that when asked about the anomalous procession of Mars, you could sit down with a pencil and graphing calculator for an hour and tell them that GR accounts for ~40 arcseconds/century.
I hope not. Mercury's relativistic perihelion precession is ~ 43 arc seconds / century. Mars's is only about 1.35 ''/cy.
That sort of thing is fairly straightforward (at least at the beginning), but GR is notorious for being slipperly.
Take your GPS example. If we are down here and traveling slowly with respect to the solid Earth, we can set up a global simultaneous frame, in which the clocks are all synchronized.
Now, launch GPS satellites up there with some velocity. There is a "pure" GR time dilation due to gravity (these satellites are more outside of the Earth's potential than us ground-huggers) and also a SR term. You need a solution fro the Earth's field to handle the Earth's field, but the Earth rotates slowly, so the Schwarzschild solution applies. So, let t be the coordinate time a Schwarzschild solution scaled to the Earth, so that the proper time (the time measured at a clock at radial coordinate r and total velocity v) Tau is
d Tau / d t = 1 - GM/rc^2 - 1/2(v/c)^2 + higher order stuff.
Sounds pretty simple (the first term being pure GR, the second, "really" SR, from the Lorentz transformation). Except
- we use clocks at the surface of the Earth, in what's effectively a proper time, not a coordinate time. - we are moving in an Earth-centered frame (due to the rotation of the Earth), but our distance from the geocenter depends on our latitude (due to our self-same rotation causing the Earth's equatorial bulge), so that effect largely cancels - the satellites are both moving and at some higher r (so their clocks tick faster). Note that in a circular orbit v is a function of r, and so the SR and GR effects partially cancel (this trips up a lot of beginners).
If you parse all of that, you should be able to calculate the relativistic correction applied to the GPS clocks, to make them appear (down here) to keep our proper time.
For "extra credit," figure out why GPS can ignore the Shapiro delay (at least, for people on the surface of the Earth).
If you can do all of this, you can start to calculate what a clock on your probe to a black hole would read. The math is not that hard, the physics is straightforward, and yet it is still easy to get a sign wrong or forget some term and make hash of your results. (That's why I never trust people who ignore c and G and the like - they tend to get their signs wrong too:)
MTW is a deep book. It can be exasperating (and its treatment of experimental GR is almost laughably out of date), but you can always get more from it.
For the rest, I would recommend Wald and even Weinberg.
What do you really want to do ? (My guess is that you are not sure.)
If you want to be able to write down and solve Einstein equations for some case, you need vector and tensor algebra, geometry and calculus. Many people who work in GR never do this (for others, it's all they do). If you are interested in some more particular case (black holes or gravitational radiation, say), you need to understand Einstein's equations at some level, plus whatever approximations or simplifications are used in that area (transverse traceless gauge or post-Newtonian approximations, for example). Also, you should get to where you understand Lorentz transforms in your sleep. If you can't do and understand Lorentz transforms, the actual GR math will likely be beyond you.
What I would recommend is to buy Misner, Thorne and Wheeler, and read and follow "track 1." I would allocate 1 year for that.
Who knows? I would not assume that this is all it appears to be. We may want the Russians to do something (improve some system on the Soyuz, say) and may be using this for leverage.
First, please note that this is not about supplying the ISS, it's about getting the crew there. NASA is worried about the safety of Soyuz.
Also, note that the flight of the Soyuz is not dependent on NASA. NASA doesn't get that call, although they could yank their astronauts from the vehicle, they can't ground it.
So, there is little to no chance that the ISS will be abandoned. I predict the Russians will keep a crew there, regardless of NASA's decision.
Well, that's what I get for not RTFA first. Celebrities don't have to pay, at least for now. Companies, however, do
There are no corporate trademarks on the reserved list. Companies that want to make sure their brands do not appear with a.xxx extension are expected to pay between $200 and $650 to to make sure they are removed from the pool of available names
Most of the people I know who deal in domain names feel that the new ICANN TLD policy is primarily about domain name extortion, rather than actually providing a service, so pardon the cynicism.
It has been hypothesized (by Anders Sandberg and others) that an advanced intelligence might convert a Jupiter sized mass into one large diamond computational substrate - a "Jupiter brain." Now this object is rather larger than Sandberg predicts :
"...a compact diamond structure would have a maximum radius on the order of 9760 km, somewhat larger than the Earth. Having the density doubles the possible radius and quadruples the mass, which suggests a trade-off between internal delays and computing power"
but this super-brain could presumably power itself from the nearby neutron star (thereby solving another problem mentioned by Sandberg), and surely could figure out some means of making the larger structure stable, maybe by rotation.
So, if this object was a "Jupiter brain," how could we tell from here ?
They all drink from the same teat of government money, and therefore are all in cahoots. No one working in universities or research groups has any credibility. The only people who are not biased are the ones who only have a web site, and have otherwise nothing to do with climate science.
Well, you left out the people being funded by big oil and the Koch brothers. Why would they lie ?
This argument is kept alive as a way of gaining political power and wealth by manipulating religious people. You won't stop that by having so many "evangelical scientists" no one has ever heard of making a statement.
Surely any event that could eject material from earth with sufficient energy to escape Earth's gravity well would tend to melt the ejecta at the same time,
No. Some, but not all. Here is a mechanism - impacting object hits, penetrates, and is stopped and imparts spherical shock wave into the Earth (or other planet) some depth inside the planet. (In simple terms, it explodes inside the crust of the Earth.) Some part of that shock wave is propagating near vertically up, away from the planet (including, maybe, parts that reflect from internal structure). These shocks lift material up out of what becomes the crater. For a 2 km crater (such as the Great Meteor Crater in Arizona), these shocks turn the layers in the near surface material upside down, just lifting and flipping them over in much the same way you would flip over a pancake, moves a mass of material maybe 1 km, without vaporizing any except for a small fraction near where the impactor stops. For a 100+ km crater, that some process pushes the some of the surface layers off the planet entirely (and also causes long rays, such as are found on the Moon). While some of the ejected material is vaporized, most isn't, and some is treated quite gently (for a massive explosion), gently enough that biological spores and the like could survive the experience.
30 miles down, 30,000+ miles to go. (The Amazon is 4000 miles long, but is divided into many tributaries, the total length of all the tributaries is probably a lot longer than that, but I think that is a safe lower bound.)
Mars rocks have been found on Earth, and it has been a standard assumption in planetary science for some time now that Earth rocks have also been going to Mars by the same mechanism. You wouldn't know it from the summary, but the actual paper also predicts a significant rate of mass exchange Earth -> Mars -
Gladman et al. (2005) estimated the collision rate with Mars to be about 2 orders of magnitude lower that found on the basis of our simulations. However, as also noted in their paper, our results for Mars are within the known typical errors of such probability estimations.... Both results, definite collisions with Mars and Jupiter, are of astrobiological significance,...
It's difficult for the various corporate interests to simultaneously claim to be pro-artist-rights with regard to "intellectual property" and also claim that the artist was nothing more than a day-laborer with no rights to the finished product.
If they can lie about the first, why should it be difficult to lie about the second ?
1. What is the maximum carbon fiber ribbon length can you even make with current technologies? What is the longest length of ribbon that can be made that will support its own weight with current tech?
About an inch right now, but it can be spun. No one thinks that the SE will have 100,000 long nanotubes - they will be centimeters long. Each bond is fairly weak, but the # of bonds increase with length and so short tubes can be bonded together. The real question is, how long do the fibers have to be to have a really solid bond. Longer than 1 inch, but no one knows how much more. It's unlikely to be more than a factor of 10, though.
2. What is the climate and weather going to do to the ribbon? Rain? Thunderstorm? Tornado? Hail? Even all the Sun light? A meteor strike? Lightning? Static electricity?
The big worries (to me) are meteors, space debris and radioactivity. Radioactivity may force the use of boron nitride nanotubes, which would set things back by decade probably.
3. Can you pull the ribbon into space in case something serious is taking place near the planet's surface, like a huge storm?
Yes. Easy to do at the counterweight at the far end. Would take some hours for the wave to move down and the Earth end raise up, but it is the obvious "Plan B" for a dire emergency on the ground.
4. What about fire, will this thing burn? What if a fire starts while climber is on its way, half way through?
Not in space. The last 20 km of the cable are likely to be rather different (shielded, etc.), to avoid such atmospheric problems.
5. Will there be a way to evacuate from the climber with parachutes or rockets or whatever in case of emergency?
If you are 10 km up, sure, parachute back. If you are 30,000 km up, also sure. (Detach from the cable and you're in orbit.)
There is a zone in between where bailing out will not be so good. Multiple cables will probably be necessary before this becomes a mass-market vacation option.
6. How do you make the ribbon stay in one place above the ground anyway?
It's in orbit once per day, so to "first order" it stays put. Now, it will want to move about, at the 100 meter to 1 km level, because of tides and the like. If you anchor the terrestrial end, that thus means you are imposing waves on the cable. That seems to be OK, but more work is definitely needed here IMO.
Can they can answer those questions above before talking about having simultaneous 6 climbers instead of 3? Because they have to answer those questions before they can even do 1.
But that is misleading. There are answers to all of those things (maybe imperfect). You still need to think about things like shipping throughput if you are going to sell it and get it built,, even while you are working though all of the other issues.
One of the interesting things about this conference (which I attended) is that nanoscience researchers on Friday reported substantial improvements in the ability to make carbon nanotubes. They can now "grow" 1 cm nanotube mats, which can be spun into fibers. This is a substantial improvement from even 1 year ago.
I still think that a terrestrial space elevator is a decade out, but this year has convinced me that it is coming much faster than a lot of people think.
Slashdot Mirror
You don't generally get too many hobbyists in war zones.
that when asked about the anomalous procession of Mars, you could sit down with a pencil and graphing calculator for an hour and tell them that GR accounts for ~40 arcseconds/century.
I hope not. Mercury's relativistic perihelion precession is ~ 43 arc seconds / century. Mars's is only about 1.35 ''/cy.
That sort of thing is fairly straightforward (at least at the beginning), but GR is notorious for being slipperly.
Take your GPS example. If we are down here and traveling slowly with respect to the solid Earth, we can set up a global simultaneous frame, in which the clocks are all synchronized.
Now, launch GPS satellites up there with some velocity. There is a "pure" GR time dilation due to gravity (these satellites are more outside of the Earth's potential than us ground-huggers) and also a SR term. You need a solution fro the Earth's field to handle the Earth's field, but the Earth rotates slowly, so the Schwarzschild solution applies. So, let t be the coordinate time a Schwarzschild solution scaled to the Earth, so that the proper time (the time measured at a clock at radial coordinate r and total velocity v) Tau is
d Tau / d t = 1 - GM/rc^2 - 1/2(v/c)^2 + higher order stuff.
Sounds pretty simple (the first term being pure GR, the second, "really" SR, from the Lorentz transformation). Except
- we use clocks at the surface of the Earth, in what's effectively a proper time, not a coordinate time.
- we are moving in an Earth-centered frame (due to the rotation of the Earth), but our distance from the geocenter depends on our latitude (due to our self-same rotation causing the Earth's equatorial bulge), so that effect largely cancels
- the satellites are both moving and at some higher r (so their clocks tick faster). Note that in a circular orbit v is a function of r, and so the SR and GR effects partially cancel (this trips up a lot of beginners).
If you parse all of that, you should be able to calculate the relativistic correction applied to the GPS clocks, to make them appear (down here) to keep our proper time.
For "extra credit," figure out why GPS can ignore the Shapiro delay (at least, for people on the surface of the Earth).
If you can do all of this, you can start to calculate what a clock on your probe to a black hole would read. The math is not that hard, the physics is straightforward, and yet it is still easy to get a sign wrong or forget some term and make hash of your results. (That's why I never trust people who ignore c and G and the like - they tend to get their signs wrong too :)
MTW is a deep book. It can be exasperating (and its treatment of experimental GR is almost laughably out of date), but you can always get more from it.
For the rest, I would recommend Wald and even Weinberg.
What do you really want to do ? (My guess is that you are not sure.)
If you want to be able to write down and solve Einstein equations for some case, you need vector and tensor algebra, geometry and calculus. Many people who work in GR never do this (for others, it's all they do). If you are interested in some more particular case (black holes or gravitational radiation, say), you need to understand Einstein's equations at some level, plus whatever approximations or simplifications are used in that area (transverse traceless gauge or post-Newtonian approximations, for example). Also, you should get to where you understand Lorentz transforms in your sleep. If you can't do and understand Lorentz transforms, the actual GR math will likely be beyond you.
What I would recommend is to buy Misner, Thorne and Wheeler, and read and follow "track 1." I would allocate 1 year for that.
Who knows? I would not assume that this is all it appears to be. We may want the Russians to do something (improve some system on the Soyuz, say) and may be using this for leverage.
First, please note that this is not about supplying the ISS, it's about getting the crew there. NASA is worried about the safety of Soyuz.
Also, note that the flight of the Soyuz is not dependent on NASA. NASA doesn't get that call, although they could yank their astronauts from the vehicle, they can't ground it.
So, there is little to no chance that the ISS will be abandoned. I predict the Russians will keep a crew there, regardless of NASA's decision.
First they . Now they want to take my away local time ! Things haven't been this bad since they invented the meter.
Well, that's what I get for not RTFA first. Celebrities don't have to pay, at least for now. Companies, however, do
There are no corporate trademarks on the reserved list. Companies that want to make sure their brands do not appear with a .xxx extension are expected to pay between $200 and $650 to to make sure they are removed from the pool of available names
Most of the people I know who deal in domain names feel that the new ICANN TLD policy is primarily about domain name extortion, rather than actually providing a service, so pardon the cynicism.
Of course. Uniform Domain-Name Dispute-Resolution Policy - UDRP.
There, fixed that headline for you.
It has been hypothesized (by Anders Sandberg and others) that an advanced intelligence might convert a Jupiter sized mass into one large diamond computational substrate - a "Jupiter brain." Now this object is rather larger than Sandberg predicts :
"...a compact diamond structure would have a maximum radius on the order of 9760 km, somewhat larger than the Earth. Having the density doubles the possible radius and quadruples the mass, which suggests a trade-off between internal delays and computing power"
but this super-brain could presumably power itself from the nearby neutron star (thereby solving another problem mentioned by Sandberg), and surely could figure out some means of making the larger structure stable, maybe by rotation.
So, if this object was a "Jupiter brain," how could we tell from here ?
They all drink from the same teat of government money, and therefore are all in cahoots. No one working in universities or research groups has any credibility. The only people who are not biased are the ones who only have a web site, and have otherwise nothing to do with climate science.
Well, you left out the people being funded by big oil and the Koch brothers. Why would they lie ?
Fixed the headline for you
This argument is kept alive as a way of gaining political power and wealth by manipulating religious people. You won't stop that by having so many "evangelical scientists" no one has ever heard of making a statement.
If Mars has a biology, it may involve sulfur a lot more than the Earth's does, so this is very interesting from the standpoint of seeding life between the two planets.
Surely any event that could eject material from earth with sufficient energy to escape Earth's gravity well would tend to melt the ejecta at the same time,
No. Some, but not all. Here is a mechanism - impacting object hits, penetrates, and is stopped and imparts spherical shock wave into the Earth (or other planet) some depth inside the planet. (In simple terms, it explodes inside the crust of the Earth.) Some part of that shock wave is propagating near vertically up, away from the planet (including, maybe, parts that reflect from internal structure). These shocks lift material up out of what becomes the crater. For a 2 km crater (such as the Great Meteor Crater in Arizona), these shocks turn the layers in the near surface material upside down, just lifting and flipping them over in much the same way you would flip over a pancake, moves a mass of material maybe 1 km, without vaporizing any except for a small fraction near where the impactor stops. For a 100+ km crater, that some process pushes the some of the surface layers off the planet entirely (and also causes long rays, such as are found on the Moon). While some of the ejected material is vaporized, most isn't, and some is treated quite gently (for a massive explosion), gently enough that biological spores and the like could survive the experience.
They just need to develop Googlettos!
30 miles down, 30,000+ miles to go. (The Amazon is 4000 miles long, but is divided into many tributaries, the total length of all the tributaries is probably a lot longer than that, but I think that is a safe lower bound.)
Mars rocks have been found on Earth, and it has been a standard assumption in planetary science for some time now that Earth rocks have also been going to Mars by the same mechanism. You wouldn't know it from the summary, but the actual paper also predicts a significant rate of mass exchange Earth -> Mars -
Gladman et al. (2005) estimated the collision rate with Mars to be about 2 orders of magnitude lower that found on the basis of our simulations. However, as also noted in their paper, our results for Mars are within the known typical errors of such probability estimations. ... Both results, definite collisions with Mars and Jupiter, are of astrobiological significance,...
It's difficult for the various corporate interests to simultaneously claim to be pro-artist-rights with regard to "intellectual property" and also claim that the artist was nothing more than a day-laborer with no rights to the finished product.
If they can lie about the first, why should it be difficult to lie about the second ?
For Mars, it would probably make more sense to anchor the elevator on Phobos, and live with a 500 m/sec velocity of the tip relative to the surface.
Such a Martian Space Elevator, with Phobos as the counterweight, would be possible with current materials.
1. What is the maximum carbon fiber ribbon length can you even make with current technologies? What is the longest length of ribbon that can be made that will support its own weight with current tech?
About an inch right now, but it can be spun. No one thinks that the SE will have 100,000 long nanotubes - they will be centimeters long. Each bond is fairly weak, but the # of bonds increase with length and so short tubes can be bonded together. The real question is, how long do the fibers have to be to have a really solid bond. Longer than 1 inch, but no one knows how much more. It's unlikely to be more than a factor of 10, though.
2. What is the climate and weather going to do to the ribbon? Rain? Thunderstorm? Tornado? Hail? Even all the Sun light? A meteor strike? Lightning? Static electricity?
The big worries (to me) are meteors, space debris and radioactivity. Radioactivity may force the use of boron nitride nanotubes, which would set
things back by decade probably.
3. Can you pull the ribbon into space in case something serious is taking place near the planet's surface, like a huge storm?
Yes. Easy to do at the counterweight at the far end. Would take some hours for the wave to move down and the Earth end raise up, but it is the obvious "Plan B" for a dire emergency on the ground.
4. What about fire, will this thing burn? What if a fire starts while climber is on its way, half way through?
Not in space. The last 20 km of the cable are likely to be rather different (shielded, etc.), to avoid such atmospheric problems.
5. Will there be a way to evacuate from the climber with parachutes or rockets or whatever in case of emergency?
If you are 10 km up, sure, parachute back. If you are 30,000 km up, also sure. (Detach from the cable and you're in orbit.)
There is a zone in between where bailing out will not be so good. Multiple cables will probably be necessary before this becomes a mass-market vacation option.
6. How do you make the ribbon stay in one place above the ground anyway?
It's in orbit once per day, so to "first order" it stays put. Now, it will want to move about, at the 100 meter to 1 km level, because of tides and the like. If you anchor the terrestrial end, that thus means you are imposing waves on the cable. That seems to be OK, but more work is definitely needed here IMO.
Can they can answer those questions above before talking about having simultaneous 6 climbers instead of 3? Because they have to answer those questions before they can even do 1.
But that is misleading. There are answers to all of those things (maybe imperfect). You still need to think about things like shipping throughput if you are going to sell it and get it built,, even while you are working though all of the other issues.
One of the interesting things about this conference (which I attended) is that nanoscience researchers on Friday reported substantial improvements in the ability to make carbon nanotubes. They can now "grow" 1 cm nanotube mats, which can be spun into fibers. This is a substantial improvement from even 1 year ago.
I still think that a terrestrial space elevator is a decade out, but this year has convinced me that it is coming much faster than a lot of people think.
It's like the Mafia. I just pay what they ask.