The glory of this thread. From the outermost edges of the known universe and all the philosophical implications of being within reach of answering questions we've had since we became self aware as a species...to the antique techniques that yield resources from the earth and elements that promote merriment and friendship among human hearts.

The glory of this thread. From the outermost edges of the known universe and all the philosophical implications of being within reach of answering questions we've had since we became self aware as a species...to the antique techniques that yield resources from the earth and elements that promote merriment and friendship among human hearts.

Good stuff!

Thank you, but I was just about to apologize for thread drift.

They have short articles about recent science developments. They are usually very accurate at summarizing recent research in lots of fields. Some articles are technical, others more general. Just read the ones that are interesting.

Username Protected wrote:

Truthfully, I'm a little behind on my reading of books on physics and cosmetology,

That's a joke fellows.

My most recent interests have been seeking the similarities of the politics of the pre-civil war years with those of today and the effect of news media in both those times. I found more than you might think and professional political scientist and historians are now getting aboard.

So, now, back to science. To get me more "up to date".

You guys who are more physics and engineering based, what books would you recommend that are not so dry and technical as to cause a severe case of dandruff?

Today's update from the Webb Telescope blog. They are planning on weekly updates for now.

Quote:

Now that the action-packed deployment sequence is over, we are moving into a much slower, yet deliberate, phase of the commissioning process. In the next two weeks, we will move each of the 18 primary mirror segments, and the secondary mirror, out of their launch positions. Then five months of commissioning will include 1) further cooling of the entire observatory, and of the Mid-Infrared Instrument in particular, 2) checking and then aligning the secondary and 18 mirror segments into a single coherent optical system, first with the NIRCam instrument and then with all instruments individually and in parallel, and 3) calibrating of each of the four instruments and their many scientific modes. The novelty and variety of science that this observatory can produce requires thousands of things to be checked ahead of time. But rest assured that this summer will sizzle with the hot (nay cold?) observations we will soon be sharing!

They have short articles about recent science developments. They are usually very accurate at summarizing recent research in lots of fields. Some articles are technical, others more general. Just read the ones that are interesting.

I've been a Science News reader since the late '70s. Excellent way to keep up to date, they do try to get it right with science-literate reporters.

Admittedly I haven't looked at the details but I assume there will be an orbit about L2 (as opposed to a "hover") and I don't think that it's perfectly stable. That is, I think all the other mass around makes things a little less than ideal and some mild orbital corrections will be required over time. I think you will need at least one small boost to fall into a circular orbit (if that's their goal) just like you would for any insertion.

This is where I get lost. How does an orbit (a "halo" orbit I think) occur around a point (L2) with no mass?

It may have been posted already, but Scott Manley does a fantastic job of describing Lagrange points. They’re confusing enough thinking about them in two dimensions, and my brain starts to melt when attempting to picture them in three.

It may have been posted already, but Scott Manley does a fantastic job of describing Lagrange points. They’re confusing enough thinking about them in two dimensions, and my brain starts to melt when attempting to picture them in three.

I've watched this a couple of times. I'm still bamboozeled but it just means this subject is beyond my primitive understanding of these complex subjects. I'm glad there are those that do fully understand this and make it work.

Second question I have is whether the gravitational field of the moon has any effect on the stability of the L2 point, or is the distance far enough to be out of the picture (~750k miles away from the moon).

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Username Protected wrote:

Admittedly I haven't looked at the details but I assume there will be an orbit about L2 (as opposed to a "hover") and I don't think that it's perfectly stable. That is, I think all the other mass around makes things a little less than ideal and some mild orbital corrections will be required over time. I think you will need at least one small boost to fall into a circular orbit (if that's their goal) just like you would for any insertion.

This is where I get lost. How does an orbit (a "halo" orbit I think) occur around a point (L2) with no mass?

Dan

A Lagrange orbit is still an orbit around the sun, it is just that due to the combined gravity of the earth there is an orbit at L2 that tracks the earth. L2 isn't stable, it still needs thruster burns to stay there (or make an orbit around it).

L4 and L5 points are stable, and there are asteroids that live there (also called Trojans).

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Username Protected wrote:

This is where I get lost. How does an orbit (a "halo" orbit I think) occur around a point (L2) with no mass?

Dan

I don't think the video did a good job directly answering your question. Here's how I would think of it: First, we're going to use a cylindrical coordinate system, with three axes: R - radial - moving further or closer to the earth / sun Z - height above / below the plane of the earth's ellipse T - angle, ahead or behind the earth's motion around the sun

R is the complicated one, not quite stable. However, the orbit around the L2 point is not in R, but in Z & T. Let's first think about just one of these axes, Z.

Suppose we start with Z=1000km "north" of L2 (above the earth's plane). In the Z direction, the mass of the earth / sun is at Z=0, so our satellite will begin falling south towards Z=0. Reaching Z=0, there will be no acceleration, but we will have built up speed, so we continue past Z=0, until we reach Z=-1000km. Then we'll have reached zero Z velocity again, and we'll start yoyo-ing up and down above and below L2. With no friction, this can continue forever.

Simultaneous with the oscillation in Z, we can also oscillate in T, forward and behind the earth's angle around the sun. When we are ahead of the earth, the center of mass of the earth / sun is behind us, so we accelerate backwards. Then we overshoot, end up behind the earth, and start to swing back forward. Combine the Z and T oscillations and you get an orbit around L2.

Although there is no mass at L2, the mass of the earth / sun is at the center of the plane of the L2 orbit when projected onto the plane of that orbit. The total acceleration of the satellite at any given time is in fact towards the center of gravity, but we can decompose that vector into components in our three orthogonal axes.

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Username Protected wrote:

Second question I have is whether the gravitational field of the moon has any effect on the stability of the L2 point, or is the distance far enough to be out of the picture (~750k miles away from the moon).

Dan

The moon has 1/100th the mass of the Earth. Although I'm sure it has an effect, it is likely limited. I think you can think of the Earth + moon as one object with a "wobble" caused by the motion of the moon.

Strictly speaking, the Lagrange points are analytic solutions to the three body problem, a situation that does not exist in real life. But it's close enough to describe real life phenomena, and we can use numerical models to take into account the forces from other bodies.

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Username Protected wrote:

This is where I get lost. How does an orbit (a "halo" orbit I think) occur around a point (L2) with no mass?

Dan

I don't think the video did a good job directly answering your question. Here's how I would think of it: First, we're going to use a cylindrical coordinate system, with three axes: R - radial - moving further or closer to the earth / sun Z - height above / below the plane of the earth's ellipse T - angle, ahead or behind the earth's motion around the sun

R is the complicated one, not quite stable. However, the orbit around the L2 point is not in R, but in Z & T. Let's first think about just one of these axes, Z.

Suppose we start with Z=1000km "north" of L2 (above the earth's plane). In the Z direction, the mass of the earth / sun is at Z=0, so our satellite will begin falling south towards Z=0. Reaching Z=0, there will be no acceleration, but we will have built up speed, so we continue past Z=0, until we reach Z=-1000km. Then we'll have reached zero Z velocity again, and we'll start yoyo-ing up and down above and below L2. With no friction, this can continue forever.

Simultaneous with the oscillation in Z, we can also oscillate in T, forward and behind the earth's angle around the sun. When we are ahead of the earth, the center of mass of the earth / sun is behind us, so we accelerate backwards. Then we overshoot, end up behind the earth, and start to swing back forward. Combine the Z and T oscillations and you get an orbit around L2.

Although there is no mass at L2, the mass of the earth / sun is at the center of the plane of the L2 orbit when projected onto the plane of that orbit. The total acceleration of the satellite at any given time is in fact towards the center of gravity, but we can decompose that vector into components in our three orthogonal axes.

Abram, Yes, excellent description. To explain R a little better, one can think of it this way... Your orbital period (hours to go around the sun (or any other object is based on the masses of the objects and the distance from that object)

Orbital Period = 2*PI * sqrt ( Radius^3 / (G*M)) Orbital Period is a function of sqrt ( Radius^3 / Suns Mass)

If we got rid of earth in this situation, but increased the gravitational attraction of the sun slightly, the orbit at earths radius would be a bit faster. Now, we want to get our orbital period to match earth's... How do we do that? We move a bit further away from the sun (larger, slower orbit).

So, put the earth back in - it's adding some additional gravitational attraction - that if you're in line with the sun and earth - simply adds the two gravitational attractions (+/- some relativistic amounts) to find our new gravitation component of the orbital period. Unfortunately, this is variable since earth will have very little effect if you're far from earth, and a lot more if you're closer. But, you can solve these two equations - earth + sun gravity and orbital period based on the radius and that gravity - to arrive at the "LaGrange point." Where you are a larger radius, with a slightly higher gravitational pull (earth + sun) and end up with the same orbital period - a point that stays behind the earth as it orbits the sun.

L1 is the same, but earth is reducing the effective suns gravity, hence slowing the orbit requiring a smaller orbital radius to have the same orbital period around the sun as the earth.

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