View Full Version : what is the max velocity that a star can accelerate another object to?

tommac

2010-Mar-24, 11:17 PM

if I have an empty, flat, non-expanding universe with only a star and a rock in it.

Is there a max velocity to which the star can accelerate the rock to, given an infinite amount of time?

Gravitationally, given any initial conditions you want? Yes - the star's escape velocity (as measured at the surface of the star).

tommac

2010-Mar-24, 11:57 PM

Gravitationally, given any initial conditions you want? Yes - the star's escape velocity (as measured at the surface of the star).

Sorry for such a simple question but how can that be derived?

Senor Molinero

2010-Mar-25, 12:20 AM

Escape velocity equation is

v = SQR(2.G.M/r)

G = gravitational constant

M = mass of star (or planet)

r = radius of star (or planet)

swampyankee

2010-Mar-25, 12:22 AM

Sorry for such a simple question but how can that be derived?

Just integrate F from infinity to the surface. This will give you the amount of kinetic energy the rock will acquire in its fall.

noncryptic

2010-Mar-25, 12:37 AM

It's a good thing you gave it an infinite amount of time.

mugaliens

2010-Mar-25, 08:57 AM

Gravitationally, given any initial conditions you want? Yes - the star's escape velocity (as measured at the surface of the star).

Relativisticaly speaking, not quite, and it's a touch more complicated:

if I have an empty, flat, non-expanding universe with only a star and a rock in it.

Is there a max velocity to which the star can accelerate the rock to, given an infinite amount of time?

Assuming the star is one that collapses into a black hole, and the "rock" is a single subatomic particle of the least mass, and at near-infinite distance, but not so far that the BH radiates itself away before the particle arrives, then the maximum velocity will be the slightest bit less than c.

tommac

2010-Mar-25, 03:38 PM

The reason I am asking this question was to build an analogy , a reverse analogy, of how negative mass would be able to accelerate away a smaller mass to near light speed, given an infinite amount of time. The thought experiment I was trying to figure out is if I sent a particle at a speed near the speed of light directed to some negative mass that if there was enough negative mass there would be perfect reflection of the object with 100% conservation of momentum so that it would be pushed back away from the negative mass at near the speed of light. But then it would continue to accelerate infinitely, although by quickly decreasing increments to speeds that would continuously approach the speed of light.

The difference between the the negative mass push and the positive mass pull, is that the pull ultimately would crash into the source of the gravity. However we can simulate this by starting the object infinitely far apart from the attracting mass.

Trakar

2010-Mar-25, 10:49 PM

if I have an empty, flat, non-expanding universe with only a star and a rock in it.

Is there a max velocity to which the star can accelerate the rock to, given an infinite amount of time?

Can I shape and intelligently guide the rock, and specify stellar type and initial conditions, to optimize results?

Nothing like power-surfing S. Doradus!

Seriously, I wonder if there might not be more to gain from a near approach transit with a variable aspect geometry that allowed for something like a "plate on edge" presentation until peridoradus, and then shifting to reflect maximum incident radiations. If you could coincide your exit vector along the poles you might even gain a bit more by being able to strongly interact with the doradiar magnetic field perhaps by using a dual purpose fiber mesh instead of a solid continuous surface geometry.

just some random stream thoughts, sorry to intrude.

Trakar

2010-Mar-25, 10:52 PM

The reason I am asking this question was to build an analogy , a reverse analogy, of how negative mass would be able to accelerate away a smaller mass to near light speed, given an infinite amount of time. The thought experiment I was trying to figure out is if I sent a particle at a speed near the speed of light directed to some negative mass that if there was enough negative mass there would be perfect reflection of the object with 100% conservation of momentum so that it would be pushed back away from the negative mass at near the speed of light. But then it would continue to accelerate infinitely, although by quickly decreasing increments to speeds that would continuously approach the speed of light.

The difference between the the negative mass push and the positive mass pull, is that the pull ultimately would crash into the source of the gravity. However we can simulate this by starting the object infinitely far apart from the attracting mass.

As long as the balance is equal, you are visualizing it appropriately.

Relativisticaly speaking, not quite, and it's a touch more complicated:

I was assuming that the star was a star, not a stellar remnant, and therefore the escape velocity at the surface would be only a tiny fraction of c. As far as I know, there is no star which has an escape velocity anywhere near c, so you don't need to be concerned with the relativistic effects. If the gravitating object is a stellar remnant with extremely intense surface gravity, such as a neutron star or black hole, then you're right - it is more complicated (and I'm not sure of the exact details).

TrAI

2010-Mar-27, 05:36 AM

The reason I am asking this question was to build an analogy , a reverse analogy, of how negative mass would be able to accelerate away a smaller mass to near light speed, given an infinite amount of time. The thought experiment I was trying to figure out is if I sent a particle at a speed near the speed of light directed to some negative mass that if there was enough negative mass there would be perfect reflection of the object with 100% conservation of momentum so that it would be pushed back away from the negative mass at near the speed of light. But then it would continue to accelerate infinitely, although by quickly decreasing increments to speeds that would continuously approach the speed of light.

The difference between the the negative mass push and the positive mass pull, is that the pull ultimately would crash into the source of the gravity. However we can simulate this by starting the object infinitely far apart from the attracting mass.

Negative mass is wierd, I was thinking about how gravity would behave inside a ball of negative mass, if it would be possible to create a black hole from the outside, as it were, but it just flew appart, the silly stuff has negative inertia, and moves away from something that attracts it. :doh:

Oh, If you finaly get the stuff to stick together, and introduce a piece of positive mass beside it, then things become even more silly, both of them sail of happily in the same direction at an accelerating speed, like in the diametric drive (http://en.wikipedia.org/wiki/Breakthrough_Propulsion_Physics_Program#Diametric_ drive)...:wall:

Of course, if you could make the stuff, you would gain energy while doing so, as it is made from negative energy...

astromark

2010-Mar-27, 06:34 AM

No gentlemen... NO. The understanding that negative mass would repel is wrong.

Mass has the property of space distortion. All objects of any mass have that property. There are no exceptions. Dark mater has gravity, Positively charged. Negatively charged and dropping the word charged of there does not change it. Negative mass has gravity. The only known force that is driving the eccelorating expansion of the whole universe is and has been named as Dark Energy. I do not know what that is... and nor do you.

astromark

2010-Mar-27, 06:43 AM

I suspect that the repulse force being touched upon here is a magnetic charge force. As in a solar flare and resulting plasma ejection. Magnetic forces can eject at great velocity. , but has no part of gravity force. ejection. rejection...:o:

astromark

2010-Mar-27, 07:55 AM

And thinking a little more ( a new experience )..:)and allowing for this repulse idea of Tommac's. I still find NO. because as the repulse force would diminish with distance just as gravity does... the acceleration force would be week. Now as an aside the question I see arising here is... What is the highest velocity recorded for a body of mass.?

A nova event might accelerate mater to what velocity ?

TrAI

2010-Mar-27, 09:04 AM

No gentlemen... NO. The understanding that negative mass would repel is wrong.

Mass has the property of space distortion. All objects of any mass have that property. There are no exceptions. Dark mater has gravity, Positively charged. Negatively charged and dropping the word charged of there does not change it. Negative mass has gravity. The only known force that is driving the eccelorating expansion of the whole universe is and has been named as Dark Energy. I do not know what that is... and nor do you.

Negative mass is a exotic material that is pretty much defined by the matematical calculiations for mass being used on negative numbers, it is purly hypotetical, if it existed it would have the opposite warping effect on space-time from ordinary mass. It has nothing to do with the charge of the stuff.

And thinking a little more ( a new experience )..:)and allowing for this repulse idea of Tommac's. I still find NO. because as the repulse force would diminish with distance just as gravity does... the acceleration force would be week. Now as an aside the question I see arising here is... What is the highest velocity recorded for a body of mass.?

A nova event might accelerate mater to what velocity ?

I think the premise is that you have a sandbox space, where only the forces created by the material you name apply. Gravity does have an infinite extent, you know, though there may be a limit to how far you could detect it, there is no place in space completely void of gravity.

tommac

2010-Mar-28, 12:06 AM

negative mass would repel ... it would have a negative curvature of space ... however it could be attracted by regular mass if the regular mass is greater than the negative.

No gentlemen... NO. The understanding that negative mass would repel is wrong.

Mass has the property of space distortion. All objects of any mass have that property. There are no exceptions. Dark mater has gravity, Positively charged. Negatively charged and dropping the word charged of there does not change it. Negative mass has gravity. The only known force that is driving the eccelorating expansion of the whole universe is and has been named as Dark Energy. I do not know what that is... and nor do you.

tommac

2010-Mar-28, 12:08 AM

And thinking a little more ( a new experience )..:)and allowing for this repulse idea of Tommac's. I still find NO. because as the repulse force would diminish with distance just as gravity does... the acceleration force would be week. Now as an aside the question I see arising here is... What is the highest velocity recorded for a body of mass.?

A nova event might accelerate mater to what velocity ?

it would be weak ... but infinite ... acceleration for all time even if it is minute.

tommac

2010-Mar-28, 12:28 AM

I suspect that the repulse force being touched upon here is a magnetic charge force. As in a solar flare and resulting plasma ejection. Magnetic forces can eject at great velocity. , but has no part of gravity force. ejection. rejection...:o:

No it is GR negatively curved space.

neilzero

2010-Mar-28, 08:48 PM

Infinite time confuses the issue, as there may be no main sequence stars 100 trillion years from now. G and F class star, likely can not sling shot an object faster than 186 miles per second = 0.1% of c, even with many repeated sling shot maneuvers. Worse, random close approaches are as likely to slow the rock as accelerate it. According to a post on another thread, the speed of the star (or even a compact star) in it's orbit around the galaxy limits the maximum speed gain (except close to the star) but perhaps that is incorrect? If sling shot maneuvers usually add, then there should be lots of 10% c (and faster) rocks en-route between the galaxies after 13.7 billion years. Neil

tommac

2010-Mar-29, 02:11 AM

There is only 1 star ... and the particle.

pull the particle to whatever distance you want away from the star, I do think it works out to be the escape velocity ... or at least that is what make the most sense to me.

Infinite time confuses the issue, as there may be no main sequence stars 100 trillion years from now. G and F class star, likely can not sling shot an object faster than 186 miles per second = 0.1% of c, even with many repeated sling shot maneuvers. Worse, random close approaches are as likely to slow the rock as accelerate it. According to a post on another thread, the speed of the star (or even a compact star) in it's orbit around the galaxy limits the maximum speed gain (except close to the star) but perhaps that is incorrect? If sling shot maneuvers usually add, then there should be lots of 10% c (and faster) rocks en-route between the galaxies after 13.7 billion years. Neil

WayneFrancis

2010-Mar-29, 05:31 AM

it would be weak ... but infinite ... acceleration for all time even if it is minute.

Tommac where you not the one that thought if there where looped dimensions that things would accelerate to infinity in those looped dimensions do to gravity?

If you are I'll remind you again what happens if not take this as your first lesson.

Even though gravity effects are infinite in distance this does not mean you get infinite acceleration. It just means the exact top speed is not computable. It will get to a certain basic speed then just basically increase in precision.

It is just an inverse square law and they don't go to infinity

tommac

2010-Mar-29, 07:24 PM

I was claiming infinite time ... not infinite force. As stated in one of the first replies, the answer to my question is the escape velocity of the star. This makes total sense to me, for some reason I didnt see that as being the limit ( although I did relalize that there was a non-infinite limit )

Tommac where you not the one that thought if there where looped dimensions that things would accelerate to infinity in those looped dimensions do to gravity?

If you are I'll remind you again what happens if not take this as your first lesson.

Even though gravity effects are infinite in distance this does not mean you get infinite acceleration. It just means the exact top speed is not computable. It will get to a certain basic speed then just basically increase in precision.

It is just an inverse square law and they don't go to infinity

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