The 26k miles includes inside it the diameter of the Earth. It is not 26k miles above the Earth or even 13k.
900 miles high sounds about right. 26k mile diameter is enough room of an awful lot of sats, so long as they're taught to share, play well with others, all the stuff we learn in kindergarden.
pfrit wrote:There are some very funky stable geostationary polar orbits possible (the satelite is in a solar orbit with a solar sail) but they are all well above 900 miles.
How does that work?
Geostationary - Of or having a geosynchronous orbit such that the position in such an orbit is fixed with respect to the earth.
Polar Orbits - an orbit in which a satellite passes above or nearly above both poles of the body (usually a planet such as the Earth, but possibly another body such as the Sun) being orbited on each revolution.
All Earth geosynchronous orbits have a semi-major axis of 42,164 km (26,199 mi).
Picture a small rocket with infinite impulse capability pushing an equatorial geosynchronous satellite northward. It still has a circular orbit, but it is displaced a certain amount north of the equator. With just the right amount if continuous thrust, you could cause it to "orbit" over any latitude.
Not being an expert, I couldn't say whether the radius of the orbit would have to shrink to keep it geosynchronous (I think so, but...) yet it IS possible to do. Again, not being... I don't know where the limit is to how far north or south you could push it, but I am positive that limit exists.
IIUC, if you need a rocket to hold an object in a trajectory, that's not an orbit. Orbits are time-like geodesics where the object is in free-fall. By definition, the object cannot be receiving thrust or it's in a trajectory other than an orbit. This is why when in orbit, you are essentially weightless. If there's thrust, you're not.
"Courage is not just a virtue, but the form of every virtue at the testing point." C. S. Lewis
KitemanSA wrote:With just the right amount if continuous thrust, you could cause it to "orbit" over any latitude.
Any orbit plane will contain the earth's center of mass. The orbit plane will generally precess with no thrust, without inclination change, due to oblateness of the earth. Precession, inclination, and radii changes generally occur after thrust is applied, but the resulting orbit plane will still contain the earth's center of mass, which is at a focus of a conic section. The orbit might be circular, elliptical, parabolic (unlikely) or hyperbolic. For the last two cases you are leaving the vicinity of earth, in "open" orbits. By applying a continuous thrust you can change the orbit, but its instantaneous plane will still contain earth's center of mass (ignoring moon, sun, etc. perturbations). No orbiting at constant latitude (other than the equator).
pfrit wrote:There are some very funky stable geostationary polar orbits possible (the satelite is in a solar orbit with a solar sail) but they are all well above 900 miles.
How does that work?
Geostationary - Of or having a geosynchronous orbit such that the position in such an orbit is fixed with respect to the earth.
Polar Orbits - an orbit in which a satellite passes above or nearly above both poles of the body (usually a planet such as the Earth, but possibly another body such as the Sun) being orbited on each revolution.
All Earth geosynchronous orbits have a semi-major axis of 42,164 km (26,199 mi). http://en.wikipedia.org/wiki/Geosynchronous_orbit
The satelitte is in solar orbit, not Earth orbit. It has a sail that counters the earths gravity and maintains its solar orbit. From the earth's pole, it stays in the same place directly above. Very funky idea IMHO, but the math works. There is a magic distance from the earth that minimizes the size of the sail. Closer, it has to fight earth's gravity more, Farther, and it has to apply more force to maintain the orbit as it skewed off a perfect solar orbit by the Earth. Hard to visualize, but once you do it is a "Duh" idea. Most great ideas are. It might not be terribly practical for most things other than television, but it works.
What is the difference between ignorance and apathy? I don't know and I don't care.
GIThruster wrote:IIUC, if you need a rocket to hold an object in a trajectory, that's not an orbit. Orbits are time-like geodesics where the object is in free-fall. By definition, the object cannot be receiving thrust or it's in a trajectory other than an orbit. This is why when in orbit, you are essentially weightless. If there's thrust, you're not.
To "orbit" originally meant to move in a circular path. Only in recent times did the term take on a celestial or "time-like geodesic" meaning.
AFAIUI, the item is still in orbit, just not a free-fall orbit. It is still maintaining a circular (or elliptic) path due to the influence of gravitation, it just uses other influences to more the plane of that path away from the center of the gravitational mass.
zapkitty wrote:Everyone talks about using nets to wrap and snag larger debris and stray sats. A sensible solution given the the lack of unified grappling fixtures.. or any grappling fixtures for that matter... but isn't that net the very definition of a space baggie?
This is obviously a job for Commander Quark and his Polywell-Powered Sanitation Patrol Cruiser!
More like Roger Wilco and his trusty old barge, the SCS Eureka.
KitemanSA wrote:Picture a small rocket with infinite impulse capability pushing an equatorial geosynchronous satellite northward. It still has a circular orbit, but it is displaced a certain amount north of the equator. With just the right amount if continuous thrust, you could cause it to "orbit" over any latitude.
If you have one of those gadgets on hand, you could also build it to sustain a straight downward 9,81m/s^2 thrust and keep its latitude/longitude with respect to the Earth.
In essence, you would be creating a skyhook you can place at an arbitrary altitude.
GIThruster wrote:IIUC, if you need a rocket to hold an object in a trajectory, that's not an orbit. Orbits are time-like geodesics where the object is in free-fall. By definition, the object cannot be receiving thrust or it's in a trajectory other than an orbit. This is why when in orbit, you are essentially weightless. If there's thrust, you're not.
To "orbit" originally meant to move in a circular path. Only in recent times did the term take on a celestial or "time-like geodesic" meaning.
AFAIUI, the item is still in orbit, just not a free-fall orbit. It is still maintaining a circular (or elliptic) path due to the influence of gravitation, it just uses other influences to more the plane of that path away from the center of the gravitational mass.
Firing a rocket on a satellite in an initially circular geostationary orbit to push it "north" or "south" will change the inclination of the orbit plane and stretch the orbit into an ellipse, with the earth's center of mass at one focus. With enough thrust, the ellipse will stretch into a parabola (ellipse "at infinity", the boundary between an open and closed orbit) and then continue on to a hyperbola as it escapes earth, still with the CoM at a focus.
DeltaV wrote:Firing a rocket on a satellite in an initially circular geostationary orbit to push it "north" or "south" will change the inclination of the orbit plane and stretch the orbit into an ellipse, with the earth's center of mass at one focus. With enough thrust, the ellipse will stretch into a parabola (ellipse "at infinity", the boundary between an open and closed orbit) and then continue on to a hyperbola as it escapes earth, still with the CoM at a focus.
No. This is why it was specified that it had to be infinite impulse. The path taken is not an orbit, if you think of an orbit as a freefall trajectory. If at any point you were to turn off the engine, the focus would instantly return to the Earth's CoM, but with perpetual thrust it is possible to follow a circular or elliptical path that doesn't have the Earth's CoM as a focus (it could be any path, really, so long as enough thrust is available to track it; it doesn't have to be a conic section).
For example: An airplane or helicopter can fly in a five-mile-wide circle around the North Pole, though with restrictions on altitude. A spacecraft with a high-thrust M-E drive could do it at any altitude. The path is a conic section that doesn't have the Earth's CoM as a focus.
Now realize that there is a continuum of such trajectories in between my specific example and a standard equatorial circular orbit.
Stoney3K wrote: If you have one of those gadgets on hand, you could also build it to sustain a straight downward 9,81m/s^2 thrust and keep its latitude/longitude with respect to the Earth.
In essence, you would be creating a skyhook you can place at an arbitrary altitude.
Seems it takes a lot less to shift the orbit than to stop it. I've read papers on the use of light sails to pull Geostationary Satellites out of equatorial orbit to more useful latitudes... which would open up a LOT more space in space!
DeltaV wrote:Firing a rocket on a satellite in an initially circular geostationary orbit to push it "north" or "south" will change the inclination of the orbit plane and stretch the orbit into an ellipse, with the earth's center of mass at one focus. With enough thrust, the ellipse will stretch into a parabola (ellipse "at infinity", the boundary between an open and closed orbit) and then continue on to a hyperbola as it escapes earth, still with the CoM at a focus.
No. This is why it was specified that it had to be infinite impulse. The path taken is not an orbit, if you think of an orbit as a freefall trajectory. If at any point you were to turn off the engine, the focus would instantly return to the Earth's CoM, but with perpetual thrust it is possible to follow a circular or elliptical path that doesn't have the Earth's CoM as a focus (it could be any path, really, so long as enough thrust is available to track it; it doesn't have to be a conic section).
For example: An airplane or helicopter can fly in a five-mile-wide circle around the North Pole, though with restrictions on altitude. A spacecraft with a high-thrust M-E drive could do it at any altitude. The path is a conic section that doesn't have the Earth's CoM as a focus.
Now realize that there is a continuum of such trajectories in between my specific example and a standard equatorial circular orbit.
With continuous vectoring of sufficient thrust you can fly an arbitrary trajectory, yes. I was assuming a thrust vector parallel to earth's polar axis. I took "instantaneous" orbit plane to mean the resulting orbit plane if thrust terminated at that instant. So the "orbit planes" under thrust would evolve through those containing both the instantaneous velocity vector and the earth CoM. But, you're right, under arbitrary thrust it doesn't really make sense to talk about orbit planes.
This above is why Paul March simply looked at the distance between the Earth and the Moon for his ground breaking WarpStar paper delivered back in 2007. Any future Golden Age in human spaceflight using M-E thrusters would not make use of orbits of any sort. When you can generate constant 1 Earth gee acceleration, you can fly back and forth between the Earth and the Moon in almost a straight line, and make the transit in about 4 1/2 hours or the time it now takes to fly from NY to LA. It's hard for people skilled in orbital mechanics to wrap their arms around the notion because quite frankly, it is too simple for them!
"Courage is not just a virtue, but the form of every virtue at the testing point." C. S. Lewis