Janus

C would see time at A as moving slow and at the same rate as B.

http://www.scienceforums.net/forums/showpost.php?p=217243&postcount=25

One of the best theories for the origin of the 7 day week that I know of is this: The Ancient Chaldeans named the hours of the day for the seven planets. (a planet at that time being any permanent celestrial body that moved through the Zodiac.) They ordered them by what they assumed were their distances from Earth according to the speed at which they moved through the Zodiac, from furthest to nearest. This gave them an order of Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. The sequence repeated three time each day with three days left over. (Thus if the day started with Saturn, it ended with Mars.) Each day would pick up where they left off. (If the last day ended with Mars, the next day started with Mercury.) Each day was named after the hour it started with, and they got a repeating pattern of 7 days in the order of: Saturn, Sun, Moon, Mars, Mercury, Jupiter, Venus. Over time, some of these names were exchanged for latin or saxon counterparts and thus we get: Saturday(Saturn's day) Sunday (Sun's day) Monday(Moon's day) Tuesday (Tui's(sp?) day) Wednesday (Wodin's days) Thursday (Thor's day) Friday (Freia's Day) Also somewhere along the line Sunday was shifted to the first day of the week (importance of the Sun?).

I'm going to take a stab at trying to interpret what you are trying to say here. I'll use an example of a ship passing the Earth at .99c (We will avoid moving at c, because no physical object can move at c.) Okay, let's say that this ship is moving towards a planet 7 light years away from the Earth as measured by form the Earth. Assume that the ship sets his clock to read zero the instant he passes the Earth. Now, according to Relativity, An observer on the Earth(or on our hypothetical planet) will determine that the clock on the ship will run slow by a factor of 7, and thus will read a little over 1 yr when it passes our planet. Now what I think you are asking is: Doesn't this mean that an observer riding on the ship will see himself travel 7 light years in a little over 1 year and thus see himself as traveling at almost 7c? The answer is no. And here is why: As far as the observer in the ship is concerned it is not him that is moving; It is the Earth and the Planet that is moving past him at .99c. Another thing that happens according to Relativity is that objects moving Relative to you will be measured by you as length contracted. Is this case, this means that the ship observer will measure the distance between Earth and the Planet as a only 1 ly. And since the relative speed between himself and these two planets is .99c, the time that passes on his clock between the time the Earth passes him and the planet passes him will be a little over 1yr. And thus he sees his velocity relative to the Earth as .99c, Just like the Earth sees their relative velocity as .99c.

As an example to waht Martin said: Arcturus has one of the largest proper motions of all the stars at 2.3'' a year. it is 36 ly away so in the time it take the light to reach here from there it will have moved 1' 22''. The Moon has an angular width of 30', so this means that Arcturus will have moved about 1/22 the width of the moon in the time it takes its light to get here.

You have to use a different formula for radii that lay inside the planet. No. As you hover at the center of the Earth you are at a lower gravitational potential than you are at the surface. (you would have to do work against Earth's gravity to reach the surface) Since gravitational time dilation is related to difference in potential, this means a clock hovering at the center of the Earth would run slower than one on the surface. You still get T<T'.

If you look at the formula for Gravitational time dilation I gave' date=' you will note that it is the standard SR time dilation formula with [imath']\sqrt{\frac{2GM}{r}}[/imath] in place of v. This is the formula for escape velocity. This is the initial velocity an object would have to have in order to reach an infinite distance from mass M when starting at radius R from its center. The gravitational time dilation formula is for an observer an infinite distance from mass M. Thus one way of looking at it is that the time dilation is related to the energy that has to be given up climbing from radius R to infinity. As long as this acceleration is wrt to the observer, yes. If, however, the observer is in the accelerated frame itself, then said observer will see time dilation effects akin to that of Gravitational time dilation. Clocks lying in the direction of the acceleration will be determined as running fast and clocks lying in the opposite direction will be determined as running slow. How slow or fast these clocks run is determined by the magnitude of the acceleration and the distance to these clocks from the observer. (as measured on a line parallel to the direction of the acceleration.)

To many names to keep them all straight:confused: No' date=' it is not. Gravitational time dilation is related to gravitational [i']potential[/i], not local strength of the field. The gravitational time dilation formula is:[math]T = \frac{T'}{\sqrt{1-\frac{2GM}{Rc^2}}}[/math] Where M is the mass of the planet and R is the distance from the center of the planet. Note that if both M and R increase by the same factor, that factor cancels out of the equation. On the other hand, the formula for acceleration due to gravity is: [math]a = \frac{GM}{R^2}[/math] If we increase the radius and mass by the same factor, the resulting acceleration decreases by that factor. No, there is not.

in terms of time dilation' date=' yes. According to your post, Zach is sitting at the North pole of Earth 3, so he wouldn't be moving at all wrt Bob, who is sitting at the North pole of Earth 1.

How do they end up feeling the same? Bob is traveling in a circle of Earth radius such that he feels 1g. Dave is traveling in the same circle around a planet of Earth mass, thus is essentially traveling at orbital speed and feels weightless. Perhaps you meant Bob and Frank? But even then, the local acceleration due to gravity or what you 'feel' locally does not determine what time dilation you will show. The interesting part is that Zach and Chuck will show equal time dilation.(Though Zach will feel half the g-force that Chuck does.)

Due to the way the problem was set up, I also assumed no equatorial bulge. (so that Bob, Dave and Frank all traveled in circles of equal radius. )

Archie shows no SR or Gravitional dilation Bob only shows SR dilation (even though he is accelerating, this acceleration adds no additional time dilation. Chuck shows only gravitational dilation, but it will be greater than the SR dilation shown by Bob. Dave shows the same gravitational dilation as Chuck and in addition the SR dilation of Bob. Edgar shows the only gravitational dilation but it is greater than the combined gravitational and SR dilation's shown by Dave. Frank shows the gravitaional dilation of Edgar in addition to the SR dilation shown by Bob and Dave. Gus shows only SR dilation due to his instantaneous speed at any given moment, but his average velocity will be high enough to show a greater time dilation than any of the others. On a side note, an interesting result occurs if Earth 2 has both twice the mass and twice the Radius as Earth 1

No, it is not. The equivalence of gravity and acceleration is due to the equality of 'gravitational' mass and 'inertial' mass(if I increase the gravitational mass of an object so that it attracts another mass more, I also increase its inertial mass and thus its resistance to acceleration, by the same factor). There is no such equality with magnetism. I can increase or decrease the magnetic field of an object without causing the same increase or decrease in its inertial mass and vice-versa. (I can increase the force of the magnetism of the object without increasing its resistance to acceleration.)

No more than I would count the fact that the movie Titanic accurately described many real events that took place on that ship as evidence that the characters of Rose and Jack actually existed in real life.

As pointed out time runs slow for you only as measured by someone who measures you as moving with respect to them. Now, from their standpoint it means that your clock will accumulate 1/5 of a year while you travel the distance from earth to Alpha Centauri (4.3 ly), while their clock accumulates 4.3 years. From your viewpoint, your clock will also accumulate 1/5 y, but not because your clock ran slow, but because, due to length contraction, you will measure the distance between Earth and Alpha Centauri as only being 1/5 ly, which you traveled at .999c

The Hubble has a resolution of .1 arc-secs.

It would take a telescope with an aperture of about 32,000 in. to resolve objects as small as 5 km on the surface of Pluto.

But you don't need to run into faster light waves to see a doppler effect any more that you need to run into faster sound waves to hear a doppler shift. If I'm standing on the train platform on a windless day and someone on the platform yells at me, the sound travels at the speed of sound in air towards me. If a train approaches and blows its whistle the instant it passes that person, the sound from it will travel at the same speed as the yell (they will both reach me at the same time). The train whistle will be doppler shifted however.