Mass-energy in an accelerated system

[geordief]

Suppose we have a body that is accelerated from point A to point B (and ,why not decelerated ,reaccellerated and returned to point A although this may not be necessary)

 

My understanding is that the body as a whole will lose mass in order to maintain the acceleration and eventually if the acceleration is continued there will eventually be nothing left.

 

I am wondering as to how this loss of mass is distributed through the body.

 

Is is evenly distributed so long as every part of the body is accelerated?

 

So ,if there is a timekeeping device on the body does this timekeeping device similarly lose mass and fade away to nothingness eventually?

[imatfaal]

Why would an accelerating body lose mass? Or are you thinking of a rocket burning fuel and throwing it behind to propel itself?

 

Rest mass will stay the same, kinetic energy as measured by an outside inertial frame observer will change, and velocity measured by same observer will change.

 

Remember that the moon is in orbit around the earth and thus accelerating all the time with no loss of mass, ditto earth/sun etc.

[Daecon]

I always thought that to accelerate meant to increase their speed (relative to their speed in the past). Orbiting bodies have a constant speed with no increase, don't they? It seems that I must be misunderstanding something somewhere, I think?

Edited August 4, 2016 by Daecon

[geordief]

Why would an accelerating body lose mass? Or are you thinking of a rocket burning fuel and throwing it behind to propel itself?

 

Rest mass will stay the same, kinetic energy as measured by an outside inertial frame observer will change, and velocity measured by same observer will change.

 

Remember that the moon is in orbit around the earth and thus accelerating all the time with no loss of mass, ditto earth/sun etc.

Thanks.

 

Yes the rocket idea was what set me off...

 

I will have to give it some more thought

[StringJunky]

I always thought that to accelerate meant to increase their speed (relative to their speed in the past). Orbiting bodies have a constant speed with no increase, don't they? It seems that I must be misunderstanding something somewhere, I think?

Acceleration is a vector quantity which means it has magnitude and direction values associated with it (two parameters); change the speed up or down, or change the direction, you change the acceleration. Acceleration in physics is not just an increase in speed as commonly used in daily life. It is not a scalar value where it has just a magnitude value or direction. (one parameter)

Edited August 4, 2016 by StringJunky

[Strange]

Acceleration is a vector quantity which means it has magnitude and direction values associated with it; change the speed up or down, or change the direction, you change the acceleration.

 

This makes sense because we know that force and acceleration are related (f=ma) and it takes a force to make something change direction (or, equivalently, you feel a force when, for example, you are in a car turning a corner).

[Daecon]

Ah, thank you. I was just reading the Wikipedia article on acceleration (I should get into the habit of doing that before asking questions) and you both explained it much more succinctly than Wikipedia did.

Edited August 4, 2016 by Daecon

[geordief]

In spacetime terms the moon is supposed to be following a straight line .Is there a way we can usefully define acceleration **(differently?) to mean that a body does not follow this straight (geodesic) straight line?

 

Will the body then lose mass?

 

**so not acceleration but perhaps a related concept

Edited August 4, 2016 by geordief

[swansont]

I always thought that to accelerate meant to increase their speed (relative to their speed in the past). Orbiting bodies have a constant speed with no increase, don't they? It seems that I must be misunderstanding something somewhere, I think?

 

 

Acceleration is the change in velocity per unit time. Anything that changes direction has changed velocity (it's a vector), and so has been accelerated.

[Strange]

In spacetime terms the moon is supposed to be following a straight line .Is there a way we can usefully define acceleration **(differently?) to mean that a body does not follow this straight (geodesic) straight line?

 

Will the body then lose mass?

 

**so not acceleration but perhaps a related concept

 

I think that is still acceleration. Because the moon is in free fall, it is not actually accelerating. For example, if you were in orbit or free fall, you would feel no forces acting on you, therefore you are not accelerating.

 

If you are not following that geodesic because, for example, you are standing on the surface of the Earth, then you do feel a force and (counterintuitively) you are accelerating - even though you are not moving!

 

I'm not sure where the weight loss idea comes into this ...

[geordief]

 

I think that is still acceleration. Because the moon is in free fall, it is not actually accelerating. For example, if you were in orbit or free fall, you would feel no forces acting on you, therefore you are not accelerating.

 

If you are not following that geodesic because, for example, you are standing on the surface of the Earth, then you do feel a force and (counterintuitively) you are accelerating - even though you are not moving!

 

I'm not sure where the weight loss idea comes into this ...

No , I am not sure either. Time dilation (orbiting systems) occurs without acceleration.

 

Does it also occur with acceleration (rocket propulsion) and if so is it a different process?

 

Ooops , I see I have not taken into account the fact that the moon must be approaching the Earth in freefall over an extended period . I need to get my thoughts in order once more

Edited August 4, 2016 by geordief

[J.C.MacSwell]

 

I think that is still acceleration. Because the moon is in free fall, it is not actually accelerating. For example, if you were in orbit or free fall, you would feel no forces acting on you, therefore you are not accelerating.

 

If you are not following that geodesic because, for example, you are standing on the surface of the Earth, then you do feel a force and (counterintuitively) you are accelerating - even though you are not moving!

 

I'm not sure where the weight loss idea comes into this ...

You can define a local frame where this is true, but generally I would say it is not.

[swansont]

No , I am not sure either. Time dilation (orbiting systems) occurs without acceleration.

 

Does it also occur with acceleration (rocket propulsion) and if so is it a different process?

 

 

Time dilation was measured using a rocket; Gravity Probe A.

https://en.wikipedia.org/wiki/Gravity_Probe_A

[geordief]

 

 

Time dilation was measured using a rocket; Gravity Probe A.

https://en.wikipedia.org/wiki/Gravity_Probe_A

Right and so a clock on the moon keeps the same time as one on the Earth because the Moon is freefalling into the Earth whereas a satellite is being accelerated to prevent it freefalling and so is time dilated?

 

Edit: in post#2 imatfaal said that the moon is accelerating around the Earth . Is that true if it is freefalling?

Edited August 4, 2016 by geordief

[Strange]

Right and so a clock on the moon keeps the same time as one on the Earth because the Moon is freefalling into the Earth whereas a satellite is being accelerated to prevent it freefalling and so is subject to time dilation?

 

There are two possible effects here. There is the time dilation due to the moon (or a satellite) being at a different gravitational potential than the observer on the surface of the Earth. And there is time dilation due to the relative speed between the moon (or satellite) and the observer on the earth. Both of these have to be allowed for by GPS receivers, for example.

 

I don't think acceleration per se has any effect (other than resulting in a different relative speed).

Edited August 4, 2016 by Strange

[geordief]

 

There are two possible effects here. There is the time dilation due to the moon (or a satellite) being at a different gravitational potential than the observer on the surface of the Earth. And there is time dilation due to the relative speed between the moon (or satellite) and the observer on the earth. Both of these have to be allowed for by GPS receivers, for example.

 

I don't think acceleration per se has any effect (other than resulting in a different relative speed).

So why do we get the twin paradox ? That has nothing to do with acceleration?

 

I don't see where gravitation comes into it. It is simply due to different rates of speed?

 

I am trying to work my way through this interesting but very hard document at the moment. It probably explains my OP

 

https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity

Edited August 4, 2016 by geordief

[swansont]

 

There are two possible effects here. There is the time dilation due to the moon (or a satellite) being at a different gravitational potential than the observer on the surface of the Earth. And there is time dilation due to the relative speed between the moon (or satellite) and the observer on the earth. Both of these have to be allowed for by GPS receivers, for example.

 

I don't think acceleration per se has any effect (other than resulting in a different relative speed).

 

 

These are the same issues we have with GPS, albeit different with values for the frequency shifts (and we ignore the satellite's own gravity since it's negligible)

So why do we get the twin paradox ? That has nothing to do with acceleration?

 

I don't see where gravitation comes into it. It is simply due to different rates of speed?

 

I am trying to work my way through this interesting but very document at the moment. It probably explains my OP

 

https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity

 

The twin paradox presents itself because the SR time dilation of being in different inertial frames is symmetric. The acceleration at turnaround breaks that symmetry. A satellite in orbit is not in an inertial frame, so there is no symmetry involved.

[imatfaal]

Right and so a clock on the moon keeps the same time as one on the Earth because the Moon is freefalling into the Earth whereas a satellite is being accelerated to prevent it freefalling and so is time dilated?

 

Edit: in post#2 imatfaal said that the moon is accelerating around the Earth . Is that true if it is freefalling?

 

Just to clear up so non time-dilation problems

 

If you are talking about freefall - then you are not really outside Newtonian mechanics. Freefall is the state when the only force is gravity - ie there is no counteracting force (that's why you float around - no normal force from the floor pushing against your feet as gravity drags you down). In orbit you are constantly falling towards the earth in freefall - and constantly missing because your velocity is such that it takes you around. If you are talking about the moon following a geodesic worldline in space time - ie gravity is spacetime curvature - then naming your situation freefall is a bit of a misnomer; you are under no force.

 

The situation of the moon and a satellite which has no boosters is pretty much identical - they are in orbit; you can call this free fall but why not call it orbit They have a velocity tangential to the body they are orbiting - but an acceleration due to gravity radially in towards the body they are orbiting. Because the acceleration is perpendicular to the velocity then it does not speed up or slow down the satellite/moon - it just changes its course. When a satellite or moon or planet is in a steady orbit then the amount the course changes is just enough to keep it on a repeating elliptical course around the central body

[geordief]

If you are talking about freefall - then you are not really outside Newtonian mechanics. Freefall is the state when the only force is gravity - ie there is no counteracting force (that's why you float around - no normal force from the floor pushing against your feet as gravity drags you down). In orbit you are constantly falling towards the earth in freefall - and constantly missing because your velocity is such that it takes you around. If you are talking about the moon following a geodesic worldline in space time - ie gravity is spacetime curvature - then naming your situation freefall is a bit of a misnomer; you are under no force.

 

Hmm.So the moon is accelerating in our FOR but not in its own?

 

thanks to everyone for all the corrections

[swansont]

Hmm.So the moon is accelerating in our FOR but not in its own?

 

thanks to everyone for all the corrections

 

 

Acceleration is not relative. If you are accelerating, you can tell.

[geordief]

 

 

Acceleration is not relative. If you are accelerating, you can tell.

So the Moon is accelerating wrt the Earth?

 

And you can verify this by the tidal forces on its surface (and interior)?

[J.C.MacSwell]

So the Moon is accelerating wrt the Earth?

 

And you can verify this by the tidal forces on its surface (and interior)?

You can tell if you are accelerating wrt an inertial frame. (Swansont can correct me but I think he assumed that)

 

The moon is accelerating wrt Earth's inertial frame, or I think more exactly an inertial frame tied to the cg of the Earth and Moon. You can verify it by changes in position over time.

Edited August 4, 2016 by J.C.MacSwell

[Sensei]

So the Moon is accelerating wrt the Earth?

 

And you can verify this by the tidal forces on its surface (and interior)?

Moon is moving away from Earth, just ~38 mm per year. It's ~0.1 mm per day.

 

Astronauts who landed on the Moon, leaved there special device called Retroreflector

https://en.wikipedia.org/wiki/Retroreflector

 

Read about Lunar Laser Ranging experiment

https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment

Edited August 4, 2016 by Sensei

[swansont]

Moon is moving away from Earth, just ~38 mm per year. It's ~0.1 mm per day.

 

Astronauts who landed on the Moon, leaved there special device called Retroreflector

https://en.wikipedia.org/wiki/Retroreflector

 

Read about Lunar Laser Ranging experiment

https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment

 

 

This is completely beside the point.

 

Any object moving in a circle is accelerating toward the center of the circle. If it wasn't accelerating it would be moving in a straight line.

[Sensei]

This is completely beside the point.

How it could be beside the point?

He asked "And you can verify this by the tidal forces on its surface (and interior) (of Moon) ?"

So, I explained him, how observation of moving away Moon is performed (by precise measurement of distance using Retroreflector in dozen years).

 

Any object moving in a circle is accelerating toward the center of the circle. If it wasn't accelerating it would be moving in a straight line.

 

Actually, Moon does not move in a circle, but ellipse, with perigee 356400-370400 km, and apogee 404000-406700 km.