Orbital mechanics question DSCOVER L1 orbit

In sci.space.policy message -
september.org, Sun, 15 Feb 2015 10:15:33, Jeff Findley
posted:

It looks like an orbit around the sun, but it's not. It's correct to
state that L1 is the location in space where the gravitational forces on
a satellite from the sun and the earth cancel out.

Approximating orbits by circles : for an object on the Sun-Earth line to
remain on that line at a constant distance from the barycentre, it must
have the same angular velocity as the Earth. It is well-known - IIRC,
it was even taught in schools - that the centripetal force needed for
circular motion is M w^2 r in obvious notation. As 1 AU is about 10^8
miles and L1 is about 10^6 miles inwards from Earth, the forces most
certainly do not cancel out.

Moreover, L1 & L2 were discovered by Euler, who should have also
discovered L3 except that it was semantically off-topic.

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Web http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms and links;
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On 15-02-18 00:36 , JF Mezei wrote:
DSCOVER stll orbiting earth after it is at L1.

I understand the principle of why one would say the satellite is still
orbiting earth, since over the course of a year, it technically goes
around it.

And also because the Earth still has a significant gravitational pull on
the satellite, because L1 is near us, as astronomical distances go. If
the Earth were to be removed, the satellite's path would change
significantly -- it would become an ellipse around then Sun, with the
old L1 position being the aphelium, but the perihelium would not be very
much closer to the Sun. If the Sun were to be removed, the satellite's
path would change drastically; it would become an ellipse around the
Earth, with its old L1 position being the apogee. I'm not sure, but I
suspect the perigee would be so low that the satellite would reenter.

Can't the same be said of the other planets in solar system ?

Yes, if one stretches the point. But the greater distances between the
Earth and the other planets mean that the influence of the Earth on
their motion is much less than its influence on the satellite at L1.
Also, for the massive planets like Jupiter, it is more a case of them
influencing the Earth's path.

At one point, does stating the satellite still orbits earth basically
bring back the old ideas of everything revolving around the earth ?

No, that question was about which one is moving, and which one is not,
because that was thought to have theological importance. Considering the
gravitational coupling between the Earth and the Sun, it is far more
correct to say that the Sun is still, and the Earth goes around it, than
to claim the opposite.

For an LEO object, slowing down would cause it to drop towards earth.
Accelerating would caus it to climb to higher orbit from earth.

For DSCOVER, if , once at L1, it were to slow down,

Relative to what? It is not enough to just say "slow down", that does
not specify how the velocity changes.

would it fall down towards sun, or towards earth ? Wouldn't that
determine which body it orbits ?

If you were to reduce DSCOVER's angular velocity around the Sun, it
would "fall toward the Sun" in the sense that its orbit around the Sun
would become more elliptical, with the L1 position as the aphelium, and
it would no longer keep pace with the Earth.

--
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
. @ .

In article om,
says...

On 15-02-18 01:32, Niklas Holsti wrote:

If you were to reduce DSCOVER's angular velocity around the Sun, it
would "fall toward the Sun" in the sense that its orbit around the Sun
would become more elliptical, with the L1 position as the aphelium, and
it would no longer keep pace with the Earth.


If there is no variation in distance between sun and earth, would it be
correct to state that its only velocity vector would be tangential to
the sun ? (forgetting the halo orbit around L1).

If slowing down means the satellite reduces altitude to sun, doesn't
that imply that it's orbit is solely around the sun ?

And if it increases it speed (or fires thrusters to push itself towards
earth) it would rise above L1 and its orbit would then switch from
being around the sun to being around the earth which would bring it into
highly elliptical orbit around earth ?


The way I picture it, at L1, the satellite is orbiting only the sun with
the earth acting as a static magnet that keeps the satellite at L1
altitude to compensate for its speed being too low to stay at L1. If at
L1, it is not freefalling around the earth, can it really be considered
to be in orbit around the earth ?

For the last time, a classic "orbit" is a two body simplification to
orbital mechanics. That's *not* what we have here! Sun-earth-satellite
at L1 is a *three* body problem. I really wish you would all stop
talking about a satellite at L1 like it was in a classic circular orbit.
It's not even close to that!

In fact, to stay at L1 it has to use a halo orbit, which is not at all
like a classic circular or elliptical orbit. Google "L1 halo orbit",
click on Images, and you'll see just how crazy looking the path of a
satellite at L1 has to be to remain at that location. From the frame of
reference of L1, the satellite moves in a halo orbit about L1 and it is
not an elliptical path like a classic orbit.

Jeff
--
"the perennial claim that hypersonic airbreathing propulsion would
magically make space launch cheaper is nonsense -- LOX is much cheaper
than advanced airbreathing engines, and so are the tanks to put it in
and the extra thrust to carry it." - Henry Spencer

On 15-02-18 13:41 , Jeff Findley wrote:

For the last time, a classic "orbit" is a two body simplification to
orbital mechanics. That's *not* what we have here! Sun-earth-satellite
at L1 is a *three* body problem.

We have not denied it.

I really wish you would all stop talking about a satellite at L1
like it was in a classic circular orbit.

It seems to me that the discussion is indeed about how the motion is
different from a two-body orbit, and how it is similar.

What do you want us to do, just say "it's a three-body problem" and then
shut up?

It's not even close to that!

The radius of the halo orbit around L1 is on the order of 1 million km,
which is less than 1% of the radius of the orbit of the L1 locus around
the Sun. The latter orbit is the main part of the satellite's motion
relative to the Solar System. I would say that the orbit of a satellite
at L1 is quite close to a circular orbit around the Sun.

In fact, to stay at L1 it has to use a halo orbit, which
is not at all like a classic circular or elliptical orbit.
Google "L1 halo orbit",

I already gave a link in an earlier post.

--
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
. @ .

On 15-02-18 09:22 , JF Mezei wrote:
On 15-02-18 01:32, Niklas Holsti wrote:

If you were to reduce DSCOVER's angular velocity around the Sun, it
would "fall toward the Sun" in the sense that its orbit around the Sun
would become more elliptical, with the L1 position as the aphelium, and
it would no longer keep pace with the Earth.


If there is no variation in distance between sun and earth, would it be
correct to state that its only velocity vector would be tangential to
the sun ? (forgetting the halo orbit around L1).

Yes, if we are talking about the satellite's velocity vector with
respect to the Sun, and if we indeed we forget about the halo orbit, and
about the slight eccentricity of the Earth's orbit.

If slowing down means the satellite reduces altitude to sun, doesn't
that imply that it's orbit is solely around the sun ?

And if it increases it speed (or fires thrusters to push itself towards
earth) it would rise above L1 and its orbit would then switch from
being around the sun to being around the earth which would bring it into
highly elliptical orbit around earth ?

Here I would agree with Jeff: the satellite's orbit is influenced by
both the Sun and the Earth (and other bodies like the Moon), so it
cannot be categorized into either "an orbit around the Sun" or "an orbit
around the Earth". It is a mixture.

The way I picture it, at L1, the satellite is orbiting only the sun with
the earth acting as a static magnet that keeps the satellite at L1
altitude to compensate for its speed being too low to stay at L1.

Yes... except that "magnet" is of course wrong, as the force is gravity,
not magnetism.

If at L1, it is not freefalling around the earth, can it really be considered
to be in orbit around the earth ?

See above about Jeff's comment.

--
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
. @ .

On 15-02-18 21:26 , JF Mezei wrote:
On 15-02-18 14:09, Niklas Holsti wrote:

The radius of the halo orbit around L1 is on the order of 1 million km,


is the movement around L1 technically an orbit since L1 has no mass ?

Depends on how you technically define an "orbit". In the definition at
http://en.wiktionary.org/wiki/orbit, gravitation and mass are not
necessarily required.

--
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
. @ .

If it is this complex, would one expect that keeping a craft in this point
is goind to use more fuel?
It seems to me that we are dealing with some very complex forces here and
although the tendency is for things to stay there, any other forces woould
not need to be that poweful to make it come out of the point and start
behaving differently.
Brian

--
From the Sofa of Brian Gaff Reply address is active
"Niklas Holsti" wrote in message
...
On 15-02-18 09:22 , JF Mezei wrote:
On 15-02-18 01:32, Niklas Holsti wrote:

If you were to reduce DSCOVER's angular velocity around the Sun, it
would "fall toward the Sun" in the sense that its orbit around the Sun
would become more elliptical, with the L1 position as the aphelium, and
it would no longer keep pace with the Earth.


If there is no variation in distance between sun and earth, would it be
correct to state that its only velocity vector would be tangential to
the sun ? (forgetting the halo orbit around L1).

Yes, if we are talking about the satellite's velocity vector with respect
to the Sun, and if we indeed we forget about the halo orbit, and about the
slight eccentricity of the Earth's orbit.

If slowing down means the satellite reduces altitude to sun, doesn't
that imply that it's orbit is solely around the sun ?

And if it increases it speed (or fires thrusters to push itself towards
earth) it would rise above L1 and its orbit would then switch from
being around the sun to being around the earth which would bring it into
highly elliptical orbit around earth ?

Here I would agree with Jeff: the satellite's orbit is influenced by both
the Sun and the Earth (and other bodies like the Moon), so it cannot be
categorized into either "an orbit around the Sun" or "an orbit around the
Earth". It is a mixture.

The way I picture it, at L1, the satellite is orbiting only the sun with
the earth acting as a static magnet that keeps the satellite at L1
altitude to compensate for its speed being too low to stay at L1.

Yes... except that "magnet" is of course wrong, as the force is gravity,
not magnetism.

If at L1, it is not freefalling around the earth, can it really be
considered
to be in orbit around the earth ?

See above about Jeff's comment.

--
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
. @ .

In article , says...

If it is this complex, would one expect that keeping a craft in this point
is goind to use more fuel?

Depends on the details of the "halo orbit" that it is in. Yes, halo
orbits are complex and are very weird since they're not a circular path
and there is no mass at the "center" of the point it is orbiting. But
if you do it right, it doesn't take much delta-V to stay in a "halo
orbit".

It seems to me that we are dealing with some very complex forces
here and although the tendency is for things to stay there, any
other forces woould not need to be that poweful to make it come
out of the point and start behaving differently.

This is why Orbital Mechanics was one of the hardest 500 level classes I
took at Purdue. Spacecraft Attitude Dynamics was the other 500 level
class that was quite difficult. Lots of math. Lots of derivations.
Lots of simplifications that you can't completely ignore in the real
world.

Jeff
--
"the perennial claim that hypersonic airbreathing propulsion would
magically make space launch cheaper is nonsense -- LOX is much cheaper
than advanced airbreathing engines, and so are the tanks to put it in
and the extra thrust to carry it." - Henry Spencer