Date: Sat, 17 Sep 1988 19:39-EDT
From: space-tech-request@CS.CMU.EDU
To: "~/st/lists/stdigest"
Subject: Space-tech Digest #5
Contents:
Jim Meritt Re: Senior Projects
Roger Arnold Oops [ orbit raising ]
Gordon Pusch orbit raising for EML vehicles
Gordon Pusch EML orbit raising. PS: I forgot about plane changes ...
Matt Burdick Re: orbit raising for EML vehicles
Gordon Pusch Re: EML orbit raising
Marc Ringuette Choosing EML orbits (mini-discussion)
Marc Ringuette Getting out of HEEO
------------------------------
From: telesoft!roger@ucsd.edu (Roger Arnold @prodigal)
Date: Thu, 15 Sep 88 09:12:26 PDT
To: dietz@cs.rochester.edu
Subject: Oops
Cc: space-tech@cs.cmu.edu
In the preceding message, I wrote:
> .. The two
> burn strategy will be cheaper. Because in the limit of a parabolic
> transfer orbit, the delta vee for the appogee burn will approach
> zero, and I know that the delta vee for the perigee burn to lower
> the appogee will be less than would be needed to go from the transfer
> orbit direct to the final orbit at any altitude above the perigee.
> ..
Please disregard that last bit of drivel. My brain was not fully
engaged. I don't know *what* the optimum strategy is when multiple
burns are considered. I suspect that it depends on the parameters
of the final orbit desired and the elevation of the EM launcher. But
it's certainly not hard to find a counterexample to the strategy of
going all the way to the outer boondocks to do a perigee raising
burn.
I'm going to go away. I'll be back when I have some solid numbers
(or at least semi-solid) to report.
- Roger Arnold
------------------------------
Date: Fri, 16 Sep 88 01:03 EDT
From: GORDON D. PUSCH
Subject: orbit raising for EML vehicles
To: space-tech@cs.cmu.edu
Roger Arnold writes:
>I notice that Paul's figures for perigee raising in an EML vehicle
>presume an apogee burn. This is not optimum. To match a given
>orbit with minimum delta vee for the insertion burn, you want to use
>a pre-apogee burn that both lowers the apogee and raises the perigee.
> ... [ remainder deleted ]
I think I have to dissagree with Roger on this one. Since "work" is
"force" dot "displacement", any component of thrust perpendicular to the
velocity does *ZERO* work, and is therefore essentially wasted effort.
It is true that, since the semi-major axis of the orbit is determined
only by the total energy, you can "walk" an orbit around (simultaneously
change its apogee, perigee, and angular-momentum vector) without changing
its total energy; but I can see few applications where this would be
desirable.
I think the conventional wisdom still stands: for a minimum-fuel
transfer, the transfer orbit(s) should be tangent to the initial
and final orbits, and the burns should be at the points of tangency.
Gordon D. Pusch | Try using ; if that doesn't
Physics Dept., VPI&SU | work, try . (our Node-Name
Blacksburg VA 24061 | got changed recently ... )
+-----------------------------------------------------------------------+
| "... Engineers ... Always *changin'* things ... |
| It's like a Dam' *Computer Center* in here ..." --- L. McCoy, M.D. |
| |
| Q: How many System Programmers does it take to screw in a light-bulb? |
| A: *ONE*; He holds the bulb, and the World revolves around him ... |
+-----------------------------------------------------------------------+
------------------------------
Date: Fri, 16 Sep 88 01:35 EDT
From: GORDON D. PUSCH
Subject: EML orbit raising. PS: I forgot about plane changes ...
To: space-tech@cs.cmu.edu
... oops! forgot something!
> ... you can "walk" an orbit around (simultaneously
>change its apogee, perigee, and angular-momentum vector) without changing
>its total energy; but I can see few applications where this would be
>desirable.
>
>I think the conventional wisdom still stands: for a minimum-fuel
>transfer, the transfer orbit(s) should be tangent to the initial
>and final orbits, and the burns should be at the points of tangency.
There is no choice but to have a component of thrust out-of-plane when
making plane-changes, and then the problem gets *LOTS* more complicated.
I *think* I remember reading somewhere that an optimal tranfer between
arbitrary orbits requires at most three burns ...
Gordon D. Pusch | Try using ; if that doesn't
Physics Dept., VPI&SU | work, try . (our Node-Name
Blacksburg VA 24061 | got changed recently ... )
------------------------------
From: Matt Burdick
Subject: Re: orbit raising for EML vehicles
To: space-tech@CS.CMU.EDU
Date: Fri, 16 Sep 88 8:03:48 PDT
Gordon D. Pusch writes:
> I think I have to dissagree with Roger on this one. Since "work" is
> "force" dot "displacement", any component of thrust perpendicular to the
> velocity does *ZERO* work, and is therefore essentially wasted effort.
Any component of thrust will produce some change in velocity in the
direction of the thrust, and will therefore produce some displacement,
although it may be small if the thrust is small.
>
> It is true that, since the semi-major axis of the orbit is determined
> only by the total energy, you can "walk" an orbit around (simultaneously
> change its apogee, perigee, and angular-momentum vector) without changing
> its total energy; but I can see few applications where this would be
> desirable.
I'm not sure what you mean here. If the apogee or perigee of an orbit
changes, doesn't the semi-major axis?
-matt
--
Matt Burdick
burdick%hpda@hplabs.hp.com
------------------------------
Date: Fri, 16 Sep 88 23:26 EDT
From: GORDON D. PUSCH
Subject: RE: EML orbit raising
To: space-tech@cs.cmu.edu
Matt Burdick writes:
>Gordon D. Pusch writes:
>> I think I have to dissagree with Roger on this one. Since "work" is
>> "force" dot "displacement", any component of thrust perpendicular to the
>> velocity does *ZERO* work, and is therefore essentially wasted effort.
>
>Any component of thrust will produce some change in velocity in the
>direction of the thrust, and will therefore produce some displacement,
>although it may be small if the thrust is small.
Change in *velocity* does not imply change in *energy*. The kinetic
energy is a function of the *magnitude* of the velocity only. It is easy
to show that if the force is *perpendicular* to the velocity, the
*direction* of the velocity changes, but its *magnitude* (and therefore
its kinetic energy) remains the same.
Also, note that thrust produces a change in *velocity*, not displacement.
>From the structure of Newton's Third Law, any trajectory must be
continuous and once differentiable. You can (in theory) make an
instantaneous change in velocity, but not displacement.
>> It is true that, since the semi-major axis of the orbit is determined
>> only by the total energy, you can "walk" an orbit around (simultaneously
>> change its apogee, perigee, and angular-momentum vector) without changing
>> its total energy; but I can see few applications where this would be
>> desirable.
>
>I'm not sure what you mean here. If the apogee or perigee of an orbit
>changes, doesn't the semi-major axis?
Sorry I didn't make this clearer. The change in apogee is equal and
opposite to the perigee; hence the semi-major axis remains constant.
Gordon D. Pusch | Try using ; if that doesn't
Physics Dept., VPI&SU | work, try . (our Node-Name
Blacksburg VA 24061 | got changed recently ... )
+-----------------------------------------------------------------------+
| "... Engineers ... Always *changin'* things ... |
| It's like a Dam' *Computer Center* in here ..." --- L. McCoy, M.D. |
| |
| Q: How many System Programmers does it take to screw in a light-bulb? |
| A: *ONE*; He holds the bulb, and the World revolves around him ... |
+-----------------------------------------------------------------------+
------------------------------
Date: Sat, 17 Sep 1988 18:42-EDT
From: Marc.Ringuette@CS.CMU.EDU
To: space-tech@cs.cmu.edu
Subject: Choosing EML orbits (mini-discussion)
In this message I try to address the question "What orbits can we
launch into?" This is a problem, because the "natural" HEEO to
choose changes with each launch time and the angle of the EML.
You should realize that an eccentric orbit has three degrees of freedom:
two degrees of freedom for the orbital plane, and another for the position
of the apogee within that orbital plane.
In the following discussion between Paul Dietz and me, Paul works out
how to achieve different positions of the apogee within the orbital plane,
by altering the time and angle at which the boost occurs.
I give some more comments at the end of the discussion, in which I note
that we can also determine the orbital plane in this way, and sum up
my conclusions about what orbits we can launch into.
------------------------------
From: Marc.Ringuette@CS.CMU.EDU
Orbits
======
We'd like to put all our payloads into HEEO with a common apogee. You
had suggested using polar orbits and changing the orbital plane at
apogee. That sounds good in some ways, but polar orbit is the worst
for other reasons, one being that if you aerobrake into LEO, it's a
polar LEO, which is terrible to get to by other means.
How about choosing a single equatorial HEEO, and varying muzzle velocity
and angle in order to give more windows into that orbit? Some thoughts are:
- the quantity we want to vary is the angle between the launch position
and the final apogee.
- varying launch angle will probably give apogees of approximately the
same radius, but with different angles. This is what we want(?), but
is probably impossible given realistic launchers.
- Different muzzle velocities will give HEEO's with closer or farther
apogees, but probably with different angles between launch and apogee.
This is good news (we can adjust the apogee height with small boosts
at perigee). Do you want to work out whether this works, or shall I?
------------------------------
From: dietz@cs.rochester.edu
Why necessarily an equatorial HEEO? How about at the same inclination as
your space station, which for the US would be the latitude of KSC?
I ran some numbers, and changing the muzzle velocity while leaving the
elevation of the launcher fixed does not change the orientation of
the orbit significantly. Changing the elevation of the launcher
above horizontal does change the orientation of the major axis, but
the effect is not huge.
------------------------------
[ We abandon the idea of varying muzzle angle and velocity, from this
point. It may be a useful means of reducing the delta vee required
to boost the payloads, but will probably not be a big factor. // Marc ]
------------------------------
From: dietz@cs.rochester.edu
I was thinking a little more about getting a larger window for launch from an
EML into orbits with common apogee.
In the existing scheme, we raise the perigee by firing rockets at apogee.
This minizes delta-V, but makes the launch window very small. The new idea
is to raise the perigee by firing before apogee.
Consider a vehicle launched vertically (w.r.t. a nonrotating planet) to
altitude RA. We must raise its perigee to RP. This is done by firing a
rocket perpendicularly to the line connecting the center of the earth and the
vehicle. This adds angular momentum to the orbit. Firing at altitude X, the
delta-V is about sqrt(2) X / RA (in the limit where RA >> RP). So, at X =
RA/2 the delta-V is double that required at x = RA. Actually, perhaps
a bit more is needed to make the energy of the orbit come out right, but
we can vary the muzzle velocity to fix that.
The orientation of the major axis of the elliptical orbit is changed when the
rocket is fired at X < RA. To see how much, consider the geometry of the
orbit. Let a = RP be the distance from the focus (the center of the earth)
to the perigee; let b = (RA - RP)/2 be the distance from the center of the
earth to the center of the ellipse. Then, the distance from the center of
the ellipse to the sides of the ellipse (the points on the minor axis) is
sqrt(2 a b + a**2), or sqrt(RA RP).
If we inject into this elliptical orbit at altitude X = (RA + RP)/2, we do so
at one of these side points. The major axis is displaced by theta = arcsin (
2 sqrt(RA RP) / (RA + RP) ). If we let k = RA/RP, this angle is arcsin ( 2
sqrt(k) / (k+1) ). For eccentric orbits (large k), this angle is O(k**-1/2).
If we raise the perigee before reaching the apogee of the initial
trajectory, the major axis is rotated in the prograde direction.
But if we wait until after reaching apogee, the major axis is
rotated in the retrograde direction.
If we raise perigee at altitude of (RA+RP)/2 or higher, we
need only 7 HEEO's (RA = 20 RP) or 10 HEEO's (RA = 40 RP) to
fully utilize an equatorial EML.
------------------------------
From: Marc.Ringuette@CS.CMU.EDU
Paul, your calculations make a lot of sense. You assume that the
orbital plane is fixed; but in fact if we assume the boost is
straight outward from the earth, you have a degree of freedom
in your choice of orbital planes.
I'd sum up by saying:
- The initial angle of the EML determines one parameter of the
orbital plane.
- The second parameter of the orbital plane, plus the apogee position
within the orbital plane, can be adjusted using the perigee-raising
burn. The apogee position can't be arbitrary, but can be varied plus
or minus about 30 degrees without undue extra delta vee.
- As you showed, if we start with an EML at a fixed angle, it
is possible to choose seven or so "rendezvous" HEEO's which can
be reached at any time during the day from the EML, without
undue extra delta vee being required at the boost stage.
- Another perspective on this: if we have a single HEEO that we want
all our payloads in, we have about a seventh of the day in which we
can launch from a fixed-angle EML.
[ Unpleasant detail: if we don't assume everything is equatorial,
the trajectory of the payload won't precisely intersect any point
on the desired HEEO except at the exactly correct launch time.
However, I think the needed boosts to correct this are small,
and I intend not to worry about it. ]
Delta Vee?
==========
I have a couple of rough numbers on how much delta vee we'll need. My
rule of thumb is that 500 m/s is enough in almost all circumstances. It
is possible to reduce that to 200 m/s in some cases, or to need as much as
1000 m/s. The smaller delta vees can result from choosing a more highly
eccentric orbit, or by angling the launcher to impart part of the angular
momentum; but I think it's pushing it to expect less than 500 m/s in the
normal case. The 1000 m/s numbers come about when the apogee needs to
pushed the full 30 degrees from the "natural" apogee of the EML at the
time of launch.
How much fuel will we have to carry, then? From Jim Van Zandt's numbers,
I would guess we can carry 20 percent of the payload as fuel and engine,
and achieve 500 m/s delta vee. I think this is quite realistic.
====
Hey, I like these conclusions!
I'll send a second message in a few minutes, which asks the question
"What do we do with the payloads once they're in orbit?"
------------------------------------------------------------------------
| Marc Ringuette | mnr@cs.cmu.edu | I'll be stretching my mouth |
| CMU Computer Science | 412-268-3728 | to let those big words come |
| Pittsburgh, PA 15213 | | right out. [P. Gabriel] |
------------------------------------------------------------------------
------------------------------
Date: Sat, 17 Sep 1988 19:12-EDT
From: Marc.Ringuette@CS.CMU.EDU
To: space-tech@cs.cmu.edu
Subject: Getting out of HEEO
What do we do with payloads in a highly elliptical orbit? I'd like to
make some progress toward answering this important question.
I'll start with some assumptions, which I think are only mildly aggressive.
1. EML's will be good enough in 20 years.
[ I was looking through the '84 IEEE Trans. on Magnetics like Paul Dietz
suggested, and it was encouraging! There were several pre-SDI projects
on rail guns and coaxial EML's, and my guess is that the problems will
be solved. Some of the concentration at that time was on power sources
and control questions; future work will have to deal with current
densities and bursting forces. ]
2. The shielding problem will be solved.
[ This won't be easy, and I'd be happy if we could have some more ideas
on this within our space-tech group, but I bet it's solvable. ]
3. We can achieve highly elliptical orbits by launching payloads
with solid boosters attached, and the boosters will not need to
take up more than 25% of the total mass.
[ See my "Choosing EML Orbits" message regarding the orbits; other
possible problems are the effects of high accelerations and magnetic
fields on the boosters. I think it should work out OK. ]
====
So What?
========
Given those assumptions, we can have any acceleration-resistant payload
in a highly elliptical orbit, cheaply. What do we do with this capability?
1. Send supplies and construction materials into low earth orbit.
LEO is probably the main destination for just about everything,
but how do we get it there? And how do we take advantage of
bulk supplies in orbit (orbital construction, anyone?)
2. Do something useful in HEEO. If we have acceleration-resistant
experiments, we can do them right there. This doesn't sound likely.
3. Boost things into geosynchronous orbit. All of a sudden, it is
much cheaper to get acceleration-resistant payloads into GEO. What
do we want to do there?
These seem like appealing questions to work on for a bit. If you have
ideas on any of these, please go for broke.
I'll start with this one:
Getting to LEO
==============
1. Aerobraking
==============
The most promising way of getting from HEEO to LEO is to aerobrake into
an elliptical orbit with an apogee at the altitude of LEO, then boost
into a circular LEO.
I don't know anything about aerobraking. Can somebody contribute some
info? Of course, the thing enters the atmosphere at the same speed it
left it, which is over 10 km/s. I just realized: this is almost as bad as
the launch drag problem! The advantage of aerobraking is that it can be
done in stages, in the outer atmosphere. Maybe that's a big advantage.
My guess is that it's much easier that way. Help me out, gang.
I worked it out, and in order to boost from an elliptical orbit with perigee
at radius 6500 km and apogee at 7000 km, into a circular orbit of radius
7000 km, it takes 430 m/s of thrust. So if we can get into such an orbit
(in which most of the orbital velocity is already present) then it's quite
reasonable to bring along a solid booster to do the rest.
If the aerobraking is too difficult, maybe it would be better to do a
near-horizontal launch directly into a transfer orbit. This is likely
to require a bigger boost at the top, however.
2. Slow and steady
==================
We could possibly get to a low circular orbit using solar sails or ion
drives. Since the payload is in a stable orbit, we have lots of orbits
in which to do the change. What do you think?
I'd like to see some figures on ion drives - power requirements,
thrusts, and experiments that have been done. Does anyone want to
contribute that?
3. Just boost the sucker
========================
The delta vee is 2000 to 3000 m/s (I haven't worked it out) but if we
get desperate, we could just bring along a solid booster to slow down
the payload to LEO velocity. Well, it's still better than launching
from the ground.
This has made me a bit discouraged. What we want is a simple method
that gets us mega-savings, and here I am tacking on boosters left
and right. Time for some originality. 1, 2, 3, Go!
------------------------------------------------------------------------
| Marc Ringuette | mnr@cs.cmu.edu | I'll be stretching my mouth |
| CMU Computer Science | 412-268-3728 | to let those big words come |
| Pittsburgh, PA 15213 | | right out. [P. Gabriel] |
------------------------------------------------------------------------
------------------------------
[ end ]