Saying it operated in the vacuum of space. is there a speed limit to
how fast an electromagnetic repulsion accelerator can launch an
object? Naturally, there is the speed of light barrier, but I don't
think that's possible ... or is it?
And whatever speed limit such an accelerator had, could it be reached
if the accelerator was 60,000 miles long? If so, what would the rate
of acceleration from a standing start to achieving that speed at the
end of the 60,000 miles? If 60,000 miles wouldn't be enough to
accelerate an object to that speed limit, how fast could it get at the
end of a 60,000mile run?
Thanks in advance!
Scott
Dear STJensen:
A function of the amount of energy you can deliver, how you plan
to dissipate excess heat, and how much mass you want to boost.
No.
The longer it is, the more trouble it is. The longer it is the
lower acceleration you can have, and still get a good speed.
42.
No limit. No secret number. The more engineering you put into
it, the more you get out.
David A. Smith
There have been accelerators that reach speeds of a high fraction
of c for about fifty years. They use a circular track to allow
compact electromagnets. The particles involved are usually
very light  protons etc.
Sychrotrons, cyclotrons etc.
Brian Whatcott Altus OK
The absolute speed limit is c (the speed of light). This has
been experimentally verified in all high energy accelerators.
You could add all the energy you wish to the object in
your accelerator, it still would not reach c. Get near to
it but not reach it.
You can use the special relativity equations to verify it
if you know how, or if not, I can give you an equivalent
equation very easy to use that will show you.
Andr=E9 Michaud
 Saying it operated in the vacuum of space. is there a speed limit to
 how fast an electromagnetic repulsion accelerator can launch an
 object?
Let's put it this way. How fast can a gun fire a bullet?
Let's assume the bullet leaves the gun at 1000 m/s.
The gun will recoil.
If the gun's mass is 1 kg and the bullet's mass is 1gram,
how fast does the gun go backwards?
Momentum is conserved, mV + Mv = 0
So, (1 * 1000) + (1000 * 1) = 0, the gun goes backwards at 1 m/s.
BUT! If the gun is going backwards at 1m/s then the bullet
can only be going forwards at 999 m/s. Why is that?
And what if the gun was already moving backwards at 999 m/s
when it fired? Or moving forwards at 1000 m/s?
In the vacuum of space what do these numbers mean anyway?
 Naturally, there is the speed of light barrier, but I don't
 think that's possible ... or is it?
There is no "speed of light barrier".
What we DO have is a limit to how fast the electromagnetic field
that is propelling the projectile can leave the gun.
If the projectile leaves the gun at 300,000,000 m/s and
the gun is moving (relative to what?) at 1000 m/s then
the projectile is travelling at 300,001,000 m/s.
ALL motion is relative.
Do not let cranks tell you the speed of light is... without
say"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity cv"
Ref:
formatting link
 And whatever speed limit such an accelerator had, could it be reached
 if the accelerator was 60,000 miles long? If so, what would the rate
 of acceleration from a standing start to achieving that speed at the
 end of the 60,000 miles? If 60,000 miles wouldn't be enough to
 accelerate an object to that speed limit, how fast could it get at the
 end of a 60,000mile run?

 Thanks in advance!
A baseball cannot exceed the speed of the arm that threw it.
Even if the pitcher runs forward (as a bowler in cricket does), the
speed of the ball leaving the arm is still the speed of the arm.
The speed of the ball arriving at the bat changes, all speed is
relative.
Therefore in the vacuum of space, move the accelerator,
making it longer will not help.
You don't seem to have gotten a completely straight answer,
so I'll throw my $.02 in.
No. But you could get so close to c that it would be hard
to measure the difference. The thing about the relativistic speed
limit is that it takes more and more energy as you approach
c. It makes more sense to talk about your energy, or your
relativistic "gamma" factor, than it does to talk about speed
for objects very close to c.
Thus, there are accelerators with gamma factors of 100, and
others with gamma = 1000. In both cases the velocity is just
a tiny bit different from c, but the energy of a particle with
gamma = 1000 is 10 times the energy of the same particle
with gamma = 100, and it has 10 times the momentum
also.
You can never reach v = c (gamma>oo as v>c), but there's
no limit to high gamma can be. An incredibly highenergy
particle detected a few years ago, nicknamed the "Ohmy
god particle", had a gamma somewhere in the neighborhood
of 10^20 as I recall. But still a speed v < c.
You could use work = Force * distance to figure out how
much energy you could get on such an accelerator.
Let's say you can accelerate a mass of 1 kg at 1000 g's,
i.e. you can exert a force of 9800 N on that mass. Then
over 60000 miles (96500 km) you would give the mass
9800 N * 96,500,000 m = 9.46*10^11 J.
But actually, this isn't a relativistic speed. Let's check it
with the Newtonian formula, which is OK at low speeds:
KE = 0.5*mv^2
v = sqrt(2*9.46*10^11/m) = 1.38 *10^6 m/sec, or about
0.0046 c.
That gives a gamma of 1/sqrt(1  v^2/c^2) = 1.00001
Not a sensible question since you can't achieve c.
How about "what acceleration would be required
to reach a gamma of 1000 at the end of the 60000
miles?"
So we want an energy of 1000*mc^2 = 9*10^19 J
over 96500 km, which means the force should be
9.326*10^11 N, or the (initial) acceleration should be
9.326*10^11 m/sec^2 (95 billion g's).
At that acceleration, it would reach half the speed
of light in 0.16 milliseconds, at which point it has already
traveled 121 km.
 Randy
 > Saying it operated in the vacuum of space. is there a speed limit to
 > how fast an electromagnetic repulsion accelerator can launch an
 > object?

 You don't seem to have gotten a completely straight answer,
 so I'll throw my $.02 in.

 > Naturally, there is the speed of light barrier, but I don't
 > think that's possible ... or is it?

 No. But you could get so close to c
Relative to what?
that it would be hard
 to measure the difference. The thing about the relativistic speed
 limit is that it takes more and more energy as you approach
 c.
Relative to what?
It makes more sense to talk about your energy, or your
 relativistic "gamma" factor, than it does to talk about speed
 for objects very close to c.
Relative to what?

 Thus, there are accelerators with gamma factors of 100, and
 others with gamma = 1000. In both cases the velocity is just
 a tiny bit different from c,
Relative to what?
 but the energy of a particle with
 gamma = 1000 is 10 times the energy of the same particle
 with gamma = 100, and it has 10 times the momentum
 also.

 You can never reach v = c
Relative to what?
(gamma>oo as v>c
Relative to what?
), but there's
 no limit to high gamma can be. An incredibly highenergy
 particle detected a few years ago, nicknamed the "Ohmy
 god particle", had a gamma somewhere in the neighborhood
 of 10^20 as I recall. But still a speed v < c.
Relative to what?

 > And whatever speed limit such an accelerator had, could it be reached
 > if the accelerator was 60,000 miles long?

 You could use work = Force * distance to figure out how
 much energy you could get on such an accelerator.

 Let's say you can accelerate a mass of 1 kg at 1000 g's,
 i.e. you can exert a force of 9800 N on that mass. Then
 over 60000 miles (96500 km) you would give the mass
 9800 N * 96,500,000 m = 9.46*10^11 J.

 But actually, this isn't a relativistic speed. Let's check it
 with the Newtonian formula, which is OK at low speeds:
 KE = 0.5*mv^2

 v = sqrt(2*9.46*10^11/m) = 1.38 *10^6 m/sec, or about
 0.0046 c.
Relative to what?

 That gives a gamma of 1/sqrt(1  v^2/c^2) = 1.00001
Relative to what?
 > If so, what would the rate
 > of acceleration from a standing start to achieving that speed at the
 > end of the 60,000 miles?

 Not a sensible question since you can't achieve c.
Relative to what?
Not a sensible answer,
"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity cv".  Einstein.
Cosmic rays (and the GreisenZatsepinKuzmin, GZK, limit). Protons
with 6x10^19 eV enegy are routinely observed, and that is the energy
of a wellthrown baseball. If you have the budget you can impart an
arbitrarily large energy to a body. Special Relativity then tells you
how fast it will appear to travel.
A .357 magnum handgun pulls 50,000 gravities as a bullet rides down
its barrel going from zero to 1100+ feet/second in 4.5 inches. If you
extend that barrel to a lightyear length footnotes will intrude.
A lot sooner than that  (in Newtonian mechanics) at 50,000 g (500
km/s^2) it takes 600 seconds to reach the speed of light, implying a
barrel 90 million km long  less than the length of a Golden Ship, iirc.
 Peter Fairbrother
Just a note. Cyclotrons were abandoned early in the 1940's
precisely because they couldn't get particles anywhere near
c, due to their dependence on mass remaining constant.
They then switched for circular track accelerators to the
betatron and then to the various flavors of synchrotron.
Andr=E9 Michaud
Of course you never rad my proof by wave mekanics thas a mote can
reach celerity with finite energy. Hmm, the term I was a'looking for
was coherential length, which becomes positive at .5c and above.
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