What would it be like to be at a Lagrange Point?

[PPERERA]

According to this NASA factsheet (http://www.nasa.gov/pdf/664158main_sls_fs_master.pdf ) on the Space Launch System (SLS), NASA identifies missions to a Lagrange point as a possibility. From what I understand, a Lagrange point is simply a point where the gravitational fields of two massive objects--such as the Earth and Sun--cancel each other out in accordance with Newton's Law of Universal Gravitation.

Does the Lagrange point shift and would a spacecraft have to respond to this shift in order to stay at the Lagrange point?
What would it be like--for both the spacecraft and its crew--to be at the Lagrange point?
What could we do at a Lagrange point?
And in what way could Lagrange points be useful to manned space travel?

Thanks in advance for the replies. :)

 

[phinds]

In what way do you think being at a Lagrange point would be any different for the crew than being at any other point in space? I mean, weightless is weightless. What do you think would be different?

 

[Simon Bridge]

From what I understand, a Lagrange point is simply a point where the gravitational fields of two massive objects--such as the Earth and Sun--cancel each other out in accordance with Newton's Law of Universal Gravitation.

This is not correct.

In a nutshell:
The Lagrange point is the location where the orbital period about the primary matches that of the secondary.
A useful characteristic is that they are stable - vis: an object placed there stays there.
https://en.wikipedia.org/wiki/Lagrangian_point

Does the Lagrange point shift and would a spacecraft have to respond to this shift in order to stay at the Lagrange point?

No.

What would it be like--for both the spacecraft and its crew--to be at the Lagrange point?

Pretty much the same as any free fall.

What could we do at a Lagrange point?

Whatever we want to.

And in what way could Lagrange points be useful to manned space travel?

They'd be handy places to put stuff we want to find later.

A lot has been written about Lagrange points - have you tried googling the topic?
i.e. NASA (your source) are happy to tell you what sorts of things L points are useful for.
http://www.nasa.gov/mission_pages/genesis/media/jpl-release-071702.html

 

[Chronos]

Lagrange points tend to be a bit crowed nowadays.

 

[Bandersnatch]

Lagrange points are static solutions of the restricted 3-body problem. It means that in principle a small body in a gravitational system with two massive bodies, orbiting each other in circles, can remain in those points in a static orbit (i.e., does not move w/r to the two bodies), all in one plane.

These are 'points' only if you view them in a rotating frame of reference. For all intents and purposes they are actually orbits.

The way orbits work, is that the closer you orbit a massive body, the faster you need to go. From this follows that if you put your spacecraft in an orbit that is closer or farther to the Sun than Earth, it will drift about across the sky, regularly getting on the opposite side of the Sun and back. That's usually not very handy for maintaining contact with said craft.
Putting a craft on the same orbit as Earth is not going to work either, as it'll get removed from it by Earth's attraction.

In Lagrange points, the gravitational forces from two massive bodies add up exactly in the right way to allow an orbit of the same period as the period of the two bodies (which orbit each other's centre of mass). The forces cancel out there only in a rotating reference frame (centrifugal force cancelling gravity). In a non-rotating reference frame, i.e. looking at the system from a static vantage point, the forces from the two massive bodies add up to just the right amount to keep the smaller body in an orbit of a particular radius and a particular velocity.

However, of the five points, only two: L4 and L5 are stable. A body in those points that gets nudged by some perturbation will generally tend to get back to where it was (see: tadpole orbit). A body in any of the other 3 points that gets nudged by any amount at all will never return there, drifting farther and farther.

It's easy to notice that the real solar system is not an idealised 3-body system, so those solutions are just approximate for real bodies. I disagree with @Simon Bridge here: these points shift a bit all the time because of things like eccentricity and inclination of orbits, influence of other bodies, and pretty much everything that throws a wrench in the idealised scenario described in the first paragraph of this post.

What this means, is that you may place an object in L4 or L5 and it'll stay roughly there, oscillating a bit around the exact point, even without any means of propulsion. That's why those are populated by asteroids. If you place a craft in L1, L2 or L3, you need to provide it with some means to correct the inevitable deviations.
There are ways to minimise such need for corrections (see: Lissajous orbit).

Being in a Lagrange point is like being in any other orbit - you're in free-fall and there's nothing special about it as far as what you feel.
The usefulness of those points is that it allows to place objects there that will stay in the same part of the sky (in the sidereal sense) rather than move about due to a different relative orbital velocity. It's sometimes nice to have a probe in one place.