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Changing orbits

Posted by: Ekkehard Augustin - Fri Dec 10, 2004 9:53 am
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Changing orbits 
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Post Changing orbits   Posted on: Fri Dec 10, 2004 9:53 am
In the Spaceflight Cafe it has been asked - implicitly - wether the Space Shuttle can change orbits.

The velocities required for stable circular orbits seem to suggest that changing orbits requires much time or high velocities in changing the angle to the equator. this last possibility may include strong forces.

Does changing orbits require that amount of propellant that is required too to launch a spacecraft into orbit?

The question more interesting under these aspects:

Could the ballute technology of Ball be used to change orbits? The ballute could be aside of the spacecraft instead of behind, in front of or below for this purpose.

What do you think?



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Fri Dec 10, 2004 3:04 pm
Yes, the shuttle can change it's orbit, but only slightly. It uses up all most all of it's propellant just getting off the ground and up to a minimum energy orbit. The remaining propellant can increase the altitude a few hundred miles and the plane a few degrees, but not more.

As for using a ballute for changing orbits, the answer is yes and no. The ballute would allow the shuttle to slow down using atmospheric drag at a higher altitude than it could without a ballute, but it could not speed up or change orbital planes. This is because the only force produced by the ballute is drag which is always directly opposite the direction of travel. Basically there is no way to steer it. Placing the ballute to one side would make the drag force not pass through the center of gravity of the shuttle causing it to yaw and tumble, but it would not change the direction of the force with respect to the orbital velocity which is what you would need for steering. It may be possible to steer slightly by turning the entire shuttle-ballute assemble with respect to the orbital velocity but the shuttle can already do the same thing with it's wings and thermal tiles, it just has to do it lower in the atmosphere to get measurable drag.


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Post    Posted on: Fri Dec 10, 2004 4:17 pm
This post is a continuation of a discussion of orbital mechanics in the Disposal of radioactive materials topic.

You are correct, lower orbits have a higher velocity, but to get to this higher velocity orbit from a lower velocity orbit, you need to slow down. Twice! Now you may ask how do I slow down to speed up? When you slow down from a high orbit, you start to “fall” toward the low orbit, but as you “fall” you speed up. Now it is true that your speed increase is all straight down and not at all side to side, but your new velocity is your old side to side velocity plus a vertical component. Vector addition gives a new higher velocity at an angle to vertical. So basically you speed up and change direction at the same time and the effect is seen as an increase in speed along the elliptical orbit path and not directly down. The result is that you end up lower and faster than when you started but again travelling parallel to the surface. In fact at the low point of your elliptical orbit you will be going too fast to stay in a circular orbit at that altitude and so you will coast back “uphill” to where you started. But when you get there you are in the same place and at the same speed as you were before, at a higher altitude but going too slow for a circular orbit.

The concepts of angular momentum and energy are some of the hardest in classical physics. Consider a gyroscope. If you push it forward then it tips sideways. If you push it sideways then it tips backward. It seems like an intelligent force is playing games with you. Orbital mechanics have the same characteristics. That is why people like Lagrange and Hamilton use energy to formulate their mathematical descriptions of these dynamical systems. You can do it just using Newton’s laws, but it is not so easy (not that Hamiltonians or Lagrangians are easy). Higher orbits have higher energy. The fact that the orbital speed is lower may fool you into thinking it is a lower energy, but that is because you are only thinking of kinetic energy. Your kinetic energy is 1/2MV^2. Since V is smaller and everything else is unchanged, your kinetic energy is lower. But your potential energy is GMmr. Since r is greater and everything else is the same, your potential energy is greater. Since kinetic energy depends on the square of velocity but potential energy depends only on the first power of r, your potential energy increases faster than your kinetic energy falls as you move to higher and slower orbits. So the counter-intuitive result is slower orbits have higher TOTAL energy.


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Post    Posted on: Sat Dec 11, 2004 7:40 pm
Sorry for responding without having read more than the first few sentences of your post - I will read the rest later.

Going from a lower-velocity-orbit to a higher-velocity-orbit doesn't require to slow down but - in opposite to speed up - it's required to achieve the higher velocity valid at the nwe orbit if the object should keep that orbit instead of moving further into the inner of the orbit and falling into the sun at least.

But in the discussion about the disposal of radioactive material it's inteneded that the Materials fall into the sun. If the materials (and their spacecraft, but that requires an additional post in the other thread) shouldn't achieve a more inner higher-velocity-orbit but fall into the sun they shouldn't be accelerated nor thex need to be decelerated.

It's really the higher velocity the planets at more inner orbits have tangential to their orbit what's preventing tham from falling into the sun. They got that velocity while the solar system was condensing and forming - they got it from the planetesimals that clustered to form that planets and they got it too from collisions supposedly.Thaey had been accelerated formerly - it's not the sun what gave them their high velocities and it's not a property of that orbit. It#s simply a necessary physical requirement to keep that orbit and not to fall into the sun.

If a spacecraft would orbit at Earth's orbit having Earth's tangetial velocity and would be accelrated vertical to the sun only but not tangential to Earth's orbit it not only never would achieve a more inner circular orbit - it wouldn't achieve an elliptical orbit too. It simply wpould start to spiral into the sun - seen from Vega for example.


To turn now to the initial sense of this thread the ballute technology will cause a spiral movement of a spacecraft too - as described in the article reporting Ball's idea. Using a ballute near the sun would assist the materials to fall into the sun because the corona is a region where the density of gases is higher than at the orbits of the planets.

But I don't think that ballutes are required for these purposes - concerning this I will write a post later in the thread concerning the disposal of radioactive materials.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Sun Dec 12, 2004 5:31 pm
Now I've read your post completely, campbelp2002, and see that it's true what I suppose since ashort time after my last post.

Seen from my vector calculations by seperating the orbital velocity into a vertical component and a tangential component you are arguing that the tangential component must be decreased to fall down to the orbit that is closer to the sun.

Alright - that is one possibility. But I myself am arguing by the vertical component. Instead of slowing down the tangential componentthe vertical component could be increased which would lead to the same or at least similar result as decreasing the tangential component.

To keep the closer orbit once it is achieved the vertical and the tangential component need to be readjusted.

But concerning the disposal of radioactive materials no orbit is desired - the materials really are wanted to fall into the sun instead of ending up in an orbit.

Please let me remark here that some terms may cause misunderstandings. "Higher orbits have higher energy" from my point of view should be better reformulated as "Higher orbits REQUIRE higher energy" - it's not the orbit that gives energy to an object - it's the energy that gives the orbit a higher orbit.

My own vector calculations didn't have anything to do with energy - the vectors I had in mind simply were representing velocities - more length=more velocity.

In this sense the velocity at a certain orbit is the sum of the vertical and the tangential component - regardless of which way the length or the value of a component has been caused.

What is relevant too is that at orbits there always is an equilibrium of the two components. At a circular orbit the values or lengths of the two components at each point of the orbit are identical and constant leading to constant equilibrium velocity - at an elliptical orbit the values and lengths are differing from point to point leading to varying equlibrium velocity. Except the perihelion and aphelion velocities all velocity values at the down going side are repeated at the up gong side. Except in perihelion and the aphelion the vertical component isn't vertical.



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Post    Posted on: Mon Dec 13, 2004 5:39 pm
Ekkehard Augustin wrote:
Seen from my vector calculations by seperating the orbital velocity into a vertical component and a tangential component you are arguing that the tangential component must be decreased to fall down to the orbit that is closer to the sun.

Alright - that is one possibility. But I myself am arguing by the vertical component. Instead of slowing down the tangential componentthe vertical component could be increased which would lead to the same or at least similar result as decreasing the tangential component.


Ah, now we get to the heart of the matter. Yes, I am saying you need to reduce the tangential component, but I will talk about a vertical change in this post.

In an earlier post I describe an attempt to reach the ground from a 200 mile high circular orbit by adding a downward 100 MPH vertical component. It may seem that this 100 MPH down component will bring you down in 2 hours, but it won’t. Here is my reasoning.

Let’s assume you are in a circular orbit you at a speed of 7,800 Meter per second. (I’ll put on my physics hat and use SI units.) The velocity vector is perpendicular to the radius vector (the vector from the center of the Earth to the space craft) with no component parallel to the radius vector. There is also an acceleration vector acting on the vehicle with a 10 M/S^2 downward component along the radius vector and no component perpendicular to the radius vector. This causes the velocity vector to constantly change direction but not magnitude. After orbiting 90 degrees around the Earth the velocity, radius and acceleration vectors have all changed direction by 90 degrees but have not changed in magnitude at all. After 180 degrees you are going 7,800 M/S in the opposite direction. You have accelerated 15,600 M/S without using any rocket power. When in orbit you are in effect always falling but missing the Earth by racing out over the horizon before you can reach the ground. Try not to think of an orbit as a ball attached to a string and whirling around your body because this will mess up your thinking and make orbits and weightlessness hard to understand. You are in a 10 M/S^2 gravity field but at the same time you are weightless because of your motion.

Now if a 100 M/S downward velocity change is instantly imparted to the space craft, the velocity vector will keep the same 7,800 component perpendicular to the radius vector and gain a 100 M/S downward component along the radius vector. The velocity vector has changed direction by ATN (100/7800) = 0.73 degrees and has a new magnitude of SQRT(7800^2 + 100^2) = 7,800.64 M/S. Notice that in addition to starting to move down that you have slightly increased your orbital speed. Now you are going too fast for a stable circular orbit, which would tend to throw you out to a higher orbit, and at the same time you are headed down to a lower orbit at 100 M/S. After 1 second, the 10 M/S^2 acceleration acting along the radius vector has added another 10 M/S to your vertical component (and still left the 7,800 component unchanged). Now the velocity vector has changed direction slightly more and it’s magnitude has increased another 0.14 M/S to 7,800.78 M/S. Your orbital speed is increasing as you angle toward the ground because the acceleration vector is no longer exactly perpendicular to the velocity vector. The more elliptical the orbit the more pronounced this effect because of the greater the angle between the acceleration vector and the velocity vector. Now after traveling 90 degrees around the Earth the space craft is lower, the radius and acceleration vectors have changed direction by exactly 90 degrees, the velocity vector has changed direction by a little more than 90 degrees and, most importantly, the velocity vector’s magnitude has been increasing all the while. Somewhere less than 180 degrees from the starting point the space craft will stop descending because of the increased magnitude of the velocity vector. At that point the vehicle will be travelling perpendicular to the radius vector but going too fast for a circular orbit at that altitude and it will then start moving back up. The vehicle and will pass its original altitude with a 100 M/S upward velocity component and a 7,800 M/S velocity component perpendicular to the radius vector and a magnitude of 7,800.64 M/S. It will continue up to a high point above it’s original altitude before making a complete orbit around the Earth, at which point it will be moving perpendicular to the radius and acceleration vectors and perpendiculat to the radius vector (tangent to a circular orbit) but going too slow for a circular orbit at that altitude. It will then start down and eventually pass exactly through the starting point with a 100 M/S down component along the radius vector and a 7,800 M/S component perpendicular to the radius vector and a magnitude of 7,800.64 M/S.

The confusing thing about this is the constantly changing direction of all the vectors.

So the bottom line is that a sudden velocity change directly downward does not “push” you to a lower orbit. It changes your stable circular orbit to a stable elliptical orbit that has a low point lower and a high point higher than the original circular orbit.


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Post    Posted on: Tue Dec 14, 2004 8:55 am
It would take time to think over your answer, to calculate it all myself and making graphics - I'm missing this time right now.

But there is one point I really cannot agree - the directions of vectors don't change from my point of view. It may be that here too we are arguing from different basises.

The vertical vector is a vector pointing to the center of gravity in my argumentation. The center of gravity is the center of a circular orbit too - so the vertical vector doesn't change its direction seen from the gravitational center. At a circular orbit the tangential vector always is vertical to the vertical vector - seen from the center of gravity this component doesn't change its direction too. The change of direction only occurs seen from outside the gravitational center.

So an increase of the vertical vector means an acceleration to the gravitational center. If the tangential component isn't changed too the object will begin spiraling down - if there would be no atmospherical friction.

In practice the may be the simple problem that concerning an orbit around Earth an increase of vertical velocity isn't easyly to be done whereas a decrease of the tangential component doesn't be that problem.



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Post    Posted on: Tue Dec 14, 2004 2:08 pm
Ekkehard Augustin wrote:
If the tangential component isn't changed too the object will begin spiraling down - if there would be no atmospherical friction.


No, you have it exactly backward. A spiral is only possible if there IS friction. In the absence of friction, a spiral is an IMPOSSIBLE orbit!


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Post    Posted on: Tue Dec 14, 2004 2:57 pm
That a spiral really is possible without atmospherical friction has been shown by comets falling into the sun or into Jupiter.

They really were in an orbit (elliptical), passed a significant gravitational center (sun or Jupiter) and were pulled by the center's gravitational force closer to that center which means that the gravitation increased the "vertical" component of velocity or the "vertical" vector.

But the tangential component (vector) wasn't increased which meant the loss of the equilibrium of the components that is required to keep the orbit.

So the comets have flown a course going closer and closer to the center - that course was a curve each point of which was closer to the center then the point befor it. That's a property of spirals.

Sun and Jupiter are extended bodies - you may argue that there was an orbit which goes into these bodies. But really this means to fall into these bodies - the orbits were too close then to be complete. They were barred by the surface of that body.

An orbit can become a spiral if the equilibrium of the components of velocity is lost - "spiral" doesn't necessarily mean that it has to go around the center one or several times. It only means that even without an obstacle the course never will not return into itself - into its initial point.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

EDIT: Because it just this moment came to my mind - relevant here isn't wether an object is moving spirally or parabolic but only the fact that something can miss to keep an orbit around the sun, to get into an orbit around the sun. It can be moved out of each circular or elliptical orbit simply by gravitation or acceleration caused by engines - the equlibrium of the velocity components the equilibirum between gravitational force, the force responsible for the tangential component of velocity, and the centrifugal force can be lost. This loss is sufficient to cause the object to fall into the sun.


Last edited by Ekkehard Augustin on Wed Dec 15, 2004 11:25 am, edited 1 time in total.



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Post    Posted on: Tue Dec 14, 2004 5:12 pm
Ekkehard Augustin wrote:
That a spiral really is possible without atmospherical friction has been shown by comets falling into the sun or into Jupiter.


All comets that fall into the Sun are travelling in parabolic orbits, not spirals. None of the periodic comets (like Halley's comet) that has been observed repeatedly passing the Sun has ever fallen into the Sun. All the comets that DO fall into the sun are "new" comets that have not been observed before. They were already on a collision path to the Sun thousands of years ago when they were still out past Pluto. We just didn't notice them until they got close to the Sun.
The comet that hit Jupiter was one of these too. It just happened to hit Jupiter before it got all the way to the Sun. If it had missed Jupiter, it may or may not have hit the Sun. If it had missed Jupiter and the Sun it would have coasted back out to the far outer solar system and not be seen again for thousands or millions of years. Most comets do just that, they are seen passing the sun once and are never seen again. Just a few are in well known close orbits, like Halley's comet.


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Post    Posted on: Wed Dec 15, 2004 11:14 am
May be - but there are other examples of spiral courses of boddies or materials in space described by Astrophysics.

1. The processes initiating the creation of a planetary system start with irregular movements of dusts and gases.

Randomly - by obstacles, light etc. - portions of dust and gases form wide clusters far away from beginning nuclear fusion. These clusters begin to influence the irregular movements of the dusts and gases in their vicinity giving these movements certain directions and causing structure within all these movements. Most of the materials in the vicinity of the clusters begin to move around the clusters instead of going straight ahead.

Now the clusters of material and the materials in their vicinity begin to increase their density. Increasing their density while being in motion around a cluster or the center of the cluster they are parts of already means to be closer to the cluster or the center of the cluster after a completion of 360° movement than the previous completion of 360° movement. This is spiraling movement.

2. I have articles of "Spektrum der Wissenschaften - the german version of "Scientific American" saying that after formation of the planets of the solar system they first moved very irregularly compared to their actual movements and Neptune for example really moved several AUs to the outer edge of our system. But they allways went around sun - so the irregular movements and the movement of Neptune to the outer edge must have been spirals instead of parabolas or hyperbolas.

3. When a component of a double star system is at its end of life and forms a neutron star while the other component remains a normal star the neutron star often begins to pull material from the normals star. already the first arriving material goes around the neutron star but is closer to the surface of the neutron star after each completion of 360° and then impacts that surface - this is a spiral movement. The result is an accretion disk.

Stars going around a black hole often are going spirals too.

All these spirals are formed by gravitation when there is no equilibrium between the vectors representing the components of velocity. At least in case 2 and 3 friction doesn't matter.

If I find the time required I will look into some books written by astronomers to quote them.

When sun collapses in the very far future it still will be rotating - which means spiral movements during the collaps. This won't be caused by friction only because the collapse will be caused by gravitation and the loss of its equilibrium to pressure by radiation. The collapse will go on on much faster than it would go on by friction only.



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Post    Posted on: Wed Dec 15, 2004 12:00 pm
To add something concerning the comets. The Scientists still are assuming that there is Oort's Cloud far beyond the outer edge of the Kuiper Belt. Oort's Cloud according to the scientists is formed by comets partially and these comets are going around sun at nearly circular orbits.

The orbits of comets leaving Oort's Cloud for the inner solar system have been disturbed by any events that reshaped the orbits to another course - which then can be another and now extremely elliptical orbit or a parabolic or hyperbolic course. These too are examples showing that something thrown out of its initial orbit can fail to achieve another orbit without friction being involved. Even if a comet coming in at a parabolic course falls into Jupiter shows this.

All this shows, that besides elliptical orbits something not being an orbit can be the result of the disturbance of an orbit - regardless of the source of the disturbance.



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Post    Posted on: Wed Dec 15, 2004 1:55 pm
You are correct that there are examples of spirals, but they all involve tidal friction or relativity or some mechanism to slowly and continuously remove energy and momentum from the system. If we limit ourselves to a brief pulse of rocket power then coast in a conservative orbit (where conservation of energy is obeyed) and watch for short time periods (years and not millennia), then spirals never occur.

I'll put all future posts on this subject to the disposal of radioactive waste topic so as not to split the discussion between two topics.


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Post    Posted on: Wed Apr 13, 2005 1:31 pm
To turn to the original topic of this thread - there is quite another possibility to change the orbit. This possibility would enable to chnage to a crossing orbit.

It's a derivative of the space elevator concept and it might have been thought about in another thread.

The space elevator is designed to catapult a vehicle or an object into the interplanetary space if released beyond the geostationary altitude. The space elevator is rotating around Earth's axis.

Now I could imagine a tether or a beam or so that doesn't rotate around Earth's axis and the axis it is rotating around really isn't parallel to Earth's axis - it might be rotating nearly parallel to Earth's surface while orbiting Earth.

Then a vehicle could dock to that object and move along its rotating part outside. It could stop when it is at a section rotating by a special desired velocity expressed by km/s. If released in a moment when the rotating part is not moving parallel to the orbit of the object then the vehicle would leave the object's orbit and it would be inserted into a crossing orbit.

What about it?



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Post    Posted on: Wed Apr 13, 2005 1:38 pm
If I understand you correctly, you are talking about releasing an object from the space elevator at a lower point, below geosynchronous orbit. I was actually thinking about that myself just yesterday and there are interesting possibilities.


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