Some peculiarities of racing in orbit

Discussion in 'General Fitness' started by mcconnel, Sep 13, 2003.

  1. mcconnel

    mcconnel Guest

    I spent much of my long run Saturday afternoon trying to make sense of the Columbia tragedy. Like
    just about everyone else I failed in that, but the effort did make me consider some interesting
    issues about motion -- getting from here to there. Inasmuch as this group is very much interested
    in getting from here to there, hopefully sooner rather than later, a discussion of these seems
    somewhat on topic.

    One of the first things I wondered when I heard about the probable damage from a piece of foam
    striking the left wing during launch was "why didn't they look and see if the damage were serious
    enough to warrant corrective action?" I had in mind some scheme involving hooking up with the space
    station and having all 7 astronauts camp out there while waiting to be rescued.

    As shuttle program director Ron Dittemore explained, this idea is fraught with difficulties and
    illustrates misconceptions many people have about motion in orbit. At any given moment the shuttle
    and space station were many thousands of miles apart, but what are thousands of miles to a ship
    capable of moving at thousands of miles per hour? Unfortunately, catching up with the distant space
    station isn't quite as simple as catching another car on the freeway. For one thing, the station is
    in a different orbit altogether; the analogy of catching a car on a different freeway is somewhat
    closer to the truth, but even that is misleading.

    Suppose, e.g., you first match your orbit with the space station's (sort of like getting on the
    correct freeway,) and then attempt to "catch up" with it by speeding up in the direction along the
    orbit. If you don't speed up, you'll never catch up, but if you do try to speed up, you'll merely
    move into a higher orbit! When you finally pull abreast of the space station you may find yourself
    many miles above it.

    To put it another way, a race in orbit would have a curious feature: try to speed up and you'd end
    up going uphill!

    To take an even more extreme example, suppose astronomers discovered a comet streaking toward the
    sun from the distant edges of the solar system on a hyperbolic orbit. Hyperbolic means that the
    comet is moving too fast to ever fall into permanent orbit around the sun. (This is not uncommon for
    comets. Many of them visit the inner solar system only once, whipping around the sun and thereafter
    returning to interstellar space, never to be seen again.) Let's say someone proposes sending a
    spacecraft out to meet the comet in order to study it, take pictures, or even land and have a look
    around. Simple, you say. Just send the spacecraft out in such a way that it will arrive at some
    point at the same time the comet does. Unfortunately, if you do this is a naive way, the comet will
    whip by you so fast you will probably not even see it. What you really have to do is to match your
    orbit with the comet's. This involves at least accelerating to the enormous velocity needed to enter
    a hyperbolic (escape) orbit around the sun.

    The key, then, to understanding rendezvous manouevers in space is the concept of matching orbits.
    But, as explained above, it is not enough just to match orbits. You must do so in exactly the right
    way, so that at the instant you reach the correct orbit you also find your goal object in exactly
    the same spot on that orbit as you are. Needless to say, this takes some very careful planning (i.e,
    mathematics,) to arrange.

    --
    ************************************************************************
    Terry R. McConnell Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150 [email protected]
    http://barnyard.syr.edu/~tmc Are we there yet?
    ************************************************************************
     
    Tags:


  2. Jake Lee

    Jake Lee Guest

    <[email protected]> wrote in message news:[email protected]...
    > I spent much of my long run Saturday afternoon trying to make sense of the Columbia tragedy. Like
    > just about everyone else I failed in that, but the effort did make me consider some interesting
    > issues about motion -- getting from here to there. Inasmuch as this group is very much interested
    in
    > getting from here to there, hopefully sooner rather than later, a
    discussion
    > of these seems somewhat on topic.
    >
    > One of the first things I wondered when I heard about the probable damage
    from
    > a piece of foam striking the left wing during launch was "why didn't they look and see if the
    > damage were serious enough to warrant corrective action?" I had in mind some scheme involving
    > hooking up with the space station and having all 7 astronauts camp out there while waiting to be
    > rescued.
    >
    > As shuttle program director Ron Dittemore explained, this idea is fraught with difficulties and
    > illustrates misconceptions many people have about motion in orbit. At any given moment the shuttle
    > and space station were many thousands of miles apart, but what are thousands of miles to a ship
    > capable of moving at thousands of miles per hour? Unfortunately, catching up with the distant
    > space station isn't quite as simple as catching
    another
    > car on the freeway. For one thing, the station is in a different orbit altogether; the analogy of
    > catching a car on a different freeway is somewhat closer to the truth, but even that is
    > misleading.
    >
    > Suppose, e.g., you first match your orbit with the space station's (sort
    of like
    > getting on the correct freeway,) and then attempt to "catch up" with it by speeding up in the
    > direction along the orbit. If you don't speed up, you'll never catch up, but if you do try to
    > speed up, you'll merely move
    into
    > a higher orbit! When you finally pull abreast of the space station you may find yourself many
    > miles above it.
    >
    > To put it another way, a race in orbit would have a curious feature: try
    to
    > speed up and you'd end up going uphill!
    >
    > To take an even more extreme example, suppose astronomers discovered a
    comet
    > streaking toward the sun from the distant edges of the solar system on a hyperbolic orbit.
    > Hyperbolic means that the comet is moving too fast to ever fall into permanent orbit around the
    > sun. (This is not uncommon for comets. Many of them visit the inner solar system only once,
    > whipping
    around
    > the sun and thereafter returning to interstellar space, never to be seen again.) Let's say someone
    > proposes sending a spacecraft out to meet the
    comet
    > in order to study it, take pictures, or even land and have a look around. Simple, you say. Just
    > send the spacecraft out in such a way that it will arrive at some point at the same time the
    > comet does.
    Unfortunately,
    > if you do this is a naive way, the comet will whip by you so fast you will probably not even see
    > it. What you really have to do is to match your
    orbit
    > with the comet's. This involves at least accelerating to the enormous velocity needed to enter a
    > hyperbolic (escape) orbit around the sun.
    >
    > The key, then, to understanding rendezvous manouevers in space is the
    concept
    > of matching orbits. But, as explained above, it is not enough just to match orbits. You must do so
    > in exactly the right way, so that at the
    instant
    > you reach the correct orbit you also find your goal object in exactly the same spot on that orbit
    > as you are. Needless to say, this takes some very careful planning (i.e, mathematics,) to arrange.
    >

    Yes, it is difficult to do, but it's not exactly rocket science, now, is it?


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  3. Mike Conway

    Mike Conway Guest

    >From: [email protected] ()

    >One of the first things I wondered when I heard about the probable damage from a piece of foam
    >striking the left wing during launch was "why didn't they look and see if the damage were serious
    >enough to warrant corrective action?"

    From the AP:

    "While Columbia was still in orbit, NASA engineers analyzed launch footage frame-by-frame and were
    unable to determine for certain whether the shuttle was damaged by the insulation. But they ran
    computer analyses for different scenarios and different assumptions about the weight of the foam,
    its speed, and where under the left wing it might have hit, even looking at the possibility of tiles
    missing over an area of about 7 inches by 30 inches, NASA said.

    The half-page engineering report - issued on Day 12 of the 16-day flight - indicated ''the potential
    for a large damage area to the tile.'' But the analyses showed ''no burn-through and no
    safety-of-flight issue,'' the report concluded.

    High-level officials at NASA said they agreed at the time with the engineers' assessment."

    *************************************

    How do you think these people (the NASA engineers) feel now? Apparently, objects have fallen from
    one part of the shuttle to another during liftoff before, specifically to Columbia during a launch
    in 1992, where the tiles were apparently damaged but not enough to affect anything.

    Sad, sad, sad.

    Mike C
     
  4. Sam

    Sam Guest

    The point is moot since this mission did not carry the docking device although your explanation of
    the different orbits is good.

    <[email protected]> wrote in message news:[email protected]...
    > I spent much of my long run Saturday afternoon trying to make sense of the Columbia tragedy. Like
    > just about everyone else I failed in that, but the effort did make me consider some interesting
    > issues about motion -- getting from here to there. Inasmuch as this group is very much interested
    in
    > getting from here to there, hopefully sooner rather than later, a
    discussion
    > of these seems somewhat on topic.
    >
    > One of the first things I wondered when I heard about the probable damage
    from
    > a piece of foam striking the left wing during launch was "why didn't they look and see if the
    > damage were serious enough to warrant corrective action?" I had in mind some scheme involving
    > hooking up with the space station and having all 7 astronauts camp out there while waiting to be
    > rescued.
    >
    > As shuttle program director Ron Dittemore explained, this idea is fraught with difficulties and
    > illustrates misconceptions many people have about motion in orbit. At any given moment the shuttle
    > and space station were many thousands of miles apart, but what are thousands of miles to a ship
    > capable of moving at thousands of miles per hour? Unfortunately, catching up with the distant
    > space station isn't quite as simple as catching
    another
    > car on the freeway. For one thing, the station is in a different orbit altogether; the analogy of
    > catching a car on a different freeway is somewhat closer to the truth, but even that is
    > misleading.
    >
    > Suppose, e.g., you first match your orbit with the space station's (sort
    of like
    > getting on the correct freeway,) and then attempt to "catch up" with it by speeding up in the
    > direction along the orbit. If you don't speed up, you'll never catch up, but if you do try to
    > speed up, you'll merely move
    into
    > a higher orbit! When you finally pull abreast of the space station you may find yourself many
    > miles above it.
    >
    > To put it another way, a race in orbit would have a curious feature: try
    to
    > speed up and you'd end up going uphill!
    >
    > To take an even more extreme example, suppose astronomers discovered a
    comet
    > streaking toward the sun from the distant edges of the solar system on a hyperbolic orbit.
    > Hyperbolic means that the comet is moving too fast to ever fall into permanent orbit around the
    > sun. (This is not uncommon for comets. Many of them visit the inner solar system only once,
    > whipping
    around
    > the sun and thereafter returning to interstellar space, never to be seen again.) Let's say someone
    > proposes sending a spacecraft out to meet the
    comet
    > in order to study it, take pictures, or even land and have a look around. Simple, you say. Just
    > send the spacecraft out in such a way that it will arrive at some point at the same time the
    > comet does.
    Unfortunately,
    > if you do this is a naive way, the comet will whip by you so fast you will probably not even see
    > it. What you really have to do is to match your
    orbit
    > with the comet's. This involves at least accelerating to the enormous velocity needed to enter a
    > hyperbolic (escape) orbit around the sun.
    >
    > The key, then, to understanding rendezvous manouevers in space is the
    concept
    > of matching orbits. But, as explained above, it is not enough just to match orbits. You must do so
    > in exactly the right way, so that at the
    instant
    > you reach the correct orbit you also find your goal object in exactly the same spot on that orbit
    > as you are. Needless to say, this takes some very careful planning (i.e, mathematics,) to arrange.
    >
    > --
    > ************************************************************************
    > Terry R. McConnell Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150 [email protected]
    > http://barnyard.syr.edu/~tmc Are we there yet?
    > ************************************************************************
     
  5. Sam

    Sam Guest

    "Mike Conway" <mp[email protected]> wrote in message news:[email protected]...
    > >From: [email protected] ()
    >
    > >One of the first things I wondered when I heard about the probable damage from a piece of foam
    > >striking the left wing during launch was "why didn't they look and see if the damage were serious
    > >enough to warrant corrective action?"
    >
    > From the AP:
    >
    > "While Columbia was still in orbit, NASA engineers analyzed launch footage frame-by-frame and were
    > unable to determine for certain whether the
    shuttle was
    > damaged by the insulation. But they ran computer analyses for different scenarios and different
    > assumptions about the weight of the foam, its
    speed,
    > and where under the left wing it might have hit, even looking at the possibility of tiles missing
    > over an area of about 7 inches by 30 inches,
    NASA
    > said.
    >
    > The half-page engineering report - issued on Day 12 of the 16-day flight - indicated ''the
    > potential for a large damage area to the tile.'' But the analyses showed ''no burn-through and no
    > safety-of-flight issue,'' the
    report
    > concluded.
    >
    > High-level officials at NASA said they agreed at the time with the
    engineers'
    > assessment."
    >
    > *************************************
    >
    > How do you think these people (the NASA engineers) feel now? Apparently, objects have fallen from
    > one part of the shuttle to another during liftoff before, specifically to Columbia during a launch
    > in 1992, where the tiles
    were
    > apparently damaged but not enough to affect anything.
    >
    > Sad, sad, sad.
    >
    > Mike C

    As more evidence rolls in, this will be clarified. But stuff I heard this morning
    indicates the damage of the piece falling during ascension is not the cause.
     
  6. Mike Tennent

    Mike Tennent Guest

    "Tim Downie" <[email protected]> wrote:

    >If you find a fault and *can't* repair it and there's no chance of a rescue mission, you might well
    >wish that you hadn't known about it before re-entry.
    >
    >Tim

    Precisely. If they had known there was damage, there's nothing they could have done about it.

    Not enough fuel to reach the ISS orbit. No docking ring if they did. No "repair kit" if they could
    get to the wing. Newton. (For every action, etc. In space, if you push on something, you go the
    other way unless you're anchored to it. There is absolutely nothing on the wing of the shuttle to
    anchor to. Hence, no way to apply a new tile.)

    Sometimes, there are situations that have no solutions. In this case, if they did have verification
    of some damage, perhaps all they could have done is pray. They could be given a choice - stay in
    orbit and slowly die or try to re-enter with damaged tiles.

    I'd choose the second option.

    Mike Tennent "IronPenguin" Operating Traffic Lights Crossbucks Special Effects Lighting
    http://www.ironpeng.com/ipe
     
  7. Steve Common

    Steve Common Guest

    "Tim Downie" <[email protected]> wrote:

    >An appealing idea but I suspect that without carrying an unfeasibly large bag of spares and tools,
    >the number of repairs that they could realistically do would be very limited.

    The idea wasn't to mend it but to get around it by using the backup procedure. I had been rather
    stupid in assuming that there was an emergency reentry capsule or similar. Apparently this isn't
    the case...
     
  8. Chris Smith

    Chris Smith Guest

    Mike Tennent wrote:

    > Precisely. If they had known there was damage, there's nothing they could have done about it.
    >
    > Not enough fuel to reach the ISS orbit. No docking ring if they did. No "repair kit" if they could
    > get to the wing. Newton. (For every action, etc. In space, if you push on something, you go the
    > other way unless you're anchored to it. There is absolutely nothing on the wing of the shuttle to
    > anchor to. Hence, no way to apply a new tile.)
    >
    > Sometimes, there are situations that have no solutions. In this case, if they did have
    > verification of some damage, perhaps all they could have done is pray. They could be given a
    > choice - stay in orbit and slowly die or try to re-enter with damaged tiles.

    Have you read about the third option I saw somewhere? Not sure of its authenticity, but to
    summarize: if NASA concluded that there was sufficient damage to the shuttle that normal re-entry
    would likely be fatal, there is an option to use a different angle of descent (steeper) that would
    doom the shuttle but permit some kind of high-altitude parachute exit by the crew. Maybe this was an
    early news story that referred to systems on newer shuttles, I don't have a reference, but I thought
    it was interesting. If true, the decision would have to be made to jettison a mega-billion-dollar
    shuttle to save the crew--in a risky maneuver that might fail. chris
     
  9. Steve Common

    Steve Common Guest

    Mike Tennent <[email protected]> wrote:

    >Sometimes, there are situations that have no solutions. In this case, if they did have verification
    >of some damage, perhaps all they could have done is pray. They could be given a choice - stay in
    >orbit and slowly die or try to re-enter with damaged tiles.

    Or find something else. Everyone here forgotten that "surely dead" Apollo mission?
     
  10. Ron Natalie

    Ron Natalie Guest

    "Chris Smith" <[email protected]> wrote in message news:[email protected]...
    > > you go the other way unless you're anchored to it. There is absolutely nothing on the wing of
    > > the shuttle to anchor to. Hence, no way to apply a new tile.)

    Saw an interview the otherday with some NASA guy saying they had investigated this earlier and had
    not found any adhesive that would work properly in a vacuum.
     
  11. mcconnel

    mcconnel Guest

    In article <[email protected]>, Robert Grumbine <[email protected]> wrote:
    >
    > Really it is 'just' a matter of matching orbits. The problem is that an orbit is really a 6
    > dimensional entity. You want to be in the same position (3 dimensions) and going the same
    > velocity (3 more), at the same time (not a dimension because you don't necessarily care about
    > which time it is that you meet up, but 7 dimensions if you
    >do).
    >

    You are talking about the orbit in phase space? But orbit is commonly used to refer to the spatial
    part alone. For example, the `orbit' equation in celestial mechanics yields an orbit in this sense.
    Additional information and calculation (e.g, Kepler's equation) is needed in order to locate the
    body along its orbit.

    The public understands orbit in the latter sense; inasmuch as the article was addressing public
    misconceptions (or potential misconceptions,) it was IMO the more appropriate interpretation.

    Moreover, if you share a (3 dimensional) orbit and are at the same place on it at the same time,
    then you necessarily share a 6 dimensional orbit; so the distinction is unimportant in any case.
    (Proof: the orbital parameters determine the angular momentum vector and the total energy
    completely. That leaves two degrees of freedom -- the time of periapsis and the location of the time
    origin. If you are in the same place at the same time as the other guy, that fixes another dof. The
    remaining one is arbitrary and irrelevent.)

    What does this have to do with running? Well, I didn't run today, so at no time did I enter low
    earth orbit. (As you do many times during a run.)

    Why didn't I run today? I always take Sunday off, following a Saturday long run and preceeding a
    Monday track workout. It is the most jealously guarded feature of my running program.

    --
    ************************************************************************
    Terry R. McConnell Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150 [email protected]
    http://barnyard.syr.edu/~tmc Are we there yet?
    ************************************************************************
     
  12. In article <[email protected]>, <[email protected]> wrote:
    >In article <[email protected]>, Robert Grumbine <[email protected]> wrote:
    >>
    >> Really it is 'just' a matter of matching orbits. The problem is that an orbit is really a 6
    >> dimensional entity. You want to be in the same position (3 dimensions) and going the same
    >> velocity (3 more), at the same time (not a dimension because you don't necessarily care about
    >> which time it is that you meet up, but 7 dimensions if you
    >>do).
    >
    >You are talking about the orbit in phase space?

    Yes, pretty much.

    >But orbit is commonly used to refer to the spatial part alone. For example, the `orbit' equation in
    >celestial mechanics yields an orbit in this sense. Additional information and calculation (e.g,
    >Kepler's equation) is needed in order to locate the body along its orbit.

    If you're trying to dock, the location along the orbit is important.

    In celestial mechanics, however, the phase space approach is common. Indeed, unavoidable if you're
    trying to do much of anything (examine crossings, stability, trajectory, ...) The keplerian
    elements stand at more than 3.

    >The public understands orbit in the latter sense; inasmuch as the article was addressing public
    >misconceptions (or potential misconceptions,) it was IMO the more appropriate interpretation.

    But you and I are math geeks.

    >Moreover, if you share a (3 dimensional) orbit and are at the same place on it at the same time,
    >then you necessarily share a 6 dimensional orbit; so the distinction is unimportant in any case.
    >(Proof: the orbital parameters determine the angular momentum vector and the total energy
    >completely. That leaves two degrees of freedom -- the time of periapsis and the location of the
    >time origin. If you are in the same place at the same time as the other guy, that fixes another
    >dof. The remaining one is arbitrary and irrelevent.)

    Imagine two circles with a common center. They can easily be arranged to cross at only two points
    (ex: let one be an equatorial orbit and the other be polar). There are two free parameters left
    (inclination and longitude of their mutual node) still.

    Perhaps we're crossing cultures, as I'm more a physics geek than math. If you mean by orbit 'the
    set of all points the body passes through', then I think I understand and agree with you. The
    thing is, that's not how I (physics types more generally) think of such things. I (we?) work more
    with observables. We have not, for instance, observed a full orbit of Pluto about the sun, in
    which case we couldn't really say that we know its orbit in the 'set of all points' sense. On the
    other hand, we do know its location in the phase space, which lets us believe that we can compute
    its future location pretty well (modulo chaos, which apparently is on the 10's of millions of
    years time scale out there).

    >What does this have to do with running? Well, I didn't run today, so at no time did I enter low
    >earth orbit. (As you do many times during a run.)

    Alas (?) that the orbits intersect the surface of the earth. Brings up a question: assuming a
    specified, uniform, density, at what radius would a body's escape velocity be low enough for a
    runner to have to worry about it?

    --
    Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
    Sagredo (Galileo Galilei) "You present these recondite matters with too much evidence and ease; this
    great facility makes them less appreciated than they would be had they been presented in a more
    abstruse manner." Two New Sciences
     
  13. mcconnel

    mcconnel Guest

    In article <[email protected]>, Robert Grumbine <[email protected]> wrote:
    >In article <[email protected]>, <[email protected]> wrote:
    >>In article <[email protected]>, Robert Grumbine <[email protected]> wrote:
    >>>
    >>
    >>You are talking about the orbit in phase space?
    >
    > Yes, pretty much.
    >
    [snip]
    >
    > But you and I are math geeks.

    If that weren't clear before, it certainly is now.

    > Perhaps we're crossing cultures, as I'm more a physics geek than math. If you mean by orbit 'the
    > set of all points the body passes through', then I think I understand and agree with you.

    Yes, that was the intent. Same orbital parameters: semi-major axis, inclination, eccentricity,
    longitude of ascending node, longitude of perihelion, time of perihelion passage. I guess you were
    talking about orbits having the "same shape." Not what I meant.

    >
    >>What does this have to do with running? Well, I didn't run today, so at no time did I enter low
    >>earth orbit. (As you do many times during a run.)
    >
    > Alas (?) that the orbits intersect the surface of the earth. Brings up a question: assuming a
    > specified, uniform, density, at what radius would a body's escape velocity be low enough for a
    > runner to have to worry about it?
    >

    Should be pretty simple to figure out. Remind me to assign it as an exercise so I can find out
    the answer.

    That reminds me of an old Arthur C. Clarke story. A man is stranded on Phobos (moon of Mars) with a
    starship trying to kill him. That's right: one unarmed man against an entire starship with nuclear
    weapons. The man wins because he can go halfway across the moon with a single bound and is able to
    keep the moon between him and the ship at all times. The only thing he has to worry about is just
    what you mention: if he jumps a bit too far he can jump right into orbit, to be left a sitting
    (well, floating) duck.

    --
    ************************************************************************
    Terry R. McConnell Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150 [email protected]
    http://barnyard.syr.edu/~tmc Are we there yet?
    ************************************************************************
     
  14. In article <[email protected]>, <[email protected]> wrote:
    >In article <[email protected]>, Robert Grumbine <[email protected]> wrote:

    [snip]

    >> Alas (?) that the orbits intersect the surface of the earth. Brings up a question: assuming a
    >> specified, uniform, density, at what radius would a body's escape velocity be low enough for a
    >> runner to have to worry about it?
    >>
    >
    >Should be pretty simple to figure out. Remind me to assign it as an exercise so I can find out
    >the answer.

    No fair copying my trick!

    >That reminds me of an old Arthur C. Clarke story. A man is stranded on Phobos (moon of Mars) with a
    >starship trying to kill him. That's right: one unarmed man against an entire starship with nuclear
    >weapons. The man wins because he can go halfway across the moon with a single bound and is able to
    >keep the moon between him and the ship at all times. The only thing he has to worry about is just
    >what you mention: if he jumps a bit too far he can jump right into orbit, to be left a sitting
    >(well, floating) duck.

    Fun story. Tales from the White Hart, I think.

    The win, we must add, is because he was to be making a rendezvous with a big nasty ship from his
    own side. 'All' he had to do was to stay alive for help to arrive. But it was fun that his angular
    velocity was able to outstrip the battleship's (ship not being able to orbit such a small body).

    --
    Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
    Sagredo (Galileo Galilei) "You present these recondite matters with too much evidence and ease; this
    great facility makes them less appreciated than they would be had they been presented in a more
    abstruse manner." Two New Sciences
     
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