Janus

It's run by Waste Management, the same company that does normal garbage pickup. It's covered in our normal garbage fees. The city does regulate them (in order to operate a garbage collection company, you have to do recycling and compost/yard debris). The compost/yard debris is taken to a composting facility and the finished compost is sold to landscapers, agriculture, and residents. Because of the recycling, which is picked up every week, our actual garbage is only picked up every two weeks, and even then, most times my wife and I don't fill the garbage can between pick-ups.

If I understand correctly, some "compostable" plastics are meant to go to a commercial composting facility rather than thrown in with regular compost. In other words, you can't just toss them in the compost pile with the banana peels and coffee grounds and expect to them to decompose in the same way. Where we live we do have compost/yard debris pickup and you can throw the compostable plastic bags* in with it ( but not other types of compostable plastic items). I think a lot has to do with the thickness of the plastic. *We have a small compost pail lined with one of these types of bag. When full, we just tie up the bag and toss it into the yard debris can.

The acceleration of the expansion was discovered a couple of decades ago. This was due to a study involving Type 1A supernovae. We had learned that these types of supernovae always reach the same peak brightness. This made them a "standard candle". You could tell how far away one was by measuring how bright it appeared to us. It never really was thought that the rate of the expansion of the universe was constant. That is because the gravitational attraction of everything in it was expected to slow the expansion over time. The one thing we didn't know was if this would be enough to eve completely stop the expansion. The study's original intent was to answer this question. Now the supernovae standard candle gave us a measure of a galaxy's distance and red-shift its speed of recession. The other factor that comes into play is that the further the galaxy is from us, the further back in time the light we are seeing left it. We are seeing a red-shift based on what was happening at that time. If the universe was expanding at a constant rate, then the ratio between distance and red-shift would be the same for all galaxies no matter what distance they are. If the expansion were slowing with time, it would not be a constant ratio with the ratio changing in a particular manner. The magnitude of this change would give you a measure of the rate at which the universe's expansion. The study found such a deviation, but in the opposite direction than what they expected. The red-shift/distance ratio changed in a manner that indicated that the universe was expanding slower in the past than it is now. Instead of slowing down as time went by, it was speeding up. "Dark energy" was the term coined for whatever was driving this acceleration. The exact nature of Dark energy is still a mystery, and there are competing hypothesizes as to what it actually is.

This isn't Risa... I knew I shoulda taken that left turn at Aldebaran!"

As Strange as pointed out, Dark matter, is actually proposed to explain why the observable universe behaves as if it has more mass than we can see in the form of visible matter. Dark energy is the term given to whatever is causing the expansion of the universe to accelerate ( you don't need dark matter for the universe to expand, only for that expansion rate to increase over time.) Both contain the word "dark", but that is just due to laziness when it came to naming conventions. "dark" matter was chosen because the matter didn't interact with light. "dark" energy was chosen, because "Hey, we already have "dark" matter", and not because there was any suspected relationship between the two.

A second used to de defined as 1/86400 of one mean solar day. But with the ever increasing need for accuracy and the knowledge that the Earth's rotation rate was not constant, this was changed to a set fraction of the tropical year (at the start of a particular epoch). This was finally changed to today's definition of "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K). This particular number of periods was chosen so that the duration of the second exactly matched that of the one based on the tropical year. This was a more practical standard as you can't very well go back in time to check the accuracy of your clock against the length of the tropical year in 1900, but you can check it against the radiation emitted by a caesium-133 atom.

An atomic particle is at rest with respect to itself. Thus an Electron's rest mass is the mass itself would measure. Again, if you want to know the particle's energy (including the energy equivalence of its rest mass) relative to some other frame, then you need to account for the other forms of energy. But these energies won't be the same in all frame, and thus different frames would have different values for the total energy for the particle. This is what makes rest mass such a useful concept. It is a value that all frames can agree on. It is frame invariant rather than frame dependent.

The precession period is indirectly proportional to the torque and the rotational period of the planet. If you want the planet to still have a day-night period the same as the Earth, you need to increase the torque. The torque is supplied by tidal forces. Tidal forces fall off by the cube of the distance and directly with the mass of the object causing them. For the Earth, these tidal forces are produced by the Moon and Sun, with the Moon being the larger contributor. So you would need some combination of increased mass of Sun and Moon and distance to them to get the needed amount. Changing either the mass of or distance to the Sun changes the length of the year and in both cases the changes needed to increase the torque shortens the year. Which in turn means that the precession period has to shorten, leading to needing more torque required, meaning you have to adjusted the mass/distance again... It becomes a viscous circle. You'd have to work out if a "sweet spot" even exists. Then there is the fact that increasing the Sun's mass would change its spectral class. Changing the Moon's distance and mass would result in either a very massive or very close Moon, in either case, it would likely be extremely swollen in the sky. The other problem is that if you increase the tidal forces enough to provide the type of torque you would need for such a fast precession, you also have tidal forces so strong that they would very quickly lead to tidal locking. Not only that, but with an ocean covered world like the Earth, the vast majority of the land surface would be under water twice a day due to the rising of the tides.

Like strange, I'm not sure what you mean here. If you are referring to E=mc2, there is no need to "fix" m. "m" in this equation already means the "rest" or invariant mass, which is a quantity all frames agree on. E=mc2 is a special case equation for dealing with the energy equivalence of the rest mass of a system. For other situations, such as when the mass we are considering is moving with respect to the observer frame, you have to use the more general equation: E = sqrt(p2c2+m2c4) where m is the still the invariant mass. p is the relativistic momentum. Sometimes the "effective" mass of a system include the mass equivalence of the "binding energies" holding the system together. So for example, with the short-lived arrangement called "positronium", which consists of a electron and proton bound together in a manner similar to the way a proton and electron are bound together in a hydrogen atom, the "mass" of the pair is greater than what you would get if you just consider the rest masses of the electron and proton. You would get more energy from the eventual annihilation of positonium than you would from just a electron and positron that were just sitting next to each other.* As to "just theory". You have to understand that in science, "theory" means something different than it does in general everyday use. A theory in science is a rigorous model and is it an honor to have your ideas rise to the level where they are accepted as being a theory. ( Sometimes people think that there is a hierarchy which put "laws" above "theories" and that all "true" theories will eventually become laws. This isn't the case. Laws are just expressions of observed relationships or phenomenon. So for example, we have Kepler's laws of planetary motion. But these are just descriptions of the behaviors we see in planets. It wasn't until Newton developed his "theory" of gravity that we got an explanation for that behavior. And while some laws are well entrenched and pretty much considered inviolate ( the law of conservation of momentum), there are other laws that are only considered accurate over a restricted range (Boyle's law) * such a arrangement of a positron and electron just sitting next to each other is not likely to occur. More likely you will have the two particles approaching each other and drawn together. So to get the energy released you would have to account for the momentum of each of the particles at the moment of annihilation as per the equation given above.

The second equation is always the correct one, it is just as v become smaller, the answer it gives converges towards the answer given by the first equation. v is always the relative velocity between source and observer*. What the observer/source velocity "as a pair" is with respect to some other frame of reference makes no difference. *technically, the difference in velocities between the source at the moment of emission and the observer at the moment of reception. So for example, if the source and observer are at rest with respect to each other when the light is emitted, and then after that, the source accelerates to a new velocity with respect to to the observer, the observer will see no red-shift when the light emitted before that acceleration occurred gets to him. However, if the observer changes his velocity between emission and reception, he will see a frequency shift as a result of his velocity change.

Start with two parallel line ( white lines in diagram) Consider pairs of points along those line (AA and BB) The distance between A and A is the same as between B and B. The A point are further from the viewer's eye ( small oval represents the lens and vertical line the retina.) The red and blue lines are the light leaving these points, passing through the lens and forming an image on the retina. Such an image will show the two "A"s being further separated than the two "B"s. this is just the result of projecting a 3 dimensional world onto a 2 dimensional surface.

No. Start with the situation of a craft that has already matched velocity with Mars at the edge of its gravitational sphere of influence ( where Mars' gravity begins to over rule that of the Sun's on determining the trajectory). From This point the craft falls in towards Mars. To land on Mars, the total delta V needed from this point on is (roughly)equal to Mars' escape velocity at its surface: 5 km/sec. Now let's say you want to land on Phobos. First you need to match Phobos' orbital speed. If you were t just let the craft continue on a purely ballistic path, when it reached Phobos orbital distance, it would be moving at( roughly) escape velocity from Mars at that distance, which is 1.414 times the orbital speed of Phobos. Unless you are incredibly wasteful, you will plan things so that your craft passes Mars so that its velocity and Phobos velocity are in the same direction as they pass each other. This way, you only have to kill the 0.414 times Phobos orbital speed difference between the craft and Phobos to match speeds. This work out to be ~ 0.903 km/sec. From that point, in order to land on Phobos, you only require an additional delta v of 0.011km/sec, the surface escape velocity for Phobos. Total Dv ~ 0.914 km/sec ( compared to the 5 km/sec needed to land on Mars. And while some of this can be dealt with by aero-braking, the total Dv is still much greater. ) The one issue with a Phobos landing in in the timing, your craft has to arrive at Phobos' orbit at the same time that Phobos is at that point. But this isn't as big an issue as it may seem. Let's assume that your craft arrives at the proper orbital distance when Phobos is at some other point of its orbit. The solution to this is quite simple: When you do your burn, you don't do the full burn you would need to match Phobos's orbital speed. Instead, you do just enough of a burn to put yourself in a elliptical orbit, one with a longer period than Phobos, You pick an orbit so that its period is such that when you return to that point of the orbit, Phobos is at that point of the Orbit (so for instance, if Phobos was exactly on the other side of Mars, you would put yourself in an orbit with a period of just under 12 hrs. This way, Phobos completes 1 1/2 orbits in the time it takes you to complete one.) Once you make the rendezvous, you do the second burn to circularize the orbit. You have just split the delta V need to match orbital speed with Phobos into two burns.

Not relative to you.

Still well short of c. And remember that escape velocity is also the velocity something dropped at rest from an infinite distance would be moving at the center of the Sun as long it was able to fall unimpeded. In other words, any dark matter that starts at or above escape velocity at any distance will be moving at or above escape velocity when it reaches the center.

The escape velocity equation given only holds if all the mass concerned it contained within that radius. To get an escape velocity of c from one solar mass, you would first have to squeeze all of the Sun's mass inside that 2968 meter radius. Escape velocity is dependent on gravitational potential. It basically works out that you are at escape velocity when KE +GPE = 0 KE = mv2/2 and outside of a mass, GPE = -GMm/r ergo escape velocity is when: mv2/2= GMm/r v2/2= GM/r v2= 2GM/r Once you pass inside of a body like the Sun, the GPE equation changes to GPE = -GMm[(3R2 - r2)/2R3] (to be fair, this is not exact for the Sun, as this assumes a constant density, and the Sun's density increases as you move inward which would need to be accounted for) where R is the radius of the body, (r is your distance from the center) If r=0, (you are at the center) is reduces to GPE = - 3GMm/2R, which makes the escape velocity v2 = 3GM/R In other words, the escape velocity from the center of a uniformly dense object is just 22.5% greater than that at the surface. Thus, if the Sun where of uniform density, the escape velocity from its center would be ~757 km/sec, compared to the 617.5 km/sec it is from the surface. Even after you factor in the the increasing density with depth, you get nowhere close to c or the formation of a event horizon.

The universe doesn't care what you believe. And what you believe what would happen is not what would happen in reality. Light is the same thing as radio waves, just at a different frequency. We already have direct evidence that light doesn't travel instantaneously. The Apollo astronauts left a reflector on the Moon. We have fired a laser at this reflector and measured the time it took to return. Laser are just a type of light. If light traveled instantly, there would have been no delay between firing the laser and seeing the reflection. As it was, the delay was the same as it would be expected if the light traveled at ~300,000 km.sec out to and back from the Moon. Lidar, which is like radar but uses light instead wouldn't work if things behaved like you claim.

The time dilation equation requires a relative velocity, which is what the v stand for. In this case, it doesn't matter if you consider it negative or positive, because you are squaring it in the equation so the result is always positive. So in this case, it is the same as their having a relative speed with respect to each other. But the key point is that the time dilation is determined by the relative speed to the frame doing the measurement, not to some other third frame. If I have a bunch of clocks moving away from a center point, they all have the same speed relative to that point, but have varying relative speeds with respect to each other, and thus each will measure the other clocks as ticking slow by various amounts. Just because relative to that central point all the clocks have the same speed and thus tick at the same rate according to someone at that central point does not mean that they all tick at the same rate according to the individual clocks. When you say two clocks have the same speed, you have to say what frame they have the same speed relative to. And to determine what either of these clocks will measure as happening to the other clock, you would have to know the relative directions of the travel of each clock in our initial frame, so that you can work out the relative speed between the clocks as measured by the clocks. If they are traveling in the same direction in that frame, then they have 0 relative speed.( according to both the clocks and the initial measurement frame) If they are moving in opposite directions at v, then each clock will measure the relative speed of the other as being: 2v/(1+v^2/c^2) And this value is what you would plug into the time dilation equation to determine what rate each clock would measure the other as running. Again, there is no absolute value you can apply to "speed", nor is there an absolute frame from which it can be measured. If you say something has a speed of x, you have to supply the reference frame that speed is measured from. And saying that "two clocks have the same speed" is meaningless by itself.

They don't have "equal velocities". Velocity combines both speed and direction. If you say that one in moving at 0.9999c in one direction relative to a given frame and the other is moving at 0.9999c in the other direction relative to that frame, it is the same as saying one has a velocity of 0.9999c and the other one has a velocity of -0.9999c. To be traveling at the same velocity, they would have to be at rest with respect to each other. And in this case, each of them would have a speed of 0.999999995... c relative to each other as measured by either. And while someone in that frame which measures both as moving at 0.9999c would say that the clock would tick at the same rate, each clock would say that the other is ticking slow ( about 0.0001 times as fast as their clock.

When it's at its closest, we would see Jupiter as it was some 35 min ago. This delay is how Ole Romer made The first quantitative measure of the speed of light. By observing eclipses of Io, one of Jupiter's satellites, he was able to note that the observed timing of these eclipses varied in a pattern that matched how the distance between the Earth and Jupiter changed. This shift in the observed timing was caused by the fact that light took longer to get from Jupiter and the Earth when it was at its furthest than it did at it closest. The amount of the shift and change in distance gave him the speed of the light.

You can never observe the other clock as completely stopping as that would require it to travel at c*, which is impossible. It can get closer and closer to c, but never actually reach it. Let's use an analogy to illustrate what is happening. imagine two people who start off walking from the same point but at an angle to each other. They have equal length strides. After so many steps, they check their progress. Each person will measure that after x number of steps they will have traveled a distance of y from the starting point in the direction they are walking. However, if they check the other person's progress against their own, they will note that the other person has traveled a shorter distance in this same direction ( the direction he, himself, is walking). So each of them measures his own progress as being perfectly normal while the other person falls further and further "behind". This is equivalently what happens with time dilation. Each of us measures time according to our frames "time axis", and frame in motion with respect measure along different time axis. This is the basic difference between the concept of space-time and the old concept of space and time. With space-time, time and space are combined and there is no absolute "time axis", but rather the time axis is frame dependent. ( a separation between two events that one frame measures as only being separated in space, could be measured as being separated in both space and time by another frame.) * Actually, this isn't really true either, If you plug c into the time dilation equation, you end up with T = t`/0 and division by 0 is undefined.

In order to be captured by the black hole, the dark matter would already have to be on an initital trajectory that crosses the event horizon. escape velocity is c for objects that originate at the event horizon. At any point further out, the escape velocity is less. So it is quite possible to have something fall in towards the black hole and skim by it outside of the event horizon. Visible matter doing this runs the risk of colliding with other matter surrounding the black hole (the accretion disk,. for example), losing orbital energy, and finding itself with an event horizon crossing trajectory even if it didn't start with one.

While dark matter is gravitationally attracted to these bodies, and will fall in towards them, there is no mechanism equivalent to electromagnetic interaction to keep it there. If you imagine a dark matter particle falling towards Earth, it will pick up speed as it gets closer and closer. It will reach the Earth moving at some great speed, pass through it, and climb away out the other side with the same velocity as it had coming in, climbing back out into space. (It pretty much behaves as visible matter would if it were falling through a tunnel bored through the Earth) Put another way, if an asteroid is moving at escape velocity with respect to the Earth, as long as its trajectory doesn't intersect the Earth itself, it will fall in towards the Earth, swing around it and head back into space never to return. On the other hand, if it hits the surface, thus converting a great deal of its velocity into heat it can be left with too little KE to climb back out of the Earth's gravity well. Dark matter will just pass through the Earth, even if on a surface intersecting trajectory, without shedding energy in this way. So, no, you would not expect to find dark matter in great quantities inside planets or stars. The only mechanisms available to Dark matter for shedding energy is the aforementioned slingshot ( which involves a third body. So for example in our last example, while the entry and exit velocities for the DM particle remain the same relative to the Earth, the Earth-dark matter interaction could reduce the dark matter's velocity with respect to the Sun, or increase it at the expense of some the Earth's orbital energy. The other mechanism is gravitational radiation emission. The acceleration of the dark matter particle due to it gravitational interaction with the Earth can cause it to produce gravitational waves which come at the expense of the KE of the particle. However, gravitational radiation is very weak, and we are talking about a minimal loss via this mechanism.

They are mounted on gimbals to keep them orientated towards the Sun, but they don't make a full rotation. The ISS orbit takes it through the Earth's shadow. So the panels rotate to follow the Sun for that part of the orbit, and then while in shadow, they just rotate back in order to be ready catch the Sun at the next sunrise. 60% of the electricity produced is used to charge the batteries to get them through the period when the Sun is eclipsed by the Earth

The ISS orientation is such that it always keeps one side always facing the Earth. This is so that the antennae always always pointed in the right direction, the windows point at the Earth, debris shielding can be arranged to be thickest in the direction of greatest risk, etc. Now if you try and add a section that rotates so that its axis always points towards the Sun, you can't do this. In addition, Since the Earth itself orbits the Sun, the axis of this rotating section would have to be changed over the course of a year in order to keep it pointing towards the Sun ( otherwise, shielding pointing at the Sun in July would be pointing away from it in Dec.), which introduces precession issues. Then there is the issue of dealing with changes of angular momentum and balance as people and equipment move in and out and around the rotating section, the mass of such a section would need to be significant to minimize these effects, or you would need some kind of active compensation with a system of sensors, computers and movable counterweights, all working together to keep things in balance.

Right. The thing with dark matter is that the initial trajectory would need to be such that it took it past the EH. With visible matter it can have an initial trajectory that takes it outside the EH and back out into space again, but through collisions with other visible matter, it can shed energy and have its trajectory altered into a EH crossing one. (it is also conceivable that an close approach with something else could gravitationally alter a dark matter particle into a EH crossing path, but it could also alter a EH crossing path into one that misses. With visible matter collisions, energy is given up via radiation leaving both parties with less KE than they started with. This increases the statistical averages for visible matter in terms of falling inside the EH.