Category Archives: Mathematics

Mathematics, Science And Society, Space, Technology and Society

Orbits And Suborbits

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I’ve updated yesterday’s piece at Ricochet to clarify, for those in comments. I’ve probably discussed this here before, but…

Per discussion in comments, there seems to be some confusion about the difference between high-altitude flight, suborbital flight, and orbital flight. As John Walker points out, orbital flight requires a minimum speed to sustain the orbit, but while that is necessary, it is not a sufficient condition. In fact, a flight can be suborbital with the same speed (energy) as an orbital flight. The best, or at least, most rigorous way to define a “suborbit” is an orbit that intersects the atmosphere and/or surface of the planet. So if you launched straight up at orbital velocity, it would still be a suborbit, because it would (after an hour or two, I haven’t done the math) fall back to the ground. So John’s numbers in terms of comparative energy are roughly correct for the particular vehicles being discussed here (XCOR Lynx and VG SpaceShipTwo), they can’t be generalized for any suborbital vehicle (e.g., a sounding rocket isn’t orbital, but it goes much higher than those passenger vehicles, often hundreds of kilometers in altitude).

The speed necessary to achieve orbit is partly a function of the mass of the body being orbited, but it is also a function of its diameter, and whether or not it has an atmosphere. If the earth were a point mass, an object tossed out at an altitude equivalent to the earth radius (that is ground level) would have very little velocity, but it would have a lot of potential energy. It would fall, gain speed, whip around the center and come back up to the person who had tossed it. That is, it would orbit. So even for the relatively low-energy suborbital vehicles discussed in this post, the reason that they’re not orbital is simply that the planet gets in the way.

One other interesting point is that, under the definition above, subsonic “parabolic” aircraft flights in the atmosphere, to offer half a minute or so of weightlessness (offered by the Zero G company), are suborbital flights, in terms of their trajectory. I put “parabolic” in quotes because in actuality, if properly flown, they are really elliptical sections, as all orbits and suborbits are. The parabola is just a close approximation if you assume a flat earth, which is a valid assumption for the short distances involved. Galileo did his original artillery tables based on flat earth, which is why beginning physics students model cannonball problems as parabolas, but modern long-range artillery has to account for the earth curvature, and it does calculate as elliptical trajectories.

Finally, one more extension. Ignoring the atmosphere, every artillery shell fired, every ball thrown or hit, every long jumper, every person who simply hops up into the air, is in a suborbit. The primary distinction for the vehicles discussed is that they are in a suborbit that reaches a specific altitude (at least a hundred kilometers to officially be in “space”), and leaves the atmosphere.

Clear as mud?

Business, Mathematics, Space, Technology and Society

Dreamchaser And Stratolaunch

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I didn’t mention this earlier in the week, but SNC is teaming with StratoLaunch to get a subscale version into orbit. If it’s 75% scale, I figure that’s about 40% of the current interior volume, which lines up with their claim of being able to carry two or three passengers (the full-scale system is designed for seven). The big advantage of such a system would be single-orbit rendezvous, and runway landing, so if it happens, there’d certainly be a market niche for it.

Business, Mathematics, Technology and Society

USB Devices

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I hadn’t realized they’re more than just memory:

“People look at these things and see them as nothing more than storage devices,” says Caudill. “They don’t realize there’s a reprogrammable computer in their hands.”

In an earlier interview with WIRED ahead of his Black Hat talk, Berlin-based Nohl had said that he wouldn’t release the exploit code he’d developed because he considered the BadUSB vulnerability practically unpatchable. (He did, however, offer a proof-of-concept for Android devices.) To prevent USB devices’ firmware from being rewritten, their security architecture would need to be fundamentally redesigned, he argued, so that no code could be changed on the device without the unforgeable signature of the manufacturer. But he warned that even if that code-signing measure were put in place today, it could take 10 years or more to iron out the USB standard’s bugs and pull existing vulnerable devices out of circulation. “It’s unfixable for the most part,” Nohl said at the time. “But before even starting this arms race, USB sticks have to attempt security.”

Caudill says that by publishing their code, he and Wilson are hoping to start that security process. But even they hesitate to release every possible attack against USB devices. They’re working on another exploit that would invisibly inject malware into files as they are copied from a USB device to a computer. By hiding another USB-infecting function in that malware, Caudill says it would be possible to quickly spread the malicious code from any USB stick that’s connected to a PC and back to any new USB plugged into the infected computer. That two-way infection trick could potentially enable a USB-carried malware epidemic. Caudill considers that attack so dangerous that even he and Wilson are still debating whether to release it.

Great.

Business, Economics, Mathematics, Media Criticism, Political Commentary, Science And Society

The Climate Science

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…is not settled:

…the crucial, unsettled scientific question for policy is, “How will the climate change over the next century under both natural and human influences?” Answers to that question at the global and regional levels, as well as to equally complex questions of how ecosystems and human activities will be affected, should inform our choices about energy and infrastructure.

But—here’s the catch—those questions are the hardest ones to answer. They challenge, in a fundamental way, what science can tell us about future climates.

Yup. The 97% “nonsensus” is multiple strawmen, because all it ever meant, to the degree that it wasn’t just BS, was that scientists agree that there is a greenhouse effect and that therefore human-generated carbon emissions can affect climate. Beyond that, there is no consensus.