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Re: What I don't understand.
Posted By: SiliconDream=PN= <querl@uclink4.berkeley.edu>	Date: 1/9/00 3:52 p.m.
In Response To: Re: What I don't understand. (Mage) > IT would also have to supply a on of straight up speed to aviod > plowing into the Halo ground curve (in addition to the sideways > counter spinning force). > If anyone can get all this stuff calculated, do it please :) Im > curious about this :) Fine, I'll do it the right way this time, neither pretending that the gravity is real and not rotation-based, nor making silly divide-by-two errors. :) So you're standing on a rotating ring, where the rim is moving at speed V, right? Now, if the ring's true gravity and atmospheric resistance are negligible, then the escape velocity is simply V, along the rim in the opposite direction from rotation. In other words, if you give yourself a very gentle upward push, and a powerful push against the spin which provides you with azimuthal velocity -V relative to the ringworld's surface, then to a non-rotating observer (by summing the velocities of you and the ground beneath your feet), you're simply drifting very slowly toward the center of the ring, not rotating at all and therefore not feeling any pseudogravity. Does that make sense? What if the ring has a small but significant amount of gravity? Then simply (okay, it's not really simple, and I beleive it's actually analytically unsolvable, but that's what Mathematica's for) calculate magnitude, E, of the necessary centripetal escape velocity, for a non-spinning ring. Do this by finding the true gravitational acceleration as a function of distance from the center, integrate from the center to the rim, multiply by 2 and take the square root. This velocity is directed centripetally; that is, it's -E in the radial direction. Then add the azimuthal velocity -V, and that's your total escape velocity. Of course, if you're firing a missile across the ring you'll want it to have a larger radial velocity, so that it doesn't take an eternity to reach the center. NOTE: this is a true velocity--that is, a vector with both radial and azimuthal components. Normally, when talking about the "escape velocity" for a star or planet we're actually referring to a speed--we know the direction of "escape velocity" is radially outwards, so we don't need to consider it as a vector. But here it's important to keep track of each component, -E radially and -V azimuthally. Next, let's consider atmosphere. Basically, you should first calculate the escape velocity for a projectile starting at the atmosphere's edge (almost the same as for a projectile starting at the ground, but slightly smaller in magnitude, with the radial component shrunk more than the azimuthal component), and then figure out what the projectile's initial velocity at the ground should be in order to have this necessary escape velocity when it leaves the atmosphere. This is a hellacious problem, it seems to me, and I can't think of any easy way of approximating it. So let's just ignore it, okay? It's not like air resistance really affects missile trajectories or anything. :) Anyway, I haven't the wit to calculate either the Halo's gravity or the approximate effect of air resistance, but I can give the basic azimuthal escape velocity when ignoring both of these obviously significant factors. It's the Halo's rotational rim speed, which is roughly 8880 m/s or 20,000 m.p.h. Wow, I did it the wrong way last time and I still got the right answer! :) So if you stand on the Halo and fire a frictionless artillery shell horizontally against its spin at 20,000 m.p.h., the shell will skim away and seem to feel no gravity. If your vision is good enough to see where the Halo starts to climb into the sky, you'll see the shell bend its path upwards and climb with it. Eventually it'll loop the Halo and come back to where you are, still at the exact same height. To fire to the center of the Halo, just boost the speed of the shell by a small amount and incline your launcher so that the horizontal speed is still 20,000 m.p.h. As the shell zooms away, it'll seem to drift upwards (more than is necessary to accommodate the upwards curve of the Halo) and will eventually drift to the center. How do you like them apples? --SiliconDream

Message Index

A few points	SiliconDream=PN=	1/8/00 11:45 p.m.
Re: A few points	Mark Levin	1/9/00 12:30 a.m.
Re: A few points	SiliconDream=PN=	1/9/00 4:00 a.m.
I saw it too.. I think...	DeusExMachina =PN=	1/9/00 4:13 a.m.
What I don't understand.	Manus_Lacatus	1/9/00 12:32 p.m.
Re: What I don't understand.	Mark Levin	1/9/00 1:26 p.m.
Re: What I don't understand.	Chris Huff	1/9/00 1:42 p.m.
Re: What I don't understand.	Mage	1/9/00 2:26 p.m.
Bungie is doing this on purpose...	Daft Shadow =PN=	1/9/00 3:19 p.m.
Re: Bungie is doing this on purpose...	Dr. Nick	1/9/00 4:37 p.m.
Re: Bungie is doing this on purpose...	SiliconDream=PN=	1/9/00 5:38 p.m.
Re: Bungie is doing this on purpose...	Mage	1/9/00 6:00 p.m.
Re: Bungie is doing this on purpose...	Daft Shadow =PN=	1/9/00 6:19 p.m.
Re: Bungie is doing this on purpose...	Mage	1/9/00 9:13 p.m.
Ouch...	Daft Shadow =PN=	1/10/00 12:06 a.m.
Re: Ouch...	Draeger	1/10/00 6:14 a.m.
I can fly....really I can...(NT)	Magh Tuireadh	1/10/00 7:44 a.m.
After a mortar hit :) NT	Draeger	1/10/00 2:51 p.m.
Re: Ouch...	Someguy	1/10/00 3:24 p.m.
Re: What I don't understand.	SiliconDream=PN=	1/9/00 3:52 p.m.
Re: What I don't understand.	Mage	1/9/00 4:15 p.m.
Heh we asked for it, but....	DeusExMachina =PN=	1/9/00 8:01 p.m.
Re: Heh we asked for it, but....	Magh Tuireadh	1/9/00 8:07 p.m.
Re: Heh we asked for it, but....	Otokam	1/9/00 8:35 p.m.
Gah....Gravity!	Magh Tuireadh	1/9/00 9:07 p.m.
Re: Gah....Gravity!	Otokam	1/10/00 2:55 a.m.
Really?	Magh Tuireadh	1/10/00 7:38 a.m.
Re: Really?	SiliconDream=PN=	1/10/00 4:18 p.m.
Unfortunately not...	SiliconDream=PN=	1/9/00 9:40 p.m.
Hey, cool!	DeusExMachina =PN=	1/10/00 12:45 a.m.
Re: What I don't understand.	Magh Tuireadh	1/9/00 8:03 p.m.
Re: What I don't understand.	SiliconDream=PN=	1/9/00 9:32 p.m.
Atmosphere?	Goat	1/9/00 4:19 p.m.
Re: Atmosphere?	Mage	1/9/00 4:20 p.m.
Re: I saw it too.. I think...	SiliconDream=PN=	1/9/00 3:05 p.m.
Re: A few points	Bachus	1/9/00 4:08 a.m.
Re: A few points	Dead Glory	1/9/00 11:51 a.m.
Re: A few points	SiliconDream=PN=	1/9/00 2:57 p.m.
Re: A few points	Bachus	1/9/00 4:24 p.m.
Re: A few points	Mage	1/9/00 4:32 p.m.