# The Naked Scientists Forum

### Author Topic: What is the relationship between mass and speed?  (Read 3771 times)

#### thedoc

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##### What is the relationship between mass and speed?
« on: 30/07/2015 03:50:03 »
Siviwe Sva Waqu asked the Naked Scientists:

What would be the one thing that would have the greatest mass in the universe? What is the relationship between mass and speed? Would this then make light the heaviest as it is the fastest?
What do you think?
« Last Edit: 30/07/2015 03:50:03 by _system »

#### PmbPhy

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##### Re: What is the relationship between mass and speed?
« Reply #1 on: 30/07/2015 13:23:32 »
Quote from: thedoc
What would be the one thing that would have the greatest mass in the universe?
There's no such object. The most massive objects in the universe seem to be black holes but there is no upper limit on the size of a black hole.

Quote from: thedoc
What is the relationship between mass and speed?
There is none. Mass is a kinematic quantity and speed is a dynamic quantity. Thus one has no dependence on the other.

Quote from: thedoc
Would this then make light the heaviest as it is the fastest?
No.

#### alancalverd

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##### Re: What is the relationship between mass and speed?
« Reply #2 on: 30/07/2015 16:55:05 »
The heaviest object in the universe is the universe itself.

#### PmbPhy

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##### Re: What is the relationship between mass and speed?
« Reply #3 on: 30/07/2015 17:59:14 »
The heaviest object in the universe is the universe itself.
The reason I didn't say that is because there's no practical way to observe that property. It's not as if you can measure the momentum of the universe and determine its inertial mass like that. And you can't set a object in orbit of the universe and use the period and distance to measure its gravitational mass.

#### alancalverd

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##### Re: What is the relationship between mass and speed?
« Reply #4 on: 31/07/2015 14:32:22 »
Fact is that we have no means of measuring mass, only of comparing masses. However, just for fun, let's consider

m = m0/√(1 - v2/c2)

which may be familiar.

We know that distant bodies in the universe are retreating from us, and thus us from them, at an accelerating rate.

Now consider planet X with an orbiting moon, rushing away from us at a finite and increasing v. Since the mass of both planet and moon will be increasing, so will their mutual gravitational force. Describe the change in the moon's orbit. Note that "from the viewpoint of a stationary observer on earth" is irrelevant: if you are standing on X, is the moon getting closer or further away?

#### PmbPhy

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##### Re: What is the relationship between mass and speed?
« Reply #5 on: 01/08/2015 04:49:49 »
Quote from: alancalverd
Fact is that we have no means of measuring mass, only of comparing masses.
I disagree. We only need a way to determine what one unit of mass is. Currently it's defined by comparing it to a platinum bar that is kept . Now its determined by using the constants of nature. See: https://en.wikipedia.org/wiki/Kilogram
Quote
The kilogram is the only SI base unit with an SI prefix ("kilo", symbol "k") as part of its name. It is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units in the SI system are defined relative to the kilogram, so its stability is important. ... The 118-year-old cylinder that is the international prototype for the metric mass, kept tightly under lock and key outside Paris, is mysteriously losing weight — if ever so slightly".
I suppose its because of this last comment that there is a proposition to change it to be defined in terms of the fundamental constants of nature. However we can certainly measure the mass of an object without having that bar or a copy of it where we take the measurements. For example; place a charged particle in a cyclotron and measure the speed v and the radius of the circle R in which the particle moves and you can determine the mass of the object from that and the magnitude of the magnetic field. See:
http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

The relationship is  p = qBR = mv
Quote from: alancalverd
However, just for fun, let's consider

m = m0/√(1 - v2/c2)

which may be familiar.
Certainly. Especially to me.  [^] But what does this have to do with your argument below?

Quote from: alancalverd
We know that distant bodies in the universe are retreating from us, and thus us from them, at an accelerating rate.
Are you referring to the accelerating expansion of the universe?

Quote from: alancalverd
Now consider planet X with an orbiting moon, rushing away from us at a finite and increasing v.
Since you refer to "us" it means that you're referring to a particular frame of reference. However you haven't made it clear at this point what that frame of reference is. Would you mind stating it for us, please? Thank you.

If by "us" you mean that those observers who are standing on the planet then why is the moon rushing away from us at a finite and increasing v. That's not possible for a moon in orbit of a planet when the only force acting on the moon is the gravitational field of the planet. I.e. since the definition of moon is a large round object like the moon that circles around a planet then the total energy of the moon is less than zero (where the zero of the gravitational potential is taken to be at infinity) the motion of the moon  must be in an ellipse with a circular orbit being a special case of an elliptical orbit. Why are you phrasing this motion as rushing away from us at a finite and increasing v since when the moon is moving away its speed is decreasing in order for the total energy to be conserved, i.e. when moving away from the planet the gravitational field of the planet does a negative amount of work on the moon thus reducing the kinetic energy and therefore reducing its speed.

Quote from: alancalverd
Since the mass of both planet and moon will be increasing, so will their mutual gravitational force. Describe the change in the moon's orbit.
Why is the mass of the planet increasing? From what frame of reference are you making these observations from?

Besides, that's a rather complicated problem in general relativity. I haven't worked with those kinds of problems in a few years. Do you really need me to do that or is this simply a rhetorical question?

Quote from: alancalverd
Note that "from the viewpoint of a stationary observer on earth" is irrelevant: if you are standing on X, is the moon getting closer or further away?
That depends on the kind of orbit its in. Is it moving in an elliptical orbit or a circular orbit.

#### Thebox

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##### Re: What is the relationship between mass and speed?
« Reply #6 on: 01/08/2015 09:26:25 »
The heaviest object in the universe is the universe itself.

No  its not, heavy is simply the result of the force of gravity, nothing is ''heavy'' in the entire universe.  Heavy is a result of an objects mass attracted to another mass. On earth the speed relationship is 9.81m/s2, motion is gravity based, the speed of an orbit is relative to mass and centripetal acceleration.
« Last Edit: 01/08/2015 09:29:01 by Thebox »

#### alancalverd

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##### Re: What is the relationship between mass and speed?
« Reply #7 on: 01/08/2015 09:46:18 »
Peter: By "us" I mean you and me standing on Earth, and observing planet X moving away from us at a considerable speed and distance.

It's a rhetorical question for the time being but if you have any ideas about the solution, I'd be interested in them. For simplicity we can assume a circular orbit.

I don't think we need to consider the small change of velocity when the moon M of X approaches us or recedes - it's all a very long way away and X is receding very fast compared with the orbital velocity of M.

I'm not going to lose any sleep over this, but it would make an interesting interview question!

#### Thebox

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##### Re: What is the relationship between mass and speed?
« Reply #8 on: 01/08/2015 10:15:43 »
Peter: By "us" I mean you and me standing on Earth, and observing planet X moving away from us at a considerable speed and distance.

It's a rhetorical question for the time being but if you have any ideas about the solution, I'd be interested in them. For simplicity we can assume a circular orbit.

I don't think we need to consider the small change of velocity when the moon M of X approaches us or recedes - it's all a very long way away and X is receding very fast compared with the orbital velocity of M.

I'm not going to lose any sleep over this, but it would make an interesting interview question!

If there were a planet x and planet x orbited our solar system, and planet x was at a radius beyond the suns intensity to reflect light off matter to allow us to see planet x, planet x simply may be observed always in shadow, a shadow not like blocked light, but shadow where the suns rays decline and distance in intensity and strength, and simply not enough strength to reflect sufficient light to see planet x.

Where as if you maybe you was on the outer universe looking in, you may see planet x from the daylight side.

Behind the moon looking at the earth you would see a black circle of the moon.
« Last Edit: 01/08/2015 10:45:28 by Thebox »

#### jeffreyH

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##### Re: What is the relationship between mass and speed?
« Reply #9 on: 01/08/2015 19:13:10 »
Planet X may be receding at an accelerating rate but consideration should be taken of the effect of dark energy. If space is simply expanding because of this dark energy then it could be likened to frame dragging. It may be that there is no increase in relativistic mass at all in the reference frame of planet X. Light speed comes into this problem to prohibit information transfer once expansion exceeds the light speed barrier. The frame of planet X cannot be considered superluminal at any point on its worldline.
« Last Edit: 01/08/2015 19:14:50 by jeffreyH »

#### The Naked Scientists Forum

##### Re: What is the relationship between mass and speed?
« Reply #9 on: 01/08/2015 19:13:10 »