Satellites in orbit

[Anilkumar]

There is indirect evidence in the form of a pair of orbiting neutrons stars. Theory says that they should radiate energy away in the form of gravity waves, and this should cause them to spiral closer to each other. Careful measurements have shown that they are approaching each other at the same rate as predicted by gravity wave emission. Not yet. but this is not surprising as they would be very weak and it takes extremely sensitive equipment to detect. They travel at c and are essentially "ripples in space".

 

Why the sources of Gravitational waves are only the "pair of orbiting Neutron stars"?

 

Is there any evidence to show that Gravitational waves are actually a FORM of ENERGY?

 

If so;

 

and "Because energy can not be created. It can only be converted from one form to another" ;

what "FORM" of "ENERGY" is being converted into Gravitational energy in a pair of orbiting Neutron stars? i.e. what is the BASIC - SOURCE of Gravitational energy? or "WHAT" can be CONVERTED into Gravitational energy.

[Janus]

Why the sources of Gravitational waves are only the "pair of orbiting Neutron stars"?

They aren't the only sources. They just happen to be a source that radiates at a high enough level for us to see the effects. This is because they are massive object in fast, close orbit around each other. The Earth radiates gravity waves too, it is just at so low a level that we can't measure it. Any mass that accelerates or follows a periodic motion produces gravity wave, in much the same way that a charge under the same conditions produce electromagnetic waves. But since gravity waves are some 10^40 times weaker than electromagnetic waves, thye are really really difficult to detect.

Is there any evidence to show that Gravitational waves are actually a FORM of ENERGY?

 

Back to the orbiting neutron pairs, they are losing energy at a rate consistent with that predicted by the emission of Gravity waves.

 

If so;

 

and "Because energy can not be created. It can only be converted from one form to another" ;

what "FORM" of "ENERGY" is being converted into Gravitational energy in a pair of orbiting Neutron stars? i.e. what is the BASIC - SOURCE of Gravitational energy? or "WHAT" can be CONVERTED into Gravitational energy.

 

In the case of the orbiting neutron stars this energy comes form their orbital energy. This is why they are approaching each other.

 

Be careful not to confuse gravity waves with the gravitational force or field. They bear the same relationship to each other as do the light emitted by a flashlight and the magnetic field of a magnet.

 

Electromagnetic waves (light, radiowaves, etc) carry information about changes in electromagnetic fields, and gravity waves carry information about changes in gravity fields.

Edited December 2, 2011 by Janus

[Anilkumar]

Thank you very much Janus,

 

for the painstaking explanation.

 

. . . Any mass that accelerates or follows a periodic motion produces gravity wave . . .

 

Does this mean that;

 

"If there is an isolated mass, which is static; it would exhibit Gravity but would not radiate Gravitational waves"?

 

Back to the orbiting neutron pairs, they are losing energy at a rate consistent with that predicted by the emission of Gravity waves.

 

• The Gravitational waves have not been detected yet.
• There is no concrete evidence to show that they are a form of energy.

Does this mean that the existence of Gravitational waves is a Hypothesis?

 

What prompted this Hypothsis?

 

. . . In the case of the orbiting neutron stars this energy comes form their orbital energy. This is why they are approaching each other . . .

 

What does Orbital energy mean?

 

Could you please elaborate on how Orbital energy is related to the approaching of the pair of Neutron stars?

 

. . . Be careful not to confuse gravity waves with the gravitational force or field. They bear the same relationship to each other as do the light emitted by a flashlight and the magnetic field of a magnet.

 

Electromagnetic waves (light, radiowaves, etc) carry information about changes in electromagnetic fields, and gravity waves carry information about changes in gravity fields . . .

 

Thank you for the kind forewarning. This was very informative.

Edited December 3, 2011 by Anilkumar

[imatfaal]

Thank you very much Janus,

 

for the painstaking explanation.

 

 

Does this mean that;

 

"If there is an isolated mass, which is static; it would exhibit Gravity but would not radiate Gravitational waves"?

 

An accelerating electric charge gives rise to electromagnetic wave just as an accelerating massive body gives rise to gravitational waves. the static object will not give off waves

 

 

• The Gravitational waves have not been detected yet.
• There is no concrete evidence to show that they are a form of energy.

Does this mean that the existence of Gravitational waves is a Hypothesis?

 

What prompted this Hypothsis?

They follow from General Relativity - and I believe it was Einstein who first predicted their existence

 

What does Orbital energy mean?

 

Could you please elaborate on how Orbital energy is related to the approaching of the pair of Neutron stars?

 

 

 

Thank you for the kind forewarning. This was very informative.

 

Orbital energy is the sum of the total (ie both bodies) kinetic energy and the total potential energy of a two body system in orbit around each other (or around a central point).

[math] \epsilon_{orbital}= \epsilon_{kinetic} + \epsilon_{potential} = \frac{(orbital velocity)^2}{2} - \frac{G(sum of masses)}{radius} [/math]

 

This sum stays constant - unless energy is either added or removed from the system. One method of removing energy is the emission of gravitational waves. Waves carry energy (and other properties) out of the system. A reduction in the sum of energies causes the orbiting bodies to spiral into each other and get faster. In the case of the neutron stars mentioned we have been able to detect the speeding up of the orbital rotation.

 

They aren't the only sources. They just happen to be a source that radiates at a high enough level for us to see the effects. This is because they are massive object in fast, close orbit around each other. The Earth radiates gravity waves too, it is just at so low a level that we can't measure it. Any mass that accelerates or follows a periodic motion produces gravity wave, in much the same way that a charge under the same conditions produce electromagnetic waves. But since gravity waves are some 10^40 times weaker than electromagnetic waves, thye are really really difficult to detect.

 

To slightly clarify and expand on Janus's excellent answer - some accelerations, periodic motions, and behaviours give rise to gravitational waves and others do not. the earth - sun system will radiate gravitational waves due to earths orbit, but the earth's mass spread out into a disc around the sun whilst still orbitting (think asteroid belt) will not radiate. The earth will not radiate due to its rotation on its own axis (save the infinitesimal amount that the earth is not symmetrical about axis of rotation) but a tumbling irregular planetoid will radiate. When there is spherical/cylindrical symmetry then the acceleration/behaviour is unlikely to cause gravitational waves

Edited December 3, 2011 by imatfaal

[michel123456]

An accelerating electric charge gives rise to electromagnetic wave just as an accelerating massive body gives rise to gravitational waves. the static object will not give off waves

So you say those waves are relative to the observer. An observer at rest with the object will observe no waves, and an observer in a state of motion will observe waves.

 

(...)This sum stays constant - unless energy is either added or removed from the system. One method of removing energy is the emission of gravitational waves. Waves carry energy (and other properties) out of the system. A reduction in the sum of energies causes the orbiting bodies to spiral into each other and get faster. In the case of the neutron stars mentioned we have been able to detect the speeding up of the orbital rotation.

 

That sounds in contradiction with the first statement. The energy of the system does not depend on the state of motion of the observer.

Edited December 3, 2011 by michel123456

[imatfaal]

So you say those waves are relative to the observer. An observer at rest with the object will observe no waves, and an observer in a state of motion will observe waves.

 

No I never said they were relative to the observer. They are created by acceleration not by motion and acceleration is not relative like uniform motion.

 

Two systems in uniform relative motion behave in a similar way and either system can be judged as stationary relative to the other one; this is not the case for an accelerating frame of reference. When a body is accelerating it is clear which body/bodies is accelerating - a system accelerates without reference to external frames - ie you can tell you are accelerating (or are in a gravitational field) in the famous windowless elevator whereas you cannot tell if you are in uniform motion/static.

 

Objects in uniform motion CANNOT radiate gravitational waves - otherwise they would lose energy, slow down and stop and that would contradict the law of preservation of linear momentum.

 

Objects in acceleration (provided not an acceleration with spherical symmetry) will radiate gravitational waves.

 

 

That sounds in contradiction with the first statement. The energy of the system does not depend on the state of motion of the observer.

 

 

As I never meant to imply / suggested that the relative uniform motion of systems can give rise to gravitational waves then the above is answered with first section

 

Offtopic Whilst there will be conservation of energy for the complete system - relativity allows us to view and calculate the kinetic energy basis frames. I can observe a lump of lead in deep space and decide that I think it is motionless (its not moving relative to the background stars) and has zero kinetic energy by my sums. If my space suit suddenly gives me a brief shove forward towards the lead pellet ending up with me moving towards it at a constant velocity of 10m/s; the idea of relativity is that I can calculate the energy of the lead pellet from my fixed frame as it moves towards me at 10m/s

Edited December 3, 2011 by imatfaal

[michel123456]

O.K. that is clear now. I was confused by your statement

(...) the static object will not give off waves (...)

[swansont]

Objects in uniform motion CANNOT radiate gravitational waves - otherwise they would lose energy, slow down and stop and that would contradict the law of preservation of linear momentum.

 

Technically you could have this, because the waves would contain momentum and energy and thus both could be preserved. The underlying problem is that it gives a preferred rest frame for objects.

[imatfaal]

Technically you could have this, because the waves would contain momentum and energy and thus both could be preserved. The underlying problem is that it gives a preferred rest frame for objects.

 

 

Yes - that makes sense now you say it like that, although I am sure I have read explained the alternative way.

 

[Anilkumar]

An accelerating electric charge gives rise to electromagnetic wave just as an accelerating massive body gives rise to gravitational waves. the static object will not give off waves

 

 

 

They follow from General Relativity - and I believe it was Einstein who first predicted their existence

 

 

 

Orbital energy is the sum of the total (ie both bodies) kinetic energy and the total potential energy of a two body system in orbit around each other (or around a central point).

[math] \epsilon_{orbital}= \epsilon_{kinetic} + \epsilon_{potential} = \frac{(orbital velocity)^2}{2} - \frac{G(sum of masses)}{radius} [/math]

 

This sum stays constant - unless energy is either added or removed from the system. One method of removing energy is the emission of gravitational waves. Waves carry energy (and other properties) out of the system. A reduction in the sum of energies causes the orbiting bodies to spiral into each other and get faster. In the case of the neutron stars mentioned we have been able to detect the speeding up of the orbital rotation.

 

 

 

To slightly clarify and expand on Janus's excellent answer - some accelerations, periodic motions, and behaviours give rise to gravitational waves and others do not. the earth - sun system will radiate gravitational waves due to earths orbit, but the earth's mass spread out into a disc around the sun whilst still orbitting (think asteroid belt) will not radiate. The earth will not radiate due to its rotation on its own axis (save the infinitesimal amount that the earth is not symmetrical about axis of rotation) but a tumbling irregular planetoid will radiate. When there is spherical/cylindrical symmetry then the acceleration/behaviour is unlikely to cause gravitational waves

 

Thank you Imatfaal,

 

for the exhaustive explanation.

[michel123456]

Technically you could have this, because the waves would contain momentum and energy and thus both could be preserved. The underlying problem is that it gives a preferred rest frame for objects.

I don't understand what you mean.

[Janus]

An accelerating electric charge gives rise to electromagnetic wave just as an accelerating massive body gives rise to gravitational waves. the static object will not give off waves

 

 

 

 

 

 

 

Orbital energy is the sum of the total (ie both bodies) kinetic energy and the total potential energy of a two body system in orbit around each other (or around a central point).

[math] \epsilon_{orbital}= \epsilon_{kinetic} + \epsilon_{potential} = \frac{(orbital velocity)^2}{2} - \frac{G(sum of masses)}{radius} [/math]

 

 

 

One small correction, that should be "product of masses" not "sum of masses"(Mm, not M+m)

 

Yes. It's why a space capsule/shuttle can dock with the ISS, even though that have different masses. They can be put into essentially identical orbits.

 

The caveat to this is that the masses need to be small compared to the object that they are orbiting.

 

The more accurate formula is

 

[math]v_o = \sqrt{\frac{GM^2}{r(M+m)}}[/math]

 

where M is the mass of the primary body being orbited and m is the mass of the orbiting body.

 

This is because the two masses orbit a common barycenter rather than the orbiting body strictly orbiting the center of the other. When M is very large compared to m, the answer comes out to being very close to that found by ignoring m.

[swansont]

I don't understand what you mean.

 

Gravity waves must have energy and momentum, so merely emitting the waves does not violate conservation of momentum. But emitting them simply because of motion would imply a preferred frame; when emissions stopped you must be at rest. That would be a preferred frame.

[imatfaal]

One small correction, that should be "product of masses" not "sum of masses"(Mm, not M+m)

 

 

Janus - I am pretty certain you are not correct. the specific orbital energy, similar to the vis-viva energy, is as I put it

 

[math] [/math]

 

[math] \epsilon_{potential} = \frac{-Gm_1m_2}{r}[/math]

 

[math] \epsilon_{kinetic} = \frac{m_1v_1^2}{2} + \frac{m_2v_2^2}{2}[/math]

 

To convert from individual velocities to a relative orbital velocity

 

[math] \epsilon_{kinetic} = \frac{m_1m_2}{m_1+m_2} \frac{v_{relative}^2}{2}[/math]

 

the first part being the reduced mass.

 

If we now add the two portions

 

[math] \epsilon_{total} = \frac{-Gm_1m_2}{r}+ \frac{m_1m_2}{m_1+m_2} \frac{v_{relative}^2}{2}[/math]

 

we then divide through by the reduced mass to tidy up

 

[math] \epsilon_{total} = \frac{m_1+m_2}{m_1m_2} \frac{(-Gm_1m_2)}{r}+ \frac{v_{relative}^2}{2}[/math]

 

[math] \epsilon_{total} = \frac{-G(m_1+ m_2)}{r}+ \frac{v_{relative}^2}{2}[/math]

[Anilkumar]

I would like to thank,

 

Scienceforums.net,

 

for providing this wonderful platform,

 

where,

 

a layman could discuss his doubts, with;

 

highly Informed Persons, who have;

 

gone to great lengths, to;

 

acquire that information.

 

This platform is doing,

 

a great service to mankind.

 

May god bless you all, those,

 

involved in the discussions and;

 

maintaining this platform.

 

And also;

the Software involved too is,

 

just marvelous.

 

Keep it up,

 

everybody.

Edited December 7, 2011 by Anilkumar