What is the escape velocity of a neutron particle (not neutron star) Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) 2019 Moderator Election Q&A - Question Collectionwhat is the difference between a blackhole and a point particleHas anyone else thought about gravity in this way?Why is there an escape velocity?How does escape velocity relate to energy and speed?What is the relation between orbital velocity and escape velocity in strongly relativistic situations?How can escape velocity be independent of the direction of projection of a body?How can escape velocity and gravitational potential be higher in weaker gravitational fields?Escape velocity at an angleNeutron star core understandingIs this definition of “escape velocity” correct?What happens if a neutron flies towards a nucleus?
How to find all the available tools in mac terminal?
Fantasy story; one type of magic grows in power with use, but the more powerful they are, they more they are drawn to travel to their source
Is it common practice to audition new musicians 1-2-1 before rehearsing with the entire band?
Should I use a zero-interest credit card for a large one-time purchase?
Do I really need to have a message in a novel to appeal to readers?
What is the meaning of the simile “quick as silk”?
What is the escape velocity of a neutron particle (not neutron star)
Where are Serre’s lectures at Collège de France to be found?
Is CEO the profession with the most psychopaths?
Why are the trig functions versine, haversine, exsecant, etc, rarely used in modern mathematics?
8 Prisoners wearing hats
Would "destroying" Wurmcoil Engine prevent its tokens from being created?
Is there such thing as an Availability Group failover trigger?
Can you use the Shield Master feat to shove someone before you make an attack by using a Readied action?
Do I really need recursive chmod to restrict access to a folder?
Crossing US/Canada Border for less than 24 hours
What would be the ideal power source for a cybernetic eye?
Maximum summed powersets with non-adjacent items
How do I find out the mythology and history of my Fortress?
Dating a Former Employee
Can melee weapons be used to deliver Contact Poisons?
Circuit to "zoom in" on mV fluctuations of a DC signal?
Is it ethical to give a final exam after the professor has quit before teaching the remaining chapters of the course?
Why didn't Eitri join the fight?
What is the escape velocity of a neutron particle (not neutron star)
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
2019 Moderator Election Q&A - Question Collectionwhat is the difference between a blackhole and a point particleHas anyone else thought about gravity in this way?Why is there an escape velocity?How does escape velocity relate to energy and speed?What is the relation between orbital velocity and escape velocity in strongly relativistic situations?How can escape velocity be independent of the direction of projection of a body?How can escape velocity and gravitational potential be higher in weaker gravitational fields?Escape velocity at an angleNeutron star core understandingIs this definition of “escape velocity” correct?What happens if a neutron flies towards a nucleus?
$begingroup$
I'm not sure if this question makes sense (if not maybe you can explain why)
But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right?
I know the gravity force generated by a neutron is really low, since it is also really small in size, what happens with that force when we are really close? is not almost infinite?
quantum-mechanics gravity quantum-gravity neutrons escape-velocity
$endgroup$
add a comment |
$begingroup$
I'm not sure if this question makes sense (if not maybe you can explain why)
But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right?
I know the gravity force generated by a neutron is really low, since it is also really small in size, what happens with that force when we are really close? is not almost infinite?
quantum-mechanics gravity quantum-gravity neutrons escape-velocity
$endgroup$
add a comment |
$begingroup$
I'm not sure if this question makes sense (if not maybe you can explain why)
But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right?
I know the gravity force generated by a neutron is really low, since it is also really small in size, what happens with that force when we are really close? is not almost infinite?
quantum-mechanics gravity quantum-gravity neutrons escape-velocity
$endgroup$
I'm not sure if this question makes sense (if not maybe you can explain why)
But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right?
I know the gravity force generated by a neutron is really low, since it is also really small in size, what happens with that force when we are really close? is not almost infinite?
quantum-mechanics gravity quantum-gravity neutrons escape-velocity
quantum-mechanics gravity quantum-gravity neutrons escape-velocity
asked 11 hours ago
EnriqueEnrique
1385
1385
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^-15$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $sqrt2Gm/r=1.7times10^-11$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
$endgroup$
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
add a comment |
$begingroup$
I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_esc=sqrt2GM/R$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67times 10^-27$ kg), and radius ($sim 1.5$ fm) comes to about $1times 10^-11$ m/s.
New contributor
$endgroup$
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "151"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f473333%2fwhat-is-the-escape-velocity-of-a-neutron-particle-not-neutron-star%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^-15$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $sqrt2Gm/r=1.7times10^-11$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
$endgroup$
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
add a comment |
$begingroup$
I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^-15$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $sqrt2Gm/r=1.7times10^-11$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
$endgroup$
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
add a comment |
$begingroup$
I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^-15$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $sqrt2Gm/r=1.7times10^-11$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
$endgroup$
I know the gravity force generated by a neutron is really low
To define the force, you need to define a second object, with some mass, that is being acted on. That can't be a second neutron, because then there would be an attraction due to the strong nuclear force that would be much greater than the attraction due to gravity. You would want to talk about a particle such as an electron or some other lepton that doesn't participate in the strong force.
what happens with that force when we are really close? is not almost infinite?
The neutron is similar to an object like the earth, in that its mass is distributed over some volume. Therefore you can't get to zero distance from all its mass. The radius of a neutron is roughly 0.8 fm ($10^-15$ m). (It's fuzzy, but the number is well defined to within about 20%, if you take some criterion like where the density falls off to half of the value at the center.) Using this radius, the escape velocity is $sqrt2Gm/r=1.7times10^-11$ m/s. The extreme smallness of this velocity confirms that gravity is too weak to matter at the atomic scale.
In reality, if you take a particle such as an electron and try to put it right at the surface of the nucleus, constraining its position to within less than ~1 fm, then by the Heisenberg uncertainty principle, it will be moving many orders of magnitude faster than escape velocity. To get this zero-point velocity to be as small as the escape velocity, you would need a very massive particle -- much more massive than any subatomic particle we know of.
answered 10 hours ago
Ben CrowellBen Crowell
54.6k6165315
54.6k6165315
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
add a comment |
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
is really low, I canno understand how a black hole can exist then, I mean for a black hole we need a very dense object right? and what is more dense than a neutron?
$endgroup$
– Enrique
8 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
@Enrique: To make a black hole, the relevant figure is not density, which would scale like $m/r^3$, but $m/r$. It actually wouldn't make sense if a neutron was an ultrarelativistic object. See physics.stackexchange.com/questions/12404/…
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
$begingroup$
Wouldn't a proper escape velocity take into consideration all 4 fundamental forces?
$endgroup$
– corsiKa
46 mins ago
add a comment |
$begingroup$
I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_esc=sqrt2GM/R$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67times 10^-27$ kg), and radius ($sim 1.5$ fm) comes to about $1times 10^-11$ m/s.
New contributor
$endgroup$
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
add a comment |
$begingroup$
I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_esc=sqrt2GM/R$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67times 10^-27$ kg), and radius ($sim 1.5$ fm) comes to about $1times 10^-11$ m/s.
New contributor
$endgroup$
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
add a comment |
$begingroup$
I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_esc=sqrt2GM/R$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67times 10^-27$ kg), and radius ($sim 1.5$ fm) comes to about $1times 10^-11$ m/s.
New contributor
$endgroup$
I'm sure a full quantum mechanical explanation exists that takes complexities at these size scales into account. But using the classical formula for escape velocity ($v_esc=sqrt2GM/R$, derived by determining the total amount of work to move a massive point particle from the surface of a massive object to an infinite distance), an estimate of the escape speed using the neutron mass ($1.67times 10^-27$ kg), and radius ($sim 1.5$ fm) comes to about $1times 10^-11$ m/s.
New contributor
New contributor
answered 10 hours ago
Cam HoughCam Hough
211
211
New contributor
New contributor
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
add a comment |
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
1.5 fm sounds more like the diameter, not the radius.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's not well-defined, just an approximation to get an estimate using classical concepts. (en.wikipedia.org/wiki/Atomic_nucleus)
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
$begingroup$
It's much better defined than a factor of 2. You simply made a mistake.
$endgroup$
– Ben Crowell
10 hours ago
4
4
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
$begingroup$
My point is using the classical description for escape velocity puts us so far away from precision of that degree that there's no point worrying about it. Call it a mistake if you want.
$endgroup$
– Cam Hough
10 hours ago
add a comment |
Thanks for contributing an answer to Physics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f473333%2fwhat-is-the-escape-velocity-of-a-neutron-particle-not-neutron-star%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown