational interaction (it needs to escape the Earth as well as the Sun). Had the vehicle decided to leave in the opposite direction (which would require a 72 km/s delta-v!), its gravity would indeed slow the Earth very slightly.

The sentence as originally stated introduced a badly formed problem. Giving an object a velocity within a frame of reference gives it energy within that same frame (in this case 12 km/s translating to 72 MJ/kg). Switching to the Sun-centered frame, we see the object go from 30 km/s to 42 km/s and hence its energy go from 450 to 882 MJ/kg, a difference of 432 MJ/kg. Without specifying the rest of the system implicated (what imparted the extra velocity to our object?), we can't make any pronouncements.

Is this explanation clear enough?

Urhixidur 17:44, 2004 Sep 8 (UTC)

Interesting example. I have again considered the energies. Assume that the ejected mass is 1/n times the mass of the spacecraft, then it is ejected at a speed of 12n km/s relative to Earth. The apparent gain of 360 MJ per kg spacecraft can be explained by the fact that the kinetic energy, relative to Earth, of the ejected mass is 72n MJ per kg spacecraft, while relative to the solar system the energy only increases 72n - 360 MJ per kg spacecraft. With a large n as in your example it is clear that the large amount of energy to reach 42 km/s has to be produced anyway in the form of kinetic energy of ejected mass. I wonder whether there is a theoretical minimum amount of energy needed for the acceleration from 30 to 42 km/s; is it actually possible to use some kinetic energy of Earth, by "pushing it away"?.--Patrick 22:12, 8 Sep 2004 (UTC)

Assume, as you do, that the reaction mass (ejecta) is the fraction 1/n of the spacecraft's original mass. In the Earth frame, the initial kinetic energies are zero because nothing's moving. In the Sun frame, the kinetic energies are 450 MJ/kg for either parts (the reaction mass and payload parts). After the explosion, in the Earth frame we have the payload going one way with 72 MJ/kg (for the fraction (n-1)/n of the spacecraft's total mass) and the reaction mass going the other (at speed 12(n-1) km/s) with 72(n-1)² MJ/kg (note the square you missed). The overall (average) energy is 72(n-1) MJ/kg. This must have come from the explosives' potential chemical energy. In the Sun frame, we have the payload now going at 882 MJ/kg, and the reaction mass at 18(7-2n)² MJ/kg, average energy 18(21+4n) MJ/kg, delta 72(n-1) MJ/kg. Energy is conserved in translating between frames.

Urhixidur 22:53, 2004 Sep 8 (UTC)

OK, that seems the same; I used n for what you call n-1, and I expressed everything in kg payload (therefore I do not have the square).--Patrick 02:08, 9 Sep 2004 (UTC)

Say what?! Even if using a unit spacecraft mass, the square of the velocity is still in the picture. Assume n = 10; in that case the craft (9/10 of it) goes at 12 km/s whilst its reaction mass (1/10 of the original mass) goes at 12*9=108 km/s (conservation of momentum). The energy of the former is 72 MJ/kg whilst that of the latter is 5832 MJ/kg --its the square of the velocity, see...

Urhixidur 03:46, 2004 Sep 9 (UTC)

That is per kg reaction mass, for 1 kg payload we have 1/9 kg reaction mass.--Patrick 12:30, 9 Sep 2004 (UTC)

I'm not sure it's to the point, but exhaust speeds of 100 km/s are way, Way, WAY out there. See Spacecraft propulsion#Table of methods and their efficiencies. Normally it's the fuel that'd be 80–90% of the loaded ship.

Somewhere this needs the minimum escape speed from both the Earth & Sun = $\sqrt{11.2^2 + 42.1^2} - 30 = 13.6\ \mathrm{km/s}$ .

—wwoods 06:56, 9 Sep 2004 (UTC)

For rocket propulsion, yes, but this is a gedanken-experiment with "cannon propulsion". In combining Earth and Sun, you are quite right. Another approximation could be to work out the energy differential in moving to the edge of Earth's Hill sphere, and then let the Sun take over.

Urhixidur 11:39, 2004 Sep 9 (UTC)

[edit] speed vs velocity

what would be a better name for the phrase? escape velocity or escape speed? the article implies that speed is more accurate, as it is a scaler. i think this makes no sense, as escape velocity implies a speed to get off a planet, right? for the magnitute of the speed is to be at its minimum, doesn't the angle of launch need to be 90°? therefore it has a direction, and it is a vector quantity - so velocity is far more appropriate?

however i dont want to remove it from the article, as i am not sure i am right. comments? mastodon 22:20, 26 November 2005 (UTC)

The angle of lauch does not matter. That is why it is a scalar. (And scalar is the correct spelling. Michael Hardy 23:02, 26 November 2005 (UTC)

why not? if the angle was 45 degrees from the normal, a launched projectile would spend longer in the higher density part of the gravitational field, so would be more strongly attracted to the body, and would need more of a force, a greater magnitude of speed to escape. am i right? or am i not wrong?

Starting with the escape velocity, the velocity is a function of elevation (see parabolic trajectory). It is true that starting at an angle of 45 degrees the increase of altitude is slower, but also the decrease of speed, because in this case the gravity is not opposite to the velocity.--Patrick 01:07, 1 December 2005 (UTC)

also to be pedantic, as seems the trend (rolls eyes), if the angle was - say - 180° from the normal, the speed would need to be a little bit bigger to escape. comments? mastodon 23:12, 30 November 2005 (UTC)

It applies only when the parabolic orbit does not intersect the planet, hence, in the case of starting from the surface, if the direction is not downward (not lower than horizontal).--Patrick 00:29, 1 December 2005 (UTC)

I added some text about this in the orbit section.--Patrick 01:05, 1 December 2005 (UTC)

It's counterintuitive. The quickest way to understand this is to see that all you need is enough kinetic energy to lift you to infinite height, and that's finite because the field strength decreases fast enough as you go up. Michael Hardy 01:45, 1 December 2005 (UTC)

Question - shouldn't escape velocity = sqrt(2G/R) instead of sqrt(2GR)?

No, but you quoted the article wrong. The article said it was sqrt(2gR), where the "g" is lowercase, i.e., the acceleration of gravity at the earth's surface, or about 9.8 m/s². However, I think you are confused with the oft-given result (in fact, it was derived earlier in this article) that the escape velocity is equal to sqrt(2Gm_e/r), where m_e is the mass of the earth and the "g" is uppercase, i.e., the universal gravitational constant, or about 6.7x10^-11 Nm²/kg², and which is also correct. However, if you use the relation that g=Gm_e/r² (which is really the definition of g), you'll be able to go between these two equivalent expresssions for the escape velocity.Jrdx 02:32, 5 December 2006 (UTC)

I'm still not convinced it can be called speed. It seems to me that since velocity is a vector, only the part of the vector that is directly opposing gravity would be helping the object escape. The other part of the vector would only be causing it to spin around the larger body. Am I missing something? --Paulie Peña 23:33, 1 March 2006 (UTC)

Indeed, you are missing something. You are absolutely right that this result is counterintuitive. But think about the sum of kinetic energy and potential energy. If the projectile's kinetic energy at its present position is more than its potential energy at infinite distance from the planet, then it will escape. Michael Hardy 00:34, 2 March 2006 (UTC)

A large horizontal speed also helps the object escape.--Patrick 02:52, 2 March 2006 (UTC)

Correct. If the motion is ONLY horizontal, with sufficient speed the object will still escape. Michael Hardy 02:42, 5 December 2006 (UTC)

Speed and velocity have two very different meaning in physics. This topic cannot be changed to escape speed. Also assuming the escape velocity of earth, that is standing on the surface of the earth, is EV, then it doesn't matter which direction the object is moving. As long as it's velocity is >= EV, it will escape earth's gravitational pull. You can throw it straight up 0 degree, 45 degree angle or event straight down 180 degree angel assuming the object can pass thru earth. Proof. Assuming you throw a ball straight down with initial velocity of EV. As the ball goes toward center of earth, it's speed will increase due to gravity. As it is at the center of earth, the ball's speed will be at its greatest. Going past it, the speed will decrease because gravity is now pullling it back. As the ball reaches the surface at the other end, it's velocity of again be EV, and it will go straight up (or down if you want to look at it that way) toward the sky. If the object is throw horizontally at 90 degree angle, the ball should just orbit the earth. Think of satellites, they are always moving parpendicular to earth. If their direction of movement is tilted toward earth, they will fall to earth. If tilted away, they will move into space. This also answer the above question of 'large horizontal speed'. And proofs if it is thrown at 45 degree angle, it will still escape earth's gravity. --NYC 16:36, 13 March 2007 (UTC)

"Think of satellites, they are always moving parpendicular to earth" Well, doesn't really relate to article, but: the satellites are always moving in the direction of the earths surface at any point, and hence are actually moving in a direction tangent to it. --Freuga (talk) 00:22, 12 March 2008 (UTC)

[edit] Definition

Patrick, I disagree with your reverting to the previous version, claiming that mine was "not an improvement." I have run the two versions by a number of people, who all agree that my version is easier to read without losing any of the content. Of course we're talking about "physics," and of course it's for a given gravitational field. The current version is redundant. - Ztrawhcs.

"In physics" is the usual way to provide context. Escape velocity is a property of a gravitational field and a position, it does not depend on the object. Your version ignores dependence of position, and suggests dependence on the object. "its gravitational field" is also confusing. --Patrick 09:52, 27 January 2006 (UTC)

your version ... suggests dependence on the object ... Touche. Good point. I still think, however, that we need not completely sacrifice readability. The intro paragraph doesn't have to scare people away with its complexity. I can just imagine an entire generation of 10 year old would-be scientists seeing the wikipedia entry on Escape Velocity and turning away in brain-twisting horror, deciding never to become scientists but instead to become garbage men. I hope you're prepared to deal with that. Ztrawhcs 21:05, 2 August 2006 (UTC)

[edit] Newer results

Somebody should review the following references, our current data seems inexact:

Annexed the number that appears in Wikipedia on escape velocity from Solar

System from Earth: 43.6 km/s. In agreement with my paper A note on Solar Escape Revisited * the correct figure is 16.6 km/s. When we get 43.6km/s or 13.6 km/s we neglect the recoil kinetic energy of the earth and that is nonnegligible in Sun's coordinate frame.

The escape velocity from a position in a field with multiple sources is

derived from the total potential energy per kg at that position, relative to infinity. The potential energies for all sources can simply be added. For the escape velocity this results in the square root of the sum of the squares of the escape velocities of all sources separately.*

For example, at the Earth's surface the escape velocity for the combination

Earth and Sun is √(11.2² + 42.1²) = 43.6 km/s. As a result, to leave the solar system requires a speed of 13.6 km/s relative to Earth in the direction of the Earth's orbital motion, since the speed is then added to the speed of 30 km/s of that motion.* Diaz-Jimenez_Anthony_P._French-MIT_Professor,_American_Journal_of_Physics,_56,_85,_1988 Diaz-Jimenez_Anthony_P._French-MIT_Professor,_American_Journal_of_Physics,_56,_86,_1988

(from OTRS) David.Monniaux 08:10, 16 February 2006 (UTC)

You mean 13.6 should be 16.6? How is that computed?--Patrick 02:44, 18 February 2006 (UTC)

Pr Diaz-Jimenez sent the Foundation several published papers that revisit the escape velocity. I can forward them to you by email (you can contact me with "send mail to"). David.Monniaux 09:23, 18 February 2006 (UTC)

Well what speed do e.g. rockets typically have to attain? If 16.6 is right then they would have to have attained that speed already. 203.218.86.162 09:28, 31 May 2006 (UTC)

[edit] formula in section 2

i have swopped the approx= and = because v is approximately the thing in the root, which exactly equals 11200. 203.218.86.162 09:28, 31 May 2006 (UTC)

[edit] Direction of rotation

I have added some clarifications on the direction of rotation of the body. Though rotation is not a must to account for the escape velocity, the direction in which the escaping body is launched is important, if the main body is rotating. --Wikicheng 04:06, 29 June 2006 (UTC)

Not at all. The escape velocity doesn't change. Rotation is irrelevant. The paragraph

"The escape velocity relative to the surface of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s to the east at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to Earth to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s relative to Earth. The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral in Florida and the European Centre Spatial Guyanais, only 5 degrees from the equator in French Guiana."

should be deleted or atleast made clearer. What you are referring to is relative velocity. For example, if I am walking away from you at 1 m/s, I have a right to say it is you who are moving away from me at 1 m/s even thought you are standing perfectly still and it is I who is actually moving. The velocity difference between launching due east and west from Cape Canaveral is because Cape Canaveral is also moving. If you view the launch from the Sun, it would observe the rocket has the same velocity whether lauching due east or west with respect to Earth.

Also what does it mean "10.735 km/s relative to Earth to escape" and "11.665 km/s relative to Earth"? Did the author mean relative to where it is launched? It cannot be relative to Earth since relative to Earth means relative to center of Earth. --NYC 17:00 13, March 2007 (UTC)

[edit] Escape velocity 50 km above the surface of Venus

I'm working on the Colonization of Venus article right now, and part of it talks about floating cities at 50km above the surface where the atmospheric pressure and temperature are the same as Earth. What would be escape velocity be there? It doesn't seem like it would be that much different from the surface given that even 9000 km from Earth doesn't even halve the number. Venus rotates extremely slowly but these theoretical cities would be up where the wind velocity causes them to whip around the planet every four days. Mithridates 05:58, 9 August 2006 (UTC)

[edit] Multiple sources

I find this section confusing. Let me give an example of why I don't understand this. Let's pretend that the earth is farther away from the sun than it really is, so that the escape velocity from the sun at this distance is 11.2 km/s, just as for the earth. So then we get that the escape velocity from sun/earth, with earth orbiting at this distance, would be sqrt(11.2^2 + 11.2^2) = 15.8 km/s. Now earth's (circular) orbital speed at this distance will be .7071*11.2 = 7.9 km/s, so we predict that we need to go at a speed of 15.8 - 7.9 = 7.9 km/s (relative to earth) in the direction of earth's orbit. But THIS IS LESS THAN EARTH'S ESCAPE VELOCITY! So, relative to the earth, the speed we need to start out with to go out to infinity is now LESS than it would be if the sun were not there?? Kier07 07:48, 4 September 2006 (UTC)

I didn't verify your number but I'll assuming they are correct. Then yes the velocity needed to escape Earth and Sun in your example is going to be less then the escape velocity of Earth alone. What the section doesn't say is, the object is allowed to "fall through" Earth. So your object starts up moving away from Earth at 7.9 km/s, eventually due to Earth's gravity, it will turn around and starting moving toward Earth. If the path doesn't collide with Earth, it will escape. If it's path collides with Earth, it's assumed to be able to fall throught it. The actualy path the object takes to escape is a swirl. It may swirl around Earth, or Sun depending on the initial conditions. Please also remember Earth is also moving so the object would not simply oscillate back and forth through Earth's center. --NYC 21:14, 14 March 2007 (UTC)

[edit] Gravity well

One section is named gravity well, yet it doesn't seem to have anything to do with gravity wells (which are things like black holes that distort spacetime as I understand from the article. Instead it's talking about a theoretical hole in a body through which an object can be dropped allowing it to reach the center. I believe the section needs to be renamed, perhaps someone with a good understanding of the concepts discussed there could find a more appropriate name? Richard001 08:59, 1 October 2006 (UTC)

Very, very late reply, but gravity wells are just the gravitational field around a planet or other body that has been mapped to a plane in three-dimensional space, where the curvature of that surface represents how strong the gravitational potential energy would be at all positive and negative Z coordinates above and below a corresponding XY coordinate on the plane; producing a hollow in the middle because potential energy builds as distance increases (the farther up a hill you go, the more potential energy you have, after all). It's merely a representation of the potential energy of gravity to allow humans to understand it and not an actual phenomenon. --Jtgibson (talk) 23:42, 27 January 2008 (UTC)

[edit] The rocket misconception again

"In physics, escape velocity is the speed where the kinetic energy of an object is equal to the magnitude of its gravitational potential energy. Escape velocity only applies to objects that have no propulsion or thrust. An object under power, like a rocket, could leave the Earth's gravity at any speed." And yet the article then goes on to state that the escape velocity at earth is 11.2 km/s. If kinetic energy needs to equal gravitational potential energy, then how can you put a number on the escape velocity without knowing the mass of the particle that may or may not be escaping? -- kanzure (talk) 14:23, 7 March 2008 (UTC)

Edit. I note that mass cancels out. Perhaps this can be included in the article. -- kanzure (talk) 14:24, 7 March 2008 (UTC)

[edit] Rockets vs. Escape Velocity

I was pleased to find the first paragraph clearly stating that the concept of escape velocity only applies to non-self-powered objects.

But then in paragraph 4 we get "a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to Earth to escape".

This seems to be a common misrepresentation in popular descriptions of space programs -- that rockets must achieve escape velocity to somehow "break free" of some imagined gravitational "barrier".

If I'm not mistaken, there's absolutely no requirement for escape velocity for a self-powered rocket -- fuel usage aside, it can take off at 1 mile per hour and just keep rising at 1 mile per hour for a thousand hours. No "barrier" to break through.

If that's accurate, the paragraph in question should be edited to describe an "unself-powered object like a bullet being shot" rather than a rocket taking off -- and a dedicated paragraph mentioning that rockets needing escape velocity is a common misconception seems advisable if the confusion is turning up even in this article.

Frankly, your remarks seem enormously confused. Rockets must indeed achieve escape velocity in order to escape. The fact that all this applies only to objects acted on by no forces except gravity does not make it inapplicable to rockets. Rockets cease to be "self-powered" when their engines stop firing, and then everything in this article applies. Certainly a rocket can continue to rise from the earth's surface at 1 mph for 1000 hours if it's got enough fuel, but what's that got to do with anything this article says? The article is about how the rocket (or other object) behaves when it's NOT doing that. The "misconception" you write of is not a mistconception at all. Michael Hardy 21:42, 19 January 2007 (UTC)

You're using the word "rocket" to mean "current rocket technology". I'm using the word "rocket" to mean "a self-powered projectile" in theoretical physics.

I'm saying it's confusing to start out with abstract theory -- where "self-powered projectile" is in contrast to "cannon ball" -- and then give a supposed illustration of that abstract theory with a device that is combining the two principals.

There needs to be an explanation about present-day rockets going into a ballistic phase at which point escape velocity comes into play.

The quote above is completely false in stating "requires an initial velocity" -- we've all seen rockets lumbering up off the launch pad.

And the point I actually came back here to bring up is, doesn't it take orbital velocity (so called) and not escape velocity (so called) to put a rocket (under ballistic propulsion) into an Earth-circling orbit?

Wouldn't leaving the Earth at escape velocity, ballistically, with no further power usage, send the rocket into an infinite parabolic or hyperbolic orbit, ending up somewhere Beyond Antares... (Not a good look for your weather satellite). —The preceding unsigned comment was added by 75.6.245.249 (talk) 10:27, 22 January 2007 (UTC).

Whether an object is self propelled or not, it has to reach the escape velocity to get out of earth's gravity. Please note that the escape velocity decreases with distance from earth. Once the object reaches the escape velocity for that height, it need not be self propelled any longer. If an object is self propelled to keep going at a steady rate of 10km/hr for a very very long time, eventually it reaches a point where the escape velocity is 10km/hr and it will be free from earth's gravity. At that moment, even if the self propulsion stops, the object will not return. If 5km per sec is the maximum velocity you can attain, then you need to take the object (using self propulsion or otherwise) to a height where the escape velocity is 5 km per sec, give it a velocity of 5 km per sec for it to escape. Basically, the object needs to be self propelled to a height where the velocity of the object crosses the escape velocity for that height-- WikiCheng | Talk 12:18, 22 January 2007 (UTC)

[edit] Constant propulsion problem

What will happen if an object is sent in the air from the Earth's surface with a speed less than escape velocity but with a constant propulsion force? Will it be able to escape earth gravity? Let see the problem under another angle for you to be sure you understand what I mean. Imagine we have a very long staircase which reaches the moon, by climbing it even by foot, will one be able to escape earth gravity and be in orbit?. Objects which do not reach the escape velocity speed fall on Earth because of the gravity resistance. But if there is a constant propulsion force, this resistance would be cancelled right? —The preceding unsigned comment was added by 24.201.98.14 (talk) 17:21, 22 January 2007 (UTC).

If you provide a constant propulsion force greater then gravity then you will escape. If you provide a propulsion force = to gravity and you have a none zero initial velocity, you will esacpe. If you had zero initial velocity you will remain where you are forever. If the propulsion force is less then gravity, you will fall. Simply put, if gravity is pulling it down, and you are pushing it up, if you are pushing harder then gravity, it will move up. If gravity is stronger it falls down. Initial speed is irrelevant. --NYC 17:16 13 March 2007 (UTC)

[edit] Derivations Section

There is a definite problem with the derivations section. There are two sections: one using g and r, and a second using G and M. The distinctions between these sections are redundant because g is derived from G, M, and r:

$g = G M / r$

In Physics, real Physics, the stuff that real world physicists work with, these two derivations are one and the same!

Stltcom 21:36, 13 July 2007 (UTC)Stltcom

[edit] Misconceptions

There is a quote in the misconceptions section that states the following: "A practical application that might involve an object leaving earth orbit at speeds much lower than the escape velocity is the hypothetical space elevator." I believe that this statement is incorrect. At the bottom of the tether, the object is in fact moving at relatively low speeds (the earth's surface at the equator is moving at roughly 1000 mph), but by the time it climbs to the end of the cable, it has accelerated to tangential speeds of thousands of miles per hour. In addition, at the end of the cable, the potential energy of the object is significantly less, which reduces the escape velocity. So the escape velocity decreases significantly, the object's velocity increases significantly, and theoretically the object could exceed the escape velocity with a sufficiently long tether. If the object leaves the end of the tether and no longer provides any propulsion of any kind, and if the object does in fact truely "escape" from the earth, then it has been accelerated to speeds in excess of the escape velocity. I believe the mistake made by whoever wrote that quote was in considering only the speed relative to the surface of the earth (the climbing speed). The fact that the frame of reference is rotating approximately once per day has a significant impact on the math that was not considered.

137.240.136.81 22:25, 11 September 2007 (UTC)

Further, I do not believe the included image adds anything to this article, in fact, the image chosen happens to be incorrect as the Space elevator requires a geosynchronous orbit and such an orbit cannot take place at a planet's pole. I'm removing the link to the image. -Verdatum (talk) 18:35, 27 November 2007 (UTC)

The misconception is actually like this: "The minimum escape speed is the speed an object must be going to get out of earths gravity well." This speed is around 25,000mph (whatever), however, you could really leave the earths gravity well at 5mph if you had a rocket to carry that much fuel. The misconception is that the escape speed needs to be understood as ballistic speed, that is, with nothing slowing it down except the acceleration of gravity. Of course, air resistance slows you down, but the physics idea usually neglects that. I have had to explain this to so many people (high school students mostly) who understood the idea to mean "You can never ever get out of earths gravity unless you are going 25,000mph (whatever)." —Preceding unsigned comment added by 129.93.28.91 (talk) 15:48, 17 April 2008 (UTC)

[edit] Wrong image

Isaac Newton's analysis of escape velocity. Projectiles A and B fall back to earth. Projectiles C and D achieve an orbit at a fixed height. Projectile E achieves escape velocity.

This image, which used to be at the top of the article, is not relevant. It shows objects being launched parallel to the surface of a planet. Escape velocity applies to objects launched directly away from a planet (perpendicular to the surface). I have removed the image. E James (talk) 22:25, 31 January 2008 (UTC)

I don't think you are correct. As the article tries to explain, escape velocity is more properly called escape speed. It doesn't matter in which direction the velocity vector initially points (as long as the resulting trajectory does not intersect the plane surface or atmosphere). The analysis only depends on the kinetic energy plus the potential energy being non-negative. I've restored the image.--agr (talk) 01:00, 1 February 2008 (UTC).

Yes, you are correct. I thought I had it figured out after reading the article and the discussion yesterday, but I was wrong. Thank you for restoring the image.

E James (talk) 17:09, 1 February 2008 (UTC)

I think the image's caption is incorrect, however: C does achieve an orbit with fixed height as claimed, but D does not. I'll edit the caption.

Laschatzer (talk) 16:37, 2 June 2008 (UTC)