The Furious Angels
FA Discussion => Off Topic => Topic started by: Da6onet on May 15, 2014, 08:06:59 pm
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So who likes watching Cosmos (http://www.cosmosontv.com)?
If you're interested in learning more about how everything in the universe works, I thought I could post questions once a week (more often if people want) to see who can come up with the correct answer first. Most will be conceptual, though for those with a little more math/physics experience, I can throw in problems that require algebraic manipulation, trig, and/or a little light calculus.
We'll pretend I asked the following question on Sunday for this week 5/11-5/17
On November 1 at 8:30 p.m. you look toward the eastern horizon and see the bright star Bellatrix (http://en.wikipedia.org/wiki/Bellatrix) rising. At approximately what time will Bellatrix rise one week later, on November 8?
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I'm estimating at possibly 7:30 in the morning, and I got this information with its right ascension and declination.
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I'm estimating at possibly 7:30 in the morning, and I got this information with its right ascension and declination.
The right ascension and declination give it's position relative to the equator and prime meridian on Earth so you can look for it in the same spot in the sky (adjusting for things like time zone and seasons). The link I posted for Bellatrix was just for fun facts (also so you'd know it was a star and not just a Harry Potter character!). You can assume at very far distances, say 250 light years (77 parsecs, 2.4 × 10^18 meters), Bellatrix does not move relative to the background over short time periods (a week is short on stellar motion time scales).
The 1st hint I'll give is that an Earth day as most people know it is not a 360 degree rotation.
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ANSWER
Because the Earth's synodic day (3) is 4 minutes longer than it's sidereal day (2), stars rise about 4 minutes earlier each night. Thus, a week later, Bellatrix will rise at about 8:02pm (8:00 pm is close enough) on November 8.
(http://astro.unl.edu/naap/motion3/graphics/sidereal_synodic.png) (http://astro.unl.edu/naap/motion3/sidereal_synodic.html)
NEW QUESTION
So I just saw a trailer for a new Chris Nolan movie - Interstellar.
http://youtu.be/zSWdZVtXT7E (http://youtu.be/zSWdZVtXT7E)
This brings up a good question for this week.
Under what circumstances can you travel faster than the speed of light? Are there examples of this in nature?
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If you were on a space ship travelling the speed of light and then walked forward, you would be moving faster than the speed of light. Not sure about examples in nature...
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If you were on a space ship travelling the speed of light and then walked forward, you would be moving faster than the speed of light. Not sure about examples in nature...
Einstein's special relativity says that to an observer outside the light speed train, time proceeds normally but you and the train are both infinitely thin. Since you traverse no extra distance, you have no additive velocity. Don't worry, in your frame of reference you appear to be walking normally across the train car, but the outside world appears to be stopped.
(http://creationwiki.org/images/9/91/Srlc1.png) (https://www.boundless.com/physics/special-relativity/consequences-of-special-relativity/length-contraction/)
1st hint General Relativity
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This brings up a good question for this week.
Under what circumstances can you travel faster than the speed of light? Are there examples of this in nature?
Isn't the theory that light travels faster then itself at a black hole or event horizon. I think it is something close to that.
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This brings up a good question for this week.
Under what circumstances can you travel faster than the speed of light? Are there examples of this in nature?
Isn't the theory that light travels faster then itself at a black hole or event horizon. I think it is something close to that.
I believe a black hole is where the gravity is so strong that light is unable to escape the pull. The event horizon is simply the point where that pull becomes so strong. I don't think that gravity speeds up light. It's not faster, but stronger. I could be wrong.
As far as I knew, any attempt at going faster than the speed of light would result in everything relative slowing down. For example, if the speed of light was 60 MPH and you were on a bus going that speed and tried to throw a ball, relative to the ball, the bus would slow down below 60 MPH since the ball cannot exceed that.
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Universal expansion shows that it is possible that some galaxies are moving away from us so rapidly that the light from them may me never reach us. Kind of like two cars traveling down the road in the same direction. One car has a head start on the other and is moving faster so that the car behind will never catch up and see the car in front of it. It's possible I suppose with universal expansion that we'll all be traveling faster than light someday
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If an object is outside of space-time and it is being pushed by the expansion of space-time, the space-time in theory can expand faster than light. This likely happened in the first trillionth of a trillionth of a second after the big bang when the universe expanded faster than light.
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comets baby; comets.
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Isn't the theory that light travels faster then itself at a black hole or event horizon. I think it is something close to that.
Light as we are defining it here are photons (that behave like waves/rays or particles depending on the situation). While some interesting things happen at the event horizon (such as Hawking radiation), the important idea there is escape velocity is exactly c (where c is the speed of light in a vacuum). Beyond the event horizon no information escapes, so it is fair to say that physics as we define it for our universe does not apply for anything inside this radius. That said, outside the black hole, all mass and energy moving through space is governed by laws of physics and thus cannot exceed the speed of light.
I believe a black hole is where the gravity is so strong that light is unable to escape the pull. The event horizon is simply the point where that pull becomes so strong. I don't think that gravity speeds up light. It's not faster, but stronger. I could be wrong.
As far as I knew, any attempt at going faster than the speed of light would result in everything relative slowing down. For example, if the speed of light was 60 MPH and you were on a bus going that speed and tried to throw a ball, relative to the ball, the bus would slow down below 60 MPH since the ball cannot exceed that.
Correct. An interesting effect of this is that if we threw Longboard into a blackhole, we would see him appear to slow down as he approached the event horizon, then stop at the event horizon. The photons that allow us to see him would be continuously red shifted and fade from view. Doesn't answer the question though! :-)
Universal expansion shows that it is possible that some galaxies are moving away from us so rapidly that the light from them may me never reach us. Kind of like two cars traveling down the road in the same direction. One car has a head start on the other and is moving faster so that the car behind will never catch up and see the car in front of it. It's possible I suppose with universal expansion that we'll all be traveling faster than light someday
If an object is outside of space-time and it is being pushed by the expansion of space-time, the space-time in theory can expand faster than light. This likely happened in the first trillionth of a trillionth of a second after the big bang when the universe expanded faster than light.
ANSWER
Objects that are within spacetime are limited to the speed of light. Spacetime itself could give two shits about speed "limits" and expands (or contracts) at whatever rate it wants, like when it grew in size by 10^50 around between 10^-40 to 10^-30 seconds after the big bang started. Today we can observe that there are galaxies with a redshift of z>1.4 (where z = 1.4 is a redshift due to moving away at c). An analogy would be two slugs on an expanding balloon (where the ballon is spacetime and the slugs are galaxies. The slugs are moving less than the speed of light in their frame of reference, but the balloon can expand very quickly, thus the slugs are moving apart faster than c.
What's troubling to some cosmologists is that we observe that all galaxies outside our local cluster (where gravity trumps dark energy), are actually accelerating away from us (and the further away, the faster the acceleration). Thus at some point in the far future we will not be able to observe anything beyond our local cluster, the galaxies will appear to freeze in space, red shift and fade from view. It possible/likely that this has already happened and why our observable universe isn't necessarily the whole thing.
There are two leading theories of moving through the universe that don't violate special relativity (moving faster than c through space) and in fact are predicted by general relativity.
1. Connect two points in space via a worm hole. This is hypothosized in general relativity as one possible way supermassive black holes form and gain so much mass so quickly (10^6-10^9 solar masses in a period of 10^5 years or so). It's not technically moving outside space time since the tunnel is just two highly warped regions of space time connecting.
2. Make use of the flexibility of spacetime (expansion/contraction). An Alcubierre warp drive, utilizing negative energy could contract the spacetime immediately in front of it while expanding it immediately behind. The ship itself would not actually be moving, rather it would be "surfing" on a spacetime wavefront.
Broin has the most correct answer so he is this week's smart ass!
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FUCK YA!!! Told ya I'm not just a contract killer!!!!
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Very confused. Broin's answer failed to make any mention of space-time. His 'answer' was simply a statement that two objects can be moving apart faster than light relative to one another's position--but neither object is traveling faster than light.
I only posted today because of how wrong the other answers were and I made clear mention of space-time being the only viable theory of faster than light travel. And even the space-time theories are thin at best.
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Broin's phrase "universal expansion" and subsequent wording correctly explains the natural example of superluminal separation. Your phrasing that spacetime can expand faster than the speed of light is just another way of saying it using the term spacetime, which is why I included your quote, but Broin posted first and you had some slightly mis-worded information in your post.
It is worth clarifying a few things.
-normal energy/matter as we know it doesn't move outside spacetime, they move with spacetime. Outside of spacetime would indicate moving in some extra dimension (in sci fi this commonly referred to as things like subspace, hyperspace, etc.) String theory theorizes this but no observational data backs it up.
-dark energy is the currently accepted name for the force expanding the universe (that is to say it fits mathematically but we don't understand what it is exactly).
-while the universe did expand rapidly during the inflationary period, it is still expanding today and is actually acceleratng it's rate of expansion-- Hubble's constant is not actually constant.
I would also argue that Einstein's theory of general relativity explains a great deal of how the universe works and there is a large quantity of evidence--binary pulsar period changes, satellites being framed dragged by Earth, and more recently gravity wave detection in the cosmic microwave background. These are all observed effects of spacetime behavior that fit predicted models.
I will admit the two ways of human spaceflight I mentioned are very far-fetched, but again, predicted by the same mathematical models. Real life physicists are trying to prove existence of these ideas (like string theory and WIMPS) and it's neat when they do (like the higgs boson, like negative energy). A theory is only thin until it's verified :-)
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i still think comet was correct;)
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i still think comet was correct;)
Ah right I forgot about your answer. So most comets come from the Kuiper Belt and Oort Cloud and are on elliptical orbits. Some comets come from outside the solar system and have hyperbolic trajectories. Both types can be modeled by
v^2 = G*(Msun + mobject)*(2/r - 1/a)
Where G is the universal gravitational constant, r distance of the object from the sun and a is it's orbit semi-major axis. Since the mass of the sun >> than the mass of a comet, this equation can be simplified to
v = 29.8*(2/r - 1/a)^0.5 where r and a are measured in AU
(G = ~6.67E-11 N*(m/kg)^2, Msun = ~1.99E30 kg, 1 AU = ~149.6 million km for those that wish to keep the equation in SI).
Let's assume the comet is from so far away that a --> infinity and that term drops out. Then lets estimate such a comet at perihelion for a couple ranges.
r = 0.9 v = 44 km/s (this is about Hale Bopp's distance/speed)
r = 0.1 v = 133 km/s
r = 0.01 v = 421 km/s (this was ISON's closest approach and it was utterly destroyed)
For comparison, our Voyager spacecraft plod along at 17km/s and LEO objects like the ISS are as low as 8km/s.
The escape velocity from the galaxy is right around 500km/s (from 8000 parsecs out that is), but our Sun isn't massive enough to fling anything that fast without it passing too close and getting destroyed.
Fun fact, based on this equation, and given that Earth is moving at 30km/s at 1 AU, the speed limit of asteroids and comets impacting Earth is ~70km/s.
I digress, these velocities are nice, but light in a vacuum travels at 300,000 km/s!
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I was focusing more on the below extract from an (admittedly Wikipedia) article and reference to superluminal.
Your question was focused on astronomy - hence my desire to turn back to comets;)
Daily sky motion[edit]
For an earthbound observer, objects in the sky complete one revolution around the Earth in 1 day. Proxima Centauri, which is the nearest star outside the solar system, is about 4 light-years away.[6] On a geostationary view Proxima Centauri has a speed many times greater than c as the rim speed of an object moving in a circle is a product of the radius and angular speed.[6] It is also possible on a geostatic view for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000 AU.[7] The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.
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Ah yeah, I should have specified actual information propagation rather apparent effects of us running into a stream photons or in the case of AGN blobs, a trigonometry trick of the eye. I think I'm going to post a math based question next just so Lithium can show you all what's up. <3 engineers.
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I was focusing more on the below extract from an (admittedly Wikipedia) article and reference to superluminal....
Objection counselor, I believe the judge has already spoken on this matter. No need to argue an already decided point. Which I believe was something like BROIN IS AWESOME! !!!
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:)
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(http://www.nap.edu/books/11991/xhtml/images/p20013a28g3001.jpg)
-Rise in average temperatures caused the Larsen B ice shelf to break up in early 2002. This ice shelf, which is about the size of Rhode Island, is thought to have been part of the Antarctic coast for the past 12,000 years.
Week of 5/25/14
Antarctica has an area of 13 million square kilometers and is covered by an icecap that varies in thickness from 300 meters near the coast to 1800 meters in the interior. Assuming that water and ice have roughly the same density, estimate the amount by which the water level of the world’s oceans would rise if Antarctica’s ice were to melt completely (you must show your maths!).
Bonus: Look up coastal cities like New York (think Manhattan) and compare their altitudes above mean sea level to the amount you calculated!