Janus

I get a rough estimate of 1.5 ly for the radius of the Sun's gravitational sphere of influence. At this distance, the tendancy for an object to travel in an independant orbit around the center of the galaxy will over ride the Sun's ability to hold the object in orbit around itself.

Escape velocity is usually figured as from the point of departure, in this case, the surface of the Earth, even if the rocket never quite reaches that velocity. For instance, assuming a rocket fires its engines until it reaches an altitude of 300 km (About Leo) . At the Surface of the Earth, Escape velocity is 11.205km/s. At 300km its is 10.950km/s. So the rocket would only have to attain 10.950km/s to escape. But the total amount of energy the rocket had to expend to do this is the same as it would have been to give the rocket a velocity of 11.205km/s at ground level. It is actually more advantagous to reach escape velocity as soon and as low as possible. When you burn most of your fuel close to the ground, you use less fuel to get the same effect because you are using less fuel to lift fuel. (If you burn your engines until you get to 300km, you have to lift at least some of the fuel to 300km, and that takes extra fuel as opposed to burning all your fuel before you reach 10km, where you only have to lift fuel a maximum of 10km.)

Imagine you are throwing a ball up in the air. As it leaves your hand it starts with an upward velocity, but immediately starts to lose it due to gravity as it climbs. Eventually it loses all its velocity, comes to a stop and then begins to fall back down. The greater the velocity it has when it leaves your hand, the higher it will travel before falling back. If Earth's gravity reached to infinity and maintained the same strength the whole way, there would be no speed at which you could throw the ball that it wouldn't fall back. But Earth's gravity doesn't do both. It does reach to infinity, but it gets weaker the further from the center of the Earth you get. (By the square of the distance; at twice the distance of the Earth's surface, it has fallen to 1/4 strength) Thus, when you throw the ball upwards, as it climbs, the force of gravity pulling it back weakens as it gets further from the Earth. As long as you throw it at less than 11km/sec, the Earth will win out and eventually slow the ball to a stop and pull it back. But at 11km/sec, something happens, the ball gains height and the pull of gravity weakens faster than the ball loses speed. As the ball climbs, it still loses speed, but at a smaller and smaller rate. No matter how high it has climbed it still has some speed left and it will never fall back to the Earth. Another way of looking at Escape velocity is that it is the speed that an object dropped from an infinite distance would be traveling when it hits the surface of the Earth. (neglecting resistance)

Yes, you are wrong here. The planets weren't created by an explosion from the sun. They were created from material left over from when the sun intially condensed from a nebula. Since this nebula was spinning in one direction, the planets and the sun all ended up revolving more or less along the same axis. I think you might being confused by the fact that the much of the material that formed our Solar system was created in an explosion of another star when it went supernova.

What happens here is not any increase in the sensitivity of hearing, merely that the brain devotes more of its sensory processing power to the sense of hearing. The ears constantly detect sounds that we are not consciously aware of. The same is true with the other senses. All this sensory input would drive us to distraction if it weren't for the fact that most of it is filtered out by a subconscious mechanism. When a person loses their sight, the brain slowly redistributes the sensory processing for sight to the other senses. The filters start letting more information from those senses through . The senses don't become more acute, just more attention is paid to them.

Actually, the idea of explosive decompression as shown in many movies doesn't happen. There will be some swelling of tissue, but nothing to that extent. A person would even stay conscious for about 10 sec, and if repressurized within 90 sec, would survive with no permanent ill effects. There is actually evidence to support this. In 1966, a technician testing a pressure suit was accidentally exposed to hard vacuum for 30 sec. He came out of it just fine.

Check out the following attachment. It shows the light clock arrangement as seen by both the person next to the clock and by the person for which the clock is moving. For the first person, the distance between emitter and mirror is ct0 (the speed of light times the time it takes to traverse the distance as measured by him. For the second person (who sees the light clock as moving) the light follows the diagonal path shown, and this distance is ct1. The distance the clock travels is vt1, where v is the velocity the clock is seen as moving. The distance between the emitter and mirror at any instant (x) can be found by x² = (ct1)²-(vt1)² Now x is the same distance the first person got by ct0, so x=ct0 and therefore: (ct1)²-(vt1)² = (ct0)² c²t1²-v²t1² = c²t0² c²t1²/c²-v²t1²/c² = t0² t1²- v²t1²/c² = t0² t1²(1-v²/c²) = t0² t1 sqrt(1-v²/c²) = t0 ( Usually this is written with t0 and t1 reversed, but I intially got them switched around when I drew the diagram, and was too lazy to go back and change it later. It doesn't effect the math any.)

The Doppler effect is a completely different effect from time dilation. Usually iin Relativity, we assume for simplicites sake that the doppler effect has been factored out, and we are just dealing with time dialtion.

Okay, you have two people and two light clocks. each prson is standing next to his light clock. For each person, the light clock next to him takes one second for the beam to travel to the mirror and back. This is true no matter what manner he uses to measure the time. (stop watch, his own pulse etc. ) Now these two people are moving relative to each other, and each watches the other. By their measurement, the other light clock takes more than one second to "tick". By extension, they have to see the timepiece used by the other person run slow by the same amount. (If he didn't, then all kinds of paradoxes would arise.) Each sees the other's clock as running slow. So this answers your first question; what happens is not that high veloctiy causes one to age more slowly, but that high relative velocity causes each to measure the other as aging more slowly. Now in the twin paradox, at the end, one twin has aged less than the other. This will be the twin that experienced an acceleration. This is because experinced acceleration also effects how you measure things. At one point of the trip he will see the other twin age much more rapidly than he does. (but only for part of the trip, for the rest of the time he sees his brother age more slowly. ) The twin who doesn't accelerate, merely sees his brother age more slowy during the trip. At the end of the trip both brother's will agree as to their relative ages, but they won't agree as to how that age diffence came about. And neither twin is more correct as to what happened. As far as each is concerned, they are the ones who measured "real" time and their brother experienced "altered time". And they are both right. This what is meant by "time is Relative".

Okay, the first thing you probably need to do is re-think the concept of "real time". Time is merely a measurement used to separate events, it is no more "real" than that. As far as the clocks go: Remember, as each observer is concerned, the light clock next to him and any other method of time measuring are in perfect sync. And, each observer also has to see that the other set of light clock and time measuring device are in sync with each other. (even though they won't be in sync with his.)

The problem with this outlook is that it doesn't result in the same set of observation for the Twins as Relativity predicts. For this outlook to be true, the twin that ages the least would have to measure the other's clock as moving faster than his during the entire trip, but he doesn't. Also, this would imply that there was an absolute reference system by which you could measure an object's velocity with respect to. This would mean we could measure the Earth's velocity around the sun with respect to it also. That would lead to the following result: When a particle accelerator fired a particle in the same direction as the Earth is moving, the Earth's velocity would be added to the particle's velocity, and if fired in the opposite direction, the Earth's velocity would be subtracted. At the near c speeds that such particles travel, even such a relatively small addition or subtraction would cause a measurable difference in the time dilation and the amount of energy needed to accelerate the particle. No such deviation has ever been measured in any accelerator experiment. Since this is the case, your second way of looking at it can't be true.

Well, if the one that goes to the Black hole orbits at an distance that cuases his oribtal speed to equal that of the one just traveling at near c, then he will experience the least time. There are two effects to take into account, his motion, and his postion in the gravity of the blackhole. If you move him out futher, you will finally reach a point where he will experience that same time as the other due to the combination of the effects. Move him evenfurther out and he will experience more time.

Plant's get their carbon from the Air (in the form of carbon dioxide.) Even though carbon is fairly rare as elements go, there is more than enough to support the plant and animal life of the Earth with some left over. (it continuely gets recycled). Long before we could use up all the carbon making up living matter, we'd run out of phosphorus, an element living tissue need's to run its metabolism. As far as life goes, it is the true bottleneck. The reason carbon forms the backbone of life, despite its rareity, is because it forms complex chains so readily.

It depends on who's doing the asking, and the exact conditions of the test. Do both ships start out at the same point and then return to that point? If so, where is this point located? Or are you jjust comparing their time rates as observed by a third observer? And if so, where is this observer located?

But that's only in mediums where light has an apparent speed below c. do not confuse the speed of light in various mediums with c. c only refers to the speed of light in a vacuum, and not to its apparent speed in any other medium.

Okay, Let's see if I can shed some light on the subject. First off, it is important to note what Relativity says about velocity and time. When we say that time slows for an object that travels at near c, it is important to understand just what this means. Relativity deals with measurements between reference frames. Thus one measures a time rate difference between himself and a frame that is moving with respect to him. If the Relative velocity remains constant, an observer in each frame will measure the other's time rate as slower. Now here is the part that trips people up: There is no way to say to choose either observer's measurements as reflecting reality better than the other's. Both observer's measurement's equally reflect "reality". Now how does one square this with the Twin paradox, where one twin returns younger than the other? First we must understand how accleration effects measurements between frames of refernce. Imagine a space ship accelerating through space. (the astronauts feel themselves pushed to the back of the ship due to this acceleration.) There is a clock in the nose of the ship and one in the tail, and they are sending time signals to each other. Because of the fact that light has a constant speed as measured by any observer, the clock in the nose will see the clock in the tail run slower,and the clock in the tail will measure the clock in the nose run faster. How much faster depends on the value of acceleration, and how far apart the clocks are separated. For any given accel, the longer the ship, the greater the time difference measured. Now, this measurement of different time rates are not limited to items in the ship. If one were to look out from within the ship to a point somewhere up ahead, you would also see the same thing; clocks further ahead of you would run faster than clocks closer. ( and conversely, if you look behind you, clocks further away would run slower. ) Note that this effect is only measured by someone undergoing the acceleration. If you watched someone else accelerate in respect to you, the only time rate difference you would measure would be due to your relative velocity. Now let's apply this to the Twin paradox. Twin A and B are sitting in spaceships at reart with each other. Twin B fires his engines, accelerate up to near c, coasts for a while, brake to a stop, turns around and returns. What Twin A measures: Twin B increases relative speed wrt himself. As he does so, Twin B's time rate will slow down until he reaches coasting speed, then it runs slow at a constant rate. He then coasts for say 10 ly, slows down, acclerates back towards Twin A, coasts again, then brakes to a stop next to Twin A. During both coasting periods Twin A will measure B's clock as running slow at a constant rate, and during the braking and turnaround, he will measure B's clock still running slow, but by a varying amount. When Twin B returns, A will say that B will be younger because B's clock ran slow practically the whole time. What B measures: As the velocity between Twin A and himself increases, he will experience the feeling of being pulled to the back of his ship. He can attribute this to two possibilities, either he is accelerating away from Twin A, or A uniform gravitational field has come into existance, and because he is firing his engines, he is standing still, and because twin A isn't, he is falling. In either case he will measure the following, Twin A's clock will run slow because of the combined effect of Increased velocity difference and the acceleration felt By B. both effects will increase as the velocity and distance increases. The engines cut out and B coasts for a time. during this period, he will measure A clock as running slow at a constant rate. After traveling a distance (this distance depends on the relative velocity between A and B. I.E. if it is .866c, then due to length contraction, the 10ly measured by A will only measure 5ly for B) B fires his engines again, though this time in the opposite direction. Thus twin A's position wrt the force felt will be opposite of it was before. B's decreasing velocity wrt A will decrease the time slowing effect he measures. The fact that he is accelerating towards Twin A will cause him to measure Twin A's clock as running faster. Because The distance between A and B are much greater now, this speed up will over shadow the slow down effect effect due to relative velocity. B will measure A's clock as running consideralby faster. This will continue after B comes to a stop and accelerates back towards A. Coasting again, and A's clock is once again seen as running slow. Braking, and A's clock runs slow due to both effects. (though the acceleration effect is small because the distance between A and B is small.) After B comes to a stop he notes that more time has accrued on A's clock and A is older. (The period he measured clock A as moving fast more than compensate for the periods it ran slow) Twin A aged more becuase his clock ran Slow, very fast, and then slow again with the very fast perod predominating. Thus both twins agree as to who is younger, and by how much, but do not agree as to how this came to be. And there is no way to choose one Twin's interpretaton of events over the other's. Each are equally valid and "Real". Which one you use depends on whether you are twin A or Twin B. This is what is meant by "Time is Relative". There is no universal "real" time rate that is modifyed by velocity. There are only the relative time rates measured from within frames, and which one is "real" depends upon which frame you work from. All that is required is that clocks that are separated into different frames agree as to their respective time differences when brought back into the same frame again. (they don't have to agree as to how the difference came about. )

First off, It would be extremely difficult to naturally get a world 1/2 the size of Earth with the same surface gravity. For this to happen the world would have to have an average density 2 times that of the Earth's (5520 kg/m³). We have an iron core now and iron has a density of 7874 kg/m³, about 42% greater than Earth average. (at the core this density increases due to pressure) The planet would have to have a average density of about 11040 kg/m³ This is only slighty less than that of Lead at 11340 kg/m³, So unless you have a planet that is mostly core, lead won't do it. Mercury, at 13456 kg/m³ is about 22% percent denser than the needed average density, so you would still need a somewhat larger core. Tungsten has a density if 19300 kg/m³, 75% more than the average density needed, which means you could get away with a somewhat smaller core. Osmium, at 22610 kg/m³ is a little over twice the needed density, so you could get away with even a smaller core. The problem is that one is unlikely to find these heavy metals in high enough concentrations to produce the cores of planets. Also, having an heavy metal core would lead to the fact of the planet being rich in heavy metals in its crust. Heavy metals tend to be toxic, which would most likely prevent life from forming. Another thing to consider: While the surface gravity would be the same, the Escape velocity wouldn't. The volume of the planet would be 1/8 of Earth's, and even with 2 times the density, its mass would be 1/4. its radius would be 1/2, so using the formula for escape velocity: v=sqrt(2GM/r) It turns out that the escape velocity would be about only 70% that of Earth's. This, in turn, effects how well the planet can hold on to its atmosphere. So, all other things being equal, it should also have a thinner atmosphere.