Bill Jones asked:
While discussing this topic of orbital decay, I wonder if someone would comment on the apparent anomoly whereby a sat in leo that encounters drag actually speeds up (since as it's altitude decreases, the orbital speed increases), and how this might be a factor in the comparison of the heating effects on an object that decays gradually from orbit vs an object like the shuttle that is taken out of orbit by actually reducing it's speed with thrust. I have my own intuitive theories on this but would like to hear more informed opinions.
What confuses people is that the orbital PERIOD (minutes/orbit) decreases with drag, and hence its reciprocal (measured in units like like orbits/day) increases. As the satellite gives up kinetic energy to heat, it falls into a lower orbit, where it must move faster. The relation is that the square of the period is proportional to the cube of the size of the orbit.
All this is is embodied in Kepler's 3rd law (see http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) which the Wiki states as:
* "The squares http://en.wikipedia.org/wiki/Square_%28algebra%29 of the orbital periods http://en.wikipedia.org/wiki/Orbital_period of planets are directly proportional http://en.wikipedia.org/wiki/Proportionality_%28mathematics%29 to the cubes http://en.wikipedia.org/wiki/Cube_%28arithmetic%29 of the semi-major axes http://en.wikipedia.org/wiki/Major_axis (the "half-length" of the ellipse) of their orbits. This means not only that larger orbits have longer periods, but also that the speed of a planet in a larger orbit is lower than in a smaller orbit."
An animated "movie" of Kepler's 3rd law can be seen at http://people.scs.fsu.edu/~dduke/kepler3.html http://people.scs.fsu.edu/%7Edduke/kepler3.html.
73, Tom
Ok, so this is exactly what I have heard, and exactly what is baffling me.
So I understand Kepler, and why the farther out you are the slower you need to go. Otherwise, in the very much weaker gravity (inverse square law) you'd go flying off into space. What I don't get is the orbit changing stuff.
To go from a low circular orbit to a higher one, you fire your rocket behind you to pick up more speed. The "point" of the burn becomes the perigee of the new elliptical orbit, and half-way around is the new apogee. Ok, so far, so good. Now, if at the instant of apogee you did nothing, you'd fall back down to perigee, and back again to apogee on the next orbit. But since you fired your rocket to speed you up in the first place, to circularize the orbit you fire your rocket at the point of apogee to slow you down, and in fact to a slower speed than you started. I would think that would make you drop more steeply down on the next orbit, probably to a lower perigee than you started. Instead, I'd think you should fire in the same direction as the first burn, to make things round, but that would make you go even faster, which Mr. Kepler said was wrong.
My head is spinning (no pun intended)... Where did I go wrong?
Greg KO6TH
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Date: Fri, 15 Feb 2008 14:52:05 -0500 From: k3io@verizon.net To: amsat-bb@amsat.org Subject: [amsat-bb] Re: Since We Are Off Topic Somewhat....
Bill Jones asked:
While discussing this topic of orbital decay, I wonder if someone would comment on the apparent anomoly whereby a sat in leo that encounters drag actually speeds up (since as it's altitude decreases, the orbital speed increases), and how this might be a factor in the comparison of the heating effects on an object that decays gradually from orbit vs an object like the shuttle that is taken out of orbit by actually reducing it's speed with thrust. I have my own intuitive theories on this but would like to hear more informed opinions.
What confuses people is that the orbital PERIOD (minutes/orbit) decreases with drag, and hence its reciprocal (measured in units like like orbits/day) increases. As the satellite gives up kinetic energy to heat, it falls into a lower orbit, where it must move faster. The relation is that the square of the period is proportional to the cube of the size of the orbit.
All this is is embodied in Kepler's 3rd law (see http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) which the Wiki states as:
* "The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axes (the "half-length" of the ellipse) of their orbits. This means not only that larger orbits have longer periods, but also that the speed of a planet in a larger orbit is lower than in a smaller orbit."An animated "movie" of Kepler's 3rd law can be seen at http://people.scs.fsu.edu/~dduke/kepler3.html .
73, Tom _______________________________________________ Sent via AMSAT-BB@amsat.org. Opinions expressed are those of the author. Not an AMSAT-NA member? Join now to support the amateur satellite program! Subscription settings: http://amsat.org/mailman/listinfo/amsat-bb
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At 03:55 PM 2/16/2008, Greg D. wrote:
To go from a low circular orbit to a higher one, you fire your rocket behind you to pick up more speed. The "point" of the burn becomes the perigee of the new elliptical orbit, and half-way around is the new apogee. Ok, so far, so good. Now, if at the instant of apogee you
Yep. :)
did nothing, you'd fall back down to perigee, and back again to apogee on the next orbit. But since you fired your rocket to speed you up in the first place, to circularize the orbit you fire your rocket at the point of apogee to slow you down, and in fact to a slower speed than you started. I would think that would make you drop more steeply down on the next orbit, probably to a lower perigee than you started.
Nope. You fire the rocket to speed you up, which raises the perigee.
Instead, I'd think you should fire in the same direction as the first burn, to make things round, but that would make you go even faster, which Mr. Kepler said was wrong.
You're forgetting that the speed of a satellite in a non circular orbit varies as the satellite moves. In fact, Kepler's Laws state that in you were able to attach a string (with a very high elasticity and low tension!) between the satellite and the point around which it is orbiting, this string would sweep out an equal area every second.
My head is spinning (no pun intended)... Where did I go wrong?
Time for a thought experiment. I'll enlist the aid of Q of Star Trek (Next Generation) fame to shrink the Earth to a point, and the satellite to a very small size (maybe the size of a grain of salt). We'll put the satellite into a highly elliptical orbit, with a perigee of 1 metre above this "Earth singularity", and an apogee of around 7000km (equal to 800km above the Earth's real surface). As our satellite orbits this imaginary shrunken Earth, it picks up speed until it's travelling at some incredible speed at perigee (any mathematicians want to work it out, might even be relativistic, but let's assume Newtonian physics apply at all times and velocities - Q can make anything happen ;) ). What happens at apogee is more interesting. We're now approximately 7000 km above the singularity, and at the instant of apogee, there is no vertical motion, the velocity is horizontal, and only a few metres per _hour_ (since the orbit is very narrow). Now, at the moment of apogee, we accelerate our tiny satellite to around 27000 km/h horizontally in the forward direction (Thanks Q for the push ;) ). Hey presto, it's now in a circular orbit, approximately 7000km above the Earth singularity. I can now get Q to put the Earth and Relativity back to normal, and we have the satellite in a nice 800km circular orbit. :)
Hope that extreme, imaginary example helps illustrate what's going on. :)
Metric was used, because that's the direction NASA and space science is headed. I can work in either system myself... ;)
73 de VK3JED http://vkradio.com
On 16 Feb 2008 at 17:32, Tony Langdon wrote:
Hope that extreme, imaginary example helps illustrate what's going on. :)
Metric was used, because that's the direction NASA and space science is headed. I can work in either system myself... ;)
Hi Tony Have a look at this NASA site one of the best tool to learn about orbital mechanics
http://solc.gsfc.nasa.gov/orbital_mech.html
Luc Leblanc VE2DWE Skype VE2DWE www.qsl.net/ve2dwe WAC BASIC CW PHONE SATELLITE
Hi Tony,
Yes, this all makes perfect sense, and is what I thought should be happening. But I distinctly remember a website talking about how to get from one orbit to another - Hohman transfers, I think - and how you needed to turn around and fire your engine in the other direction at apogee to slow you down.
Thinking back, and looking at some pictures, perhaps what they were indicating was that the rocket burn would be in the other direction when viewed from above the orbital plane. But I do remember the "slow down" phrase, and that's what stuck in my brain because it certainly seemed (and is) wrong.
Of course, now I can't find the site... Or, if I did, it's probably been corrected by now. At least, let us hope so.
Thanks for indirectly letting me know that I'm not crazy...
Greg KO6TH
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Date: Sat, 16 Feb 2008 17:32:00 +1100 To: ko6th_greg@hotmail.com; k3io@verizon.net; amsat-bb@amsat.org From: vk3jed@gmail.com Subject: Re: [amsat-bb] Re: Since We Are Off Topic Somewhat.... And drifting slightly
At 03:55 PM 2/16/2008, Greg D. wrote:
To go from a low circular orbit to a higher one, you fire your rocket behind you to pick up more speed. The "point" of the burn becomes the perigee of the new elliptical orbit, and half-way around is the new apogee. Ok, so far, so good. Now, if at the instant of apogee you
Yep. :)
did nothing, you'd fall back down to perigee, and back again to apogee on the next orbit. But since you fired your rocket to speed you up in the first place, to circularize the orbit you fire your rocket at the point of apogee to slow you down, and in fact to a slower speed than you started. I would think that would make you drop more steeply down on the next orbit, probably to a lower perigee than you started.
Nope. You fire the rocket to speed you up, which raises the perigee.
Instead, I'd think you should fire in the same direction as the first burn, to make things round, but that would make you go even faster, which Mr. Kepler said was wrong.
You're forgetting that the speed of a satellite in a non circular orbit varies as the satellite moves. In fact, Kepler's Laws state that in you were able to attach a string (with a very high elasticity and low tension!) between the satellite and the point around which it is orbiting, this string would sweep out an equal area every second.
My head is spinning (no pun intended)... Where did I go wrong?
Time for a thought experiment. I'll enlist the aid of Q of Star Trek (Next Generation) fame to shrink the Earth to a point, and the satellite to a very small size (maybe the size of a grain of salt). We'll put the satellite into a highly elliptical orbit, with a perigee of 1 metre above this "Earth singularity", and an apogee of around 7000km (equal to 800km above the Earth's real surface). As our satellite orbits this imaginary shrunken Earth, it picks up speed until it's travelling at some incredible speed at perigee (any mathematicians want to work it out, might even be relativistic, but let's assume Newtonian physics apply at all times and velocities - Q can make anything happen ;) ). What happens at apogee is more interesting. We're now approximately 7000 km above the singularity, and at the instant of apogee, there is no vertical motion, the velocity is horizontal, and only a few metres per _hour_ (since the orbit is very narrow). Now, at the moment of apogee, we accelerate our tiny satellite to around 27000 km/h horizontally in the forward direction (Thanks Q for the push ;) ). Hey presto, it's now in a circular orbit, approximately 7000km above the Earth singularity. I can now get Q to put the Earth and Relativity back to normal, and we have the satellite in a nice 800km circular orbit. :)
Hope that extreme, imaginary example helps illustrate what's going on. :)
Metric was used, because that's the direction NASA and space science is headed. I can work in either system myself... ;)
73 de VK3JED http://vkradio.com
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participants (4)
-
Greg D. -
Luc Leblanc -
Tom Clark, K3IO -
Tony Langdon