Light speed

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Jzz

E = m x c^2 (c^2 = c . . . squaring)
F = m x a

Einstein wasn't the first. He was just the first to see some things in a different light (pardon the pun).
Yes, of course and also: K.E = 1/2 mv^2

Starcrow

, ... so it turns out that there's this nice concatenation of equations that leads to the one everybody is acquainted with, & all Albert E. did was take one last step. He got a free ride all the way over to the inevitable outcome. Since there's no free lunch, according to the economists, we must make him pay for his deceit.

Let's start by quoting Tesla, the Master of Practicality: "Today's scientists have replaced experiments with mathematics, & they wander off through equation after equation & eventually build a structure that has no relation to reality. " (Modern Mechanics & Inventions, 1934)

Numbers can go only so far when trying to describe reality. They're a dead-end street. Beyond that lies Ultimate Reality, unknowable in our present state of development.

Now, quoting Jzz: "The equation E = mc^2 normally refers to rest mass (...)." The word "normally" there means there's a version of the equation that most people have never & will never see. It has a factor represented by the letter lambda added on the right side in order to deal with movement.

Blame lazy, ignorant journalists for a benighted public. They're merely scribblers who dislike reading & learning to go beyond their high school physics.

This comment already starts to look like a treatise. There's no going back to the speed of this or that.

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Atlan0101

Yes, of course and also: K.E = 1/2 mv^2
You need to first lock it into a rest frame for that one, right? General universe-wise, the velocity is always relative, thus variable, unless 'v' = 'c'. Otherwise 'v' = '0', general universe-wise. The two I state need no environmental, no specified, rest frame, right? Unless I miss my guess, the one you state fits nicely only as long as you (rest) frame it.

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Jzz

My observation. ASC opens the door that immense starlight-travel-times to Earth are not a fact. My telescope observations of M31 in Andromeda, the starlight does not need to take millions of years to reach my telescopes today Other groups are researching ASC and its implications in astronomy too.
The present speed of the Voyager 1 space craft as it zooms through interstellar space is a staggering 62000 kmh approx. Yet at this speed it would still take 16.6 million years to travel the distance of just a single light year!

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Helio

The present speed of the Voyager 1 space craft as it zooms through interstellar space is a staggering 62000 kmh approx. Yet at this speed it would still take 16.6 million years to travel the distance of just a single light year!
Did you mean 16.6 thousand years?

Jzz

Did you mean 16.6 thousand years?
One light year is approx. 9.4 x 10^12 km or 9.4 x 10^15 m . Speed of Voyager 1 space craft is 60000 kmh or 16600s not 16.6 m. So everything decreased by a thousand so 16 600 years is closer to the mark. It is still a long time. I should add my thanks to helio for setting me right.

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Helio

Helio

One light year is approx. 9.4 x 10^12 km or 9.4 x 10^15 m . Speed of Voyager 1 space craft is 60000 kmh or 16600s not 16.6 m. So everything decreased by a thousand so 16 600 years is closer to the mark. It is still a long time.
9.4E12/62000kph = 151,613,000 hours.

151,613,000/24= 6,310,000 days

6,310,000/365 = ~ 17,000 years

Jzz

billslugg

I've been off by a factor of 1,000 at least a million times.

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Pogo

Helio

I've been off by a factor of 1,000 at least a million times.

I may be the record, according to one physicist. I thought the 10^120 difference from quantum physicists was attributable to expansion, but that factor is opposite that, so I said how much I hate being off by by 10^240!! (Yes, this last no. was meant as math hyperbole. )

Pogo and billslugg

Jzz

I've been off by a factor of 1,000 at least a million times.
What is really exasperating is that I knew that the answer was that it would take around 60,000 years for Voyager 1 to reach the nearest star, yet I still went ahead and posted the ridiculous figure of 16,666,000 million years to cover a distance of one light year. Leaving this gaffe aside this means that, even after travelling a distance of one light year Voyager will still have to cover a further 3 light years making a total of 4 light years, which will take 17,000 x 4 = 68,000 years to reach Proxima Centauri!

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Jzz

I may be the record, according to one physicist. I thought the 10^120 difference from quantum physicists was attributable to expansion, but that factor is opposite that, so I said how much I hate being off by by 10^240!! (Yes, this last no. was meant as math hyperbole. )
Impressive!

Helio

The times to stars isn’t too hard to calculate somewhat accurately even though they are moving about the speed of our current rockets. Too often I see erroneous estimates for travel time because, say for Alpha Cen, their use of 4.3 lyrs as the distance is held constant, failing to note that Alpha Cen will get to a little over only 3 lyrs in about 15,000 years, IIRC.

Get the dec. and ra velocity vector sum, then get the stated radial velocity and you now have the object‘s motion (vector) relative to Earth.

But the trick, IMO, is to recognize that the y-components of both the star and the intersecting ship must match, else no intersection. I stumbled into a shooter’s video game article on their use of this trick.

Once the y-vector component is known then the ship’s x-component is found, and hence the net ship velocity for any desired intersection point. For minimum distance, make the intersection to be at 90 deg, giving us a right triangle, and easy math.

Jzz

The times to stars isn’t too hard to calculate somewhat accurately even though they are moving about the speed of our current rockets. Too often I see erroneous estimates for travel time because, say for Alpha Cen, their use of 4.3 lyrs as the distance is held constant, failing to note that Alpha Cen will get to a little over only 3 lyrs in about 15,000 years, IIRC.
The only problem is the 67,000 odd years it will take to get there. It is a difficult number to get around. After all how many people live to be a hundred? Not many. In any case I doubt if a hundred year old will be of any use in space or anywhere else. They are more less figureheads or totem pole like figures, their contribution must necessarily be minimal. Roughly 5000 years since the great pyramids of Egypt were built , yet that 5000 years encompasses almost the whole of civilised humanity.

Helio

Helio

Yes, but it’s remarkable that we have the technology today to build probes capable of arriving our neighbor in only ~21 years by reaching a 0.2c speed. SR grants fun science fiction, but sometimes fiction slips out of the bonds of fantasy, and into reality.

Jzz

Yes, but it’s remarkable that we have the technology today to build probes capable of arriving our neighbor in only ~21 years by reaching a 0.2c speed. SR grants fun science fiction, but sometimes fiction slips out of the bonds of fantasy, and into reality.
Probes yes, but manned vehicles? It is a pretty sure thing that in the not too far future the realisation will arise that it is probes that will lead the way. In fact your estimate of 0.2 c might be conservative, if enough thought were given to the subject. A continuous thrust of 1g should result, over the course of two or three months, in a significant percentage of the speed of light. With no need to worry about life support systems, and the resultant weight reduction, such a scenario might become possible with unmanned probes.