# Lagrangian Point, L1.

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#### hhhmortal

##### Guest
Hi, I'm wondering if a servicing mission to the L1 lagrangian point will ever be possible assuming launch costs are significantly reduced. If so how long will it take to get to the L1 point. At 1.5 million km away I expect a considerable amount of months.

Also, once the space craft is outside the Earth's magnetic field the radiation dosage to astronauts will increase dramatically, how much per month will this radiation dosage be, assuming current space shuttle technology is used.

Thanks.

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#### Saiph

##### Guest
well...under the conditions you list, yes, it will be possible.

We'll need better, cheaper rockets.

The time depends, of course, on how good the rockets are.

E

#### emperor_of_localgroup

##### Guest
hhhmortal":3gqsi266 said:
Hi, I'm wondering if a servicing mission to the L1 lagrangian point will ever be possible assuming launch costs are significantly reduced. If so how long will it take to get to the L1 point. At 1.5 million km away I expect a considerable amount of months.

Also, once the space craft is outside the Earth's magnetic field the radiation dosage to astronauts will increase dramatically, how much per month will this radiation dosage be, assuming current space shuttle technology is used.

Thanks.

I'm glad some one started a thread on Lagrangian Point. If there is a Lagrangian Point expert here, please explain to me. I always had trouble grasping the mechanism of a Lagrangian Point. L1 is very simple and understanble, but existence of L2, L3, L4 and L5 puzzles me. I understand the math, but physical environments in those regions seem to be not very useful. The points seem to be 'geo-synchronous' or 'solar-synchronous' points that move along with the earth around the sun, but if the math is correct, an object in those regeions must also move 'itself' with certain speed. Then where is the benefits if a spaceship must power itself to go around the sun? I'm sure, I have missed something , somewhere.

If the spaceship does not require its own power to revolve around the sun, then comes other intriguing questions:
a) Are the planets in our solar system at some form of Lagrangian Points?
b) Is the sun in a galactic Lagrangian Point?

Because all these massive objects perpetual motions baffle me.

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#### MeteorWayne

##### Guest
Lagrangian points are just places where the gravitational force from two objects is balanced. In reality, they are not stable over long periods (astronomical long periods0

And object in orbit does not require any power. That's what an orbit is.The earth has sufficient "sideways" speed in it's orbit so that it falls toward the sun at exactly the same rate as it moves in it's orbit. No further energy is required. That's the same for any planet or spacecraft orbiting the sun.

What the Lagrange points do (for earth, say) is the distance between the earth and an object in the L4 or L5 point will remain the same distance from earth, because it will be orbiting the sun at the same speed, and it won't fall toward the earth because the pull from the sun and earth are the same.

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#### Saiph

##### Guest
Actually MW, you're not quite right on the specifics of LP's.

Not even at L1, the point between the earth and sun, or more generically between the primary and secondary bodies (I'll use sun & earth to avoid confusion) is the gravity is balanced in the traditional sense.

What the points are, are points of equipotential, where the gravitational potential, due to the interactions of the sun and earth, is the exact same as that felt by the earth. In all cases the force of gravity from the sun is greater than the earths.

What this means is that an object placed at a lagrange point will orbit at the same speed (i.e. period) as the earth. This is great for stationing observation satellites, as they won't drift off in the solar system and go beyond easy communication range (like the back side of the sun).

There is a small problem, in that points 1,2, & 3 are unstable. They're balancing points, and any deviation will cause the satellite to drift off, away from the magic sweet spot, and begin to orbit at a different period...and unsynch with the earth. For these, imagine a pen, finely balanced on it's tip upon your desk. It'll stay there, until something disturbs it...then it falls over.

Here's how it works, broken down point by point:

L1: Is closer to the sun than the earth, and objects at that orbital radius would normally orbit faster than the earth. However, the earth tugs away from the sun there in such a way as to lessen (but not negate!) the sun's pull to be a force equal to that which the sun pulls on the earth.

Same force produces the same orbital period.

L2: Positioned further from the sun than the earth, I.e. opposite the earth from L1 would normally have objects orbit slower, as the suns gravity is weaker at that greater distance. However the COMBINED gravitational pull from the sun and earth, increase the gravitational pull there...to equal that which the sun exerts upon the earth...

Same force produces the same orbital period.

L3: Is on the side opposite the sun, from the earth..slightly beyond earths normal orbital radius. Again, the COMBINED gravity from earth and sun mean that at that slightly greater distance, the satellite would still feel the same force as the sun exerts upon the earth.

Same force produces the same orbital period.

L4 and L5 are a little screwier, and they aren't points, but 'zones' and are actually quite stable. Any object there acts more like a pendulum, than a balanced object. It may wander around a bit...but it's about the common center, and will always return unless disturbed.

These two 'points' are actually at earths orbital distance. The nifty thing about them is that an object placed there will always stay at the same spot in relation to earth. They won't drift away and get closer, or further by any large amount. All other regions on earths orbital track are unstable, and objects will gradually drift away and disperse.

What happens here is a complex dance with the earth and the sun, and deals with how objects move in obeyance to keplar's laws of planetary motion.

Basically if it moves outwards, the forces act to pull on it, drain it of energy, and it falls inwards...speeds up, and gets pulled on to add energy...causing it to shift outwards...and it cycles around and around the center point, never straying very far unless something from 'outside' (say Jupiter) gives it a sufficient kick to get away from the sweet spot.

These two are the hardest to visualize, and explain. I'll see if I can come up with a good easy to grasp illustration or description to help youother than that generalized piece I just handed you

M

#### MeteorWayne

##### Guest
That is what I was trying to say, but had some appointments to attend to, and in any case, my explanations would not have been as clear as yours. Thanx!

Wayne

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#### orienteer

##### Guest
Does all travel from the Earth to the moon have to travel through L1? Is L1 large enough to allow a space station to park there without blocking travel? To park at L1, would you require as much braking thrust as you required forward thrust to get there? How about magnetism? Could the force of gravity be balanced against the force of the magnetic field to create a new stationery spot? Why isn't the moon drawn toward a L point?

So much sci-fi talks about using these points, but they never explain the cost of set up.

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#### MeteorWayne

##### Guest
orienteer":2ggdoy6c said:
Does all travel from the Earth to the moon have to travel through L1?
No, in fact I don't believe any have.

Is L1 large enough to allow a space station to park there without blocking travel? To park at L1, would you require as much braking thrust as you required forward thrust to get there?
In general, spacecraft at L1 have taken slow routes to get there so they approach at slow speed and don't need much of an adjustment in velocity.

Irrelevant

Could the force of gravity be balanced against the force of the magnetic field to create a new stationery spot?

What magnetism?

Why isn't the moon drawn toward a L point?
Because L points don't "draw" anything toward them. They are just quasistable places if you get there. The moon is nowhere near any of the Sun-Earth L points.

However, the Moon and Earth create another set of less stable L pointsof their own!

MW

PS, Try looking at this:

http://en.wikipedia.org/wiki/Lagrangian_point

C

#### CalliArcale

##### Guest
emperor_of_localgroup":3n3cw03z said:
If the spaceship does not require its own power to revolve around the sun, then comes other intriguing questions:
a) Are the planets in our solar system at some form of Lagrangian Points?
b) Is the sun in a galactic Lagrangian Point?

The second one's easier to answer: no. In fact, the Sun isn't really orbiting the galactic center, at least not in the sense that the Earth is orbiting the Sun. It gravitationally bound to the galaxy, which happens to be rotating. So it's more like the sense in which the Great Red Spot goes around Jupiter -- it's not really orbiting it, because it is part of it. (The black hole at the center of our galaxy is far too distant for our Sun to orbit it at all; its gravitational influence is negligible. Much more significant is the gravity of the rest of the galaxy.)

The first one is no for the major planets, but not for all the minor planets. A natural object which orbits at a Lagrange point (specifically, 4 or 5, which are long-term stable) is referred to as a "Trojan companion", after the class of asteroids which orbit in Jupiter's L5 point -- the Trojans. They form a vast cloud, and there is another set, just as vast, at Jupiter's L4 point (the Greeks). There are also four known Mars trojans and six known Neptune trojans, though astronomers believe there are far more Neptune trojans than we know about. (Their dimness and slow motion makes it difficult to find them.) Large moons can also have trojan companions, and there are several known in the very dynamic Saturn system. For instance, Telesto leads Tethys, while Calypso trails it.

The <a href="http://en.wikipedia.org/wiki/Hilda_family">Hilda asteroids</a> are another interesting group. These asteroids have a curious orbital resonance with Jupiter. First, they have a 3:2 resonance (unlike Trojans, which are 1:1), so they go around three times for two Jupiter orbits. They are not fixed to any of the Sun-Jupiter Lagrange points, but pass through (or near) three of them on successive aphelions: L3, L4, and L5. Thus, at any given time, the entire collection of them appears to describe a triangle.

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#### orienteer

##### Guest
My first set of questions were referring to the Earth moon L points, and since all of the Apollo trips were figure eights, I believe they passed through that point. As for magnetism, we know that the Earth is a magnet, and as such, I was asking if we could launch a electro-magnet that repels the Earth at the same force as gravity is attracting it.

Some times I assume everyone is on my unique wave length. I apologize for the confusion.

M

#### MeteorWayne

##### Guest
As to the first point, I don't know for sure. It's ceratinly not a requirement that they pass through the Earth Moon L1.

As for the second, the earth's magnetic field is FAR too weak to of any value. It's barely strong enough to move a compass needle to point in the right direction.

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#### hhhmortal

##### Guest
Quote from wiki:

"The Earth–Moon L1 allows easy access to lunar and earth orbits with minimal change in velocity and would be ideal for a half-way manned space station intended to help transport cargo and personnel to the Moon and back"

Am I correct in saying that the gravitational pull of the Earth on the spacecraft is stronger than that of the Sun, before it reaches the L1, point.

Does anyone know the maximum speed of the space shuttle? (not its orbital speed) i.e. using its thrusters.

Using this I might be able to calculate a rough estimate of the time taken to get to the L1 point?

Thanks.

S

#### samkent

##### Guest
Quote from wiki:

"The Earth–Moon L1 allows easy access to lunar and earth orbits with minimal change in velocity and would be ideal for a half-way manned space station intended to help transport cargo and personnel to the Moon and back"

What benefit would be? If you are bringing people and stuff from Earth destined to the Moon, why stop half way (figure of speech)? And the same for people and stuff coming from the Moon. All this cackle about the L points is just over blown benefit hype. I know there is/was a sat at the Earth/Sun L point. Yes it was the correct point for its mission, I think it was studying the Sun, but not for most. If you want to study the Earth you want to get closer to it.

Can anyone show us any REAL benefits in placing a space station at any L point? All of our missions are passing through the L points to get somewhere else. This isn't Star Trek where visitors from the next star system arrive and can't decide "Should I visit Earth or its Moon?".

S

#### Saiph

##### Guest
Sorry, but the gravitational pull due to the sun is stronger than earth at the L1 point. As I'll show below, the suns gravity is ~33x stronger than the earths at the L1 point.

F=GMm/R^2

G is gravitational constant (6.67x10^-11), M is mass of main body, m is mass of object we're looking at (me, you, satellite, whatever), R is distance between M and m.

So for the sun we have: M = 2x10^30kg, and R between sun and earth is 1 au, or ~150,000,000km (15x10^7km), but the L1 point is ~0.01 Au from earth on the same line...so it's actually at 1au - .01au,

(6.67x10^-11)*2x10^30*m/(15x10^7-15x10^5)^2 = 6050*m

I leave m as m as it doesn't really matter, so long as we compare the force on the same object in both cases.

For earth, M = 6x10^24kg, R = ~0.01 Au, or 15x10^5km

So force = (6.67x10^-11)*6x10^24/(15x10^5)^2 = ~178*m

So to compare the two, you have 6050*m/178*m = ~33x (the 'm' cancels out...confirming I don't have to worry about it)

to double check, the sun's gravity at earth orbit is simply calculated at 1au, or 15x10^7km... producing 5928*m

The gravity at L1, the combination of both the earths force, and the suns force should equal the force of the sun on the earth at 1AU. Since the forces are in opposite directions, we subtract them, giving:

6050*m-178*m = 5872*m

Which is close enough to the calculated figure of 5928*m I found when I just did the straight calculation. Any small differences are due to my rather sloppy rounding of figures as I'm working from memory (except the 0.01AU distance for the L1, that I googled).

S

#### Saiph

##### Guest
The earth's gravity surpasses the sun at any distance closer than ~260,000 km

To put that in perspective, the moon is ~380,000 km away IIRC...so that means that the moon is actually pulled harder by the sun than the earth.

This means the moon doesn't technically orbit the earth (in the strictest sense)...but that the moon and earth co-orbit the sun, perturbing eachother as we go along.

M

#### MeteorWayne

##### Guest
hhhmortal":zcxv10qx said:
Quote from wiki:

"The Earth–Moon L1 allows easy access to lunar and earth orbits with minimal change in velocity and would be ideal for a half-way manned space station intended to help transport cargo and personnel to the Moon and back"

Am I correct in saying that the gravitational pull of the Earth on the spacecraft is stronger than that of the Sun, before it reaches the L1, point.

Does anyone know the maximum speed of the space shuttle? (not its orbital speed) i.e. using its thrusters.

Using this I might be able to calculate a rough estimate of the time taken to get to the L1 point?

Thanks.

Orbital speed is pretty much the maximum speed of the Shuttle STS. There's very little margin left. To escape earth orbit you have to go about 40% faster. You might get partway to that increase in speed with an empty shuttle, but then what's the point?

C

#### CalliArcale

##### Guest
samkent":s82w99g1 said:
What benefit would be? If you are bringing people and stuff from Earth destined to the Moon, why stop half way (figure of speech)? And the same for people and stuff coming from the Moon. All this cackle about the L points is just over blown benefit hype. I know there is/was a sat at the Earth/Sun L point. Yes it was the correct point for its mission, I think it was studying the Sun, but not for most. If you want to study the Earth you want to get closer to it.

Can anyone show us any REAL benefits in placing a space station at any L point? All of our missions are passing through the L points to get somewhere else. This isn't Star Trek where visitors from the next star system arrive and can't decide "Should I visit Earth or its Moon?".

There are actually several spacecraft at Earth-Sun L points. SOHO and ACE are in halo orbits around L1. Genesis was at L1 during its collection phase, but returned to Earth before heading out to L2 (and back again eventually -- it's a natural consequence of the way its trajectory was designed; its name is now Exodus, if I recall correctly, and they're basically using the spacecraft bus for some bonus science). WMAP is at the L2 point, mapping the cosmic microwave background. Sun-Earth L2 is actually very well suited for space telescopes (those that don't require servicing, anyway), as long as you can get them there. It's a rather high post.

If you're not in a hurry, you can exploit Lagrange points for traveling around the solar system with relatively little propellant expenditure. The math is ferocious, but doable. This is not very useful for manned spaceflight, however. Earth-Moon L2 would be useful for radio science, as it would be shielded from Earth's artificial radio emissions; most proposals look more towards using the lunar farside for that, though.

The main idea with a space station at Earth-Moon L1 is as a waypoint. You use one spacecraft to travel from Earth to the station. Then you board a second spacecraft, which is designed entirely for lunar landings and takeoffs, to fly the rest of the way. Whether or not it is practical or wise depends on who you ask. My opinion is that it is not useful yet, but might be someday. The main advantage is that you always know where it is.

E

#### emperor_of_localgroup

##### Guest
Saiph":1gj3hf5j said:
Actually MW, you're not quite right on the specifics of LP's.

Not even at L1, the point between the earth and sun, or more generically between the primary and secondary bodies (I'll use sun & earth to avoid confusion) is the gravity is balanced in the traditional sense.

What the points are, are points of equipotential, where the gravitational potential, due to the interactions of the sun and earth, is the exact same as that felt by the earth. In all cases the force of gravity from the sun is greater than the earths.

Sorry to say, but I still don't see how L2, L3, L4, L5 are possible between ONLY the sun and earth. Potential (-GM/r)at L3 by the sun and earth can not be equal, because the sun is so massive and the earth is far away from L3. There must be something else in the scene. Note, gravitational force is always attractive and can not be shielded.

The math I saw uses centripetal force of objects in Lagrange region, which means the object must be moving in an orbit. If that is the case, my question is 'what powers the object to move'? Does it use its own power?

@Calli
Thanks for info on all the Lagrangian points in our solar system, I would have never known there were so many Lagrangian points around us. But my question is have we sent any craft to Lagrangian points other than L1 (which is normal)? Have we verified the points (L2, L3, L4, L5) by sending crafts and observing their behaviors?

I think I'm missing some simple thing.

R

#### robnissen

##### Guest
Saiph":3vf75miq said:
Here's how it works, broken down point by point:

L1: Is closer to the sun than the earth, and objects at that orbital radius would normally orbit faster than the earth. However, the earth tugs away from the sun there in such a way as to lessen (but not negate!) the sun's pull to be a force equal to that which the sun pulls on the earth.

Same force produces the same orbital period.

L2: Positioned further from the sun than the earth, I.e. opposite the earth from L1 would normally have objects orbit slower, as the suns gravity is weaker at that greater distance. However the COMBINED gravitational pull from the sun and earth, increase the gravitational pull there...to equal that which the sun exerts upon the earth...

Same force produces the same orbital period.

L3: Is on the side opposite the sun, from the earth..slightly beyond earths normal orbital radius. Again, the COMBINED gravity from earth and sun mean that at that slightly greater distance, the satellite would still feel the same force as the sun exerts upon the earth.

Same force produces the same orbital period.

Thanks Saiph for that great post. I had never really understood Lagrange points until your post. I was under the impression that Lagrange points are where the gravitational pull of two bodies was equal. The problem with that explanation, is that it only explains Lagrange 1 and not the others. Now, I see I was wrong and understand Lagrange 2 and 3. I do hope you post further on Lagrange 4 and 5.

S

#### Saiph

##### Guest
emperor_of_localgroup":2kvjo52y said:
Saiph":2kvjo52y said:
Actually MW, you're not quite right on the specifics of LP's.

Not even at L1, the point between the earth and sun, or more generically between the primary and secondary bodies (I'll use sun & earth to avoid confusion) is the gravity is balanced in the traditional sense.

What the points are, are points of equipotential, where the gravitational potential, due to the interactions of the sun and earth, is the exact same as that felt by the earth. In all cases the force of gravity from the sun is greater than the earths.

Sorry to say, but I still don't see how L2, L3, L4, L5 are possible between ONLY the sun and earth. Potential (-GM/r)at L3 by the sun and earth can not be equal, because the sun is so massive and the earth is far away from L3. There must be something else in the scene. Note, gravitational force is always attractive and can not be shielded.

The math I saw uses centripetal force of objects in Lagrange region, which means the object must be moving in an orbit. If that is the case, my question is 'what powers the object to move'? Does it use its own power?

First, Lagrange points aren't restricted to ONLY the earth and sun. I merely used those to avoid confusing people with describing things as primary and secondary. It's also not just between them...but at several points around them. only L1 is between the objects. I don't think that's what you meant, but just clearing that detail up just in case.

The main point you missed is not that the gravitational potential due to the sun and earth are equal at the LP's, but that the net potential at that point is equal to the potential felt by the earth. My last post shows that the potential due to the sun is about 33x more than the earth's at the L1 point, far from equal.

The key is that the combination of the gravitational forces at the LP's create an isolated region that experiences the same NET gravitational force, as the earth experiences. This results in an area where an object can orbit in a fixed position relative to the earth, even if it's not at the same 1au orbital radius (for LP1,2,&3).

The L3 point, on the opposite side of the sun, is just slightly beyond earths normal orbit. This is because the net gravity is slightly increased at that point by earths. So nothing is shielded, it's actually combined and enhanced in this case.

The L1 point has the sun's gravity slightly reduced, as the earth's gravity pulls in the opposite direction, acting against it. So despite being closer to the sun, the gravity is, at that point, weaker than normal, and equal to the sun's gravity at 1au.

At L2, the forces again combine, causing a slightly stronger gravity, meaning an object there can orbit as if at 1au, despite being a bit further out.

L4 & 5 are more complicated, they are fixed at 1au. The thing about them is that an object there gets tugged, gently, back to that region by the combined forces of the sun & earth. So it's harder than usual to disrupt an object's orbit away from that point, and things tend to settle there naturally. It's sort of an eddy, a secondary gravitational well/dimple caused by the two objects.

the stipulation you've seen that, "the object must be moving in an orbit." to stay at those points means that you can't just magically go there, then get stuck. You have to arrive with the correct orbital path that would suffice to orbit the sun at 1au..i.e. the speed the earth moves about the sun.

Without a LP, you have to expend energy to stay at those distances, at a speed equal to earths (so you don't move relative to earth), as it isn't a 'natural' orbit. Without outside influence you'd be travelling to fast (or slow) to keep pace with the earth at any distance other than 1au. You're either closer to the sun, and travelling faster, so you need to use rockets to slow down AND keep your distance, or you're to far, and need to use rockets to speed up, but keep from moving away.

Using the LP, you've found a spot that lets the earth drag you around...meaning you don't need to use rockets for pretty intensive station-keeping. Just really minor tweaks to avoid drifting from the sweet spot (due to other planets or objects pulling on you). For L4 & 5 you don't even need those little tweaks.

As noted before, this applies to ANY 2 body system, be it earth/sun, earth/moon, sun/jupiter, etc, etc.

C

#### CalliArcale

##### Guest
emperor_of_localgroup":38s8b1nk said:
Sorry to say, but I still don't see how L2, L3, L4, L5 are possible between ONLY the sun and earth. Potential (-GM/r)at L3 by the sun and earth can not be equal, because the sun is so massive and the earth is far away from L3. There must be something else in the scene. Note, gravitational force is always attractive and can not be shielded.

The points exist for any two-body system where one is substantially larger than the other, though they are only meaningful for a third object which is of insignificant mass compared to the two large bodies (so its gravity can be safely ignored). In the real solar system, of course, it's not a two-body problem, and objects at Lagrange points may be perturbed by other large bodies.

But of course there are more points than just the Sun-Earth ones. There are Earth-Moon ones, Sun-Mars, Sun-Jupiter, Jupiter-Io, Jupiter-Europa, Saturn-Titan, etc, etc. Any two-body system where the second body is quite a bit smaller than the primary. (If the two are close in size, the points are less stable. This is part of the problem with the Earth-Moon points; the Moon is pretty massive compared to Earth.)

The math I saw uses centripetal force of objects in Lagrange region, which means the object must be moving in an orbit. If that is the case, my question is 'what powers the object to move'? Does it use its own power?

A solid body will tend to continue in a straight line at constant velocity unless acted upon by some outside force. They don't have to be powered to wind up at a Lagrange point (which is why so many asteroids have accumulated at Sun-Jupiter L4 and L5). But as only L4 and L5 are stable over long periods of time, objects at the other three points will tend to drift away from the points over time. Spacecraft using these points must therefore fire engines periodically to maintain their trajectory.

Otherwise, though, what powers the object to move is nothing. It's just running on momentum, so to speak.

But my question is have we sent any craft to Lagrangian points other than L1 (which is normal)?

Yes! We have sent a couple of spacecraft to Sun-Earth L2, most notably the WMAP spacecraft. I'm not sure, but I think the Stereo-A and Stereo-B spacecraft might wind up at Sun-Earth L4 and L5 eventually; they might have enough momentum to go right on past, though.

Have we verified the points (L2, L3, L4, L5) by sending crafts and observing their behaviors?

Not exactly. Sun-Earth L3 is tricky; we cannot observe it from Earth, because the Sun is always between us and it. A spacecraft at that point would be mute -- we could not communicate with it without some sort of relay craft, perhaps at L4 or L5. But we have observed objects passing through L1 and L2, and we have observed the behavior of natural bodies at other L4 and L5 points, specifically the Sun-Mars, Sun-Jupiter, Sun-Neptune, Saturn-Dione, and Saturn-Tethys ones.

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