FIRTH@TL-20B.ARPA (12/26/85)
There has been some discussion recently about how to get mass into stable Earth orbit, using some form of ground-based accelerator. If we consider only one mass at a time, then of course it isn't possible. When the mass leaves the accelerator, it is in free fall, and so its trajectory must return to that point - which presumably is quite close to the ground and so well within the atmosphere. Lagrange strikes again! One could also consider a mass that had aerodynamic lift, but again the answer is the same: it will return to the point where ballistic motion began; and if that was deep enough in the atmosphere to provide some lift on the way out, it will surely introduce drag on the way back in. The only way is to give the body some more impulse once it is outside the atmosphere, by means of rockets, an orbiting grabber, or whatever. However, the trick is possible if you consider TWO masses at a time. Suppose we launch a mass into orbit from a ground-based accelerator. Just to play with some numbers, suppose the orbit is an ellipse with major axis 20000 miles and minor axis 16000 miles. Perigee is then 4000 miles from the center of the Earth, ie grazing contact, and apogee is of course 16000 miles from the center or 12000 miles above the surface. Now launch TWO such masses, so that their orbits are in the same plane, but pointing away from the Earth in opposite directions. That is, the two ellipses share a common focus (the earth's center) and all three foci are in a straight line. These orbits intersect at a distance of ~6400 miles out, ie an altitude of ~2400 miles. Launch the two masses so that they meet at the point of intersection, one inbound and one outbound (and they had both better be on their first orbits, of course). Let the masses be equal. Then, they meet when travelling at the same speed (but in different directions), and with the same energy. Somehow, get then to join into one bigger mass. The combined mass will then be travelling in a new orbit, whose major axis is perpendicular to the major axes of the old orbits, and with perigee the same 6400 miles. Apogee of course will be ~13600 miles. The new mass is comfortably outside the atmosphere, and all propulsion was done on the ground. [Here follows the boring math. Given an ellipse with semimajor axis a and semiminor axis b, then the interfocal distance 2f is given by f = sqrt(a^2-b^2) and the peri- and ap- distances by a-f and a+f. Two such ellipses with a common focus, and the three foci in a straight line, intersect twice; the points of intersection being symmetrically placed about the common focus so that the line joining them passes through the common focus and is perpendicular to the major axes. The triangle formed by the common focus, either other focus, and either point of intersection is a right triangle. If the intersection point is at distance x from the common focus and y (>x) from the other focus, then x^2 + 4f^2 = y^2 (recall that 2f is interfocal distance) and x + y = 2a (the ellipse invariant) whence we may calculate x and y. Finally, recall that the energy of an elliptic orbit is -1/2a, independent of the minor axis (multiplied by GMm, of course, but we can ignore all that) ] Robert Firth -------
lcc.bob@LOCUS.UCLA.EDU (Bob English) (12/27/85)
> Date: Thu 26 Dec 85 13:26:02-EST > From: FIRTH@tl-20b.arpa > Subject: Getting stuff into Orbit > Launch the two masses so that they meet at the point of intersection, one > inbound and one outbound (and they had both better be on their first orbits, > of course). Let the masses be equal. Then, they meet when travelling at > the same speed (but in different directions), and with the same energy. > Somehow, get then to join into one bigger mass. The combined mass will > then be travelling in a new orbit, whose major axis is perpendicular to > the major axes of the old orbits, and with perigee the same 6400 miles. > Apogee of course will be ~13600 miles. The new mass is comfortably outside > the atmosphere, and all propulsion was done on the ground. If the major axis is perpendicular to the original major axes, then the point of intersection will become the apogee of the new orbit, not the perigee. Most of the orbital energy will be lost in the collision between the objects, and there won't be much left to keep them up there. I suspect this is a dead end. --bob--
ems@amdahl.UUCP (ems) (12/28/85)
> There has been some discussion recently about how to get mass into > stable Earth orbit, using some form of ground-based accelerator. > > If we consider only one mass at a time, then of course it isn't possible. > When the mass leaves the accelerator, it is in free fall, and so its > trajectory must return to that point - which presumably is quite close > to the ground and so well within the atmosphere. Lagrange strikes again! > > One could also consider a mass that had aerodynamic lift, but again the > answer is the same: it will return to the point where ballistic motion > began; and if that was deep enough in the atmosphere to provide some lift > on the way out, it will surely introduce drag on the way back in. > > The only way is to give the body some more impulse once it is outside the > atmosphere, by means of rockets, an orbiting grabber, or whatever. > Would it be possible to 'skip on the surface'? If one re-enters on a rough tangent, cannot some form of 'aerobraking' be used to modify the orbit? I must admit that the physics of it is well beyond me, but it seems intuitive that some combination of airfoil interactions on the way out and back would result in an orbit not impacting the ground. After all, we only need to change the orbit by about 100 miles out of 8000 ... (Then again, intuition and physics are often at odds, anyone can see feathers fall slower :-) BTW the discussion on two masses was marvelous, what happens if one mass is sent up, but divides in two at apogee? I know that this could be used to keep one mass in orbit. Is there a way to keep both masses in orbit by having them blasted in different directions? Can this be done with minimal delta V and fuel? (Yes, this is an invitation to the soap box...) -- E. Michael Smith ...!{hplabs,ihnp4,amd,nsc}!amdahl!ems This is the obligatory disclaimer of everything.
franka@mmintl.UUCP (Frank Adams) (12/28/85)
[Not food] I'm not going to do the math, but it seems to me there's another way to get two objects into orbit from ground-based launch. Tether them, and arrange the launch so that there is considerable spin around the center of gravity. Then when you get to orbit, release the tether. I think it is possible to for both objects to be in a stable orbit at this point. Frank Adams ihpn4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108
throopw@dg_rtp.UUCP (Wayne Throop) (12/30/85)
> Launch the two masses so that they meet at the point of intersection, one > inbound and one outbound (and they had both better be on their first orbits, > of course). Let the masses be equal. Then, they meet when travelling at > the same speed (but in different directions), and with the same energy. > Somehow, get then to join into one bigger mass. That's one *hell* of a "somehow", I expect! First, you are going to have to store or dissipate the energy of a few kilometers-per-second velocity difference in order to acomplish the "join". Then, if you haven't vaporized the cargo yet, you have to consider the accelerations that the cargo will experience during the "join". Can you say "pancake"? I knew you could. -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!dg_rtp!throopw