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Fast Efficient Orbital Transportation?


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#21 Bender

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Posted 12 February 2017 - 08:00 PM

To be accurate, only some of the Earth's lost angular momentum is transferred to the Moon, The rest is lost to tidal heating and radiated away.

Interesting. Do you have any source on the relative size of this effect with respect to the torque the moon and the earth exert on each other?


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#22 Janus

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Posted 12 February 2017 - 09:36 PM

I don't have any problem with the geometry of it (second paragraph above makes sense), but although the bolded seems straight forward and what I would expect on the one hand...on the other how is this any different from translational momentum?

 

For example a radiating particle in space viewed from any reference frame but it's own...using the same thinking should it not be being slowed by it's radiation? (obviously not...but what am I missing?)

Sorry, but I Probably wasn't clear enough with my explanation.   As I said, the Earth gives up momentum in emitting the photons, but I neglected to state how it loses that momentum.  I never meant to imply that the loss was in the form of a decrease in angular velocity, or that the emission of the photons caused a slowing of the Earth's rotation.    It was in the form of the Relativistic momentum expressed by the energy given up by the emission of the photons.

Basically, the process goes like this: Tidal friction slows the Earth's rotation, which in turns heats the Earth, this slower rotating but warmer Earth has the same angular momentum as it had before, some of it is now in the form of relativistic momentum due to the heat energy.  The warmer Earth radiates away that heat as photons which carries away angular momentum with them.( the heat lost is constantly being replaced by the above mentioned tidal friction.


Interesting. Do you have any source on the relative size of this effect with respect to the torque the moon and the earth exert on each other?

You can pretty much figure it out for yourself.  Just work out how much angular momentum the Moon gains as it climbs away from the Earth and compare that to how much angular momentum the Earth loses in the same time by its slowing.  Both these rates are well known.


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#23 J.C.MacSwell

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Posted 12 February 2017 - 09:47 PM

Sorry, but I Probably wasn't clear enough with my explanation.   As I said, the Earth gives up momentum in emitting the photons, but I neglected to state how it loses that momentum.  I never meant to imply that the loss was in the form of a decrease in angular velocity, or that the emission of the photons caused a slowing of the Earth's rotation.    It was in the form of the Relativistic momentum expressed by the energy given up by the emission of the photons.

Basically, the process goes like this: Tidal friction slows the Earth's rotation, which in turns heats the Earth, this slower rotating but warmer Earth has the same angular momentum as it had before, some of it is now in the form of relativistic momentum due to the heat energy.  The warmer Earth radiates away that heat as photons which carries away angular momentum with them.( the heat lost is constantly being replaced by the above mentioned tidal friction.

Right. I think I eventually figured it out as I posted the next day. But that is (on the scale of things and compared to the energy loss), a pretty small amount angular momentum wise. Is it not a very small effect? (not the energy loss, but the associated angular momentum loss, since it would only take away what it had...no "net recoil" on the remaining Earth from radiating)

 

I guess what I am saying is the vast majority of the angular momentum exchange would be between the Earth Moon orbit and the Earth's spin, with the very small difference radiated away.


Edited by J.C.MacSwell, 12 February 2017 - 09:57 PM.

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#24 Janus

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Posted 12 February 2017 - 11:09 PM

Right. I think I eventually figured it out as I posted the next day. But that is (on the scale of things and compared to the energy loss), a pretty small amount angular momentum wise. Is it not a very small effect? (not the energy loss, but the associated angular momentum loss, since it would only take away what it had...no "net recoil" on the remaining Earth from radiating)

 

I guess what I am saying is the vast majority of the angular momentum exchange would be between the Earth Moon orbit and the Earth's spin, with the very small difference radiated away.

As I said in the last post, you can work it out for yourself.  If you do, I think you'll be surprised.


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#25 J.C.MacSwell

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Posted 13 February 2017 - 02:39 PM

As I said in the last post, you can work it out for yourself.  If you do, I think you'll be surprised.

 

 

You can pretty much figure it out for yourself.  Just work out how much angular momentum the Moon gains as it climbs away from the Earth and compare that to how much angular momentum the Earth loses in the same time by its slowing.  Both these rates are well known.

I don't think you can simply take the difference in these two numbers and say the difference is from radiating the waste heat of the tidal process.

 

Here is my reasoning:

 

1. The dissipation/radiating takes place near the Earths surface. Even at the equator the spin speed is a very small fraction of the speed of light, so the redshift/blueshift effect has to be very small. (If all this radiation was directed East, the effect would be some 650,000 times greater)

 

2. Any difference would be much more due to absorption/dissipation/re-radiation of solar energy hitting the Earth...still related to v/c for momentum, but the energy exchange of solar is (50,000 times if my sources are contextually correct) many times greater than tidal.

 

So I am thinking the Earth would lose some angular momentum anyway, the angular momentum robbed by the moon is a much greater effect, but the angular momentum loss from dissipating tidal energy is almost insignificant in comparison.


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#26 Janus

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Posted 13 February 2017 - 08:16 PM

 

I don't think you can simply take the difference in these two numbers and say the difference is from radiating the waste heat of the tidal process.

 

Here is my reasoning:

 

1. The dissipation/radiating takes place near the Earths surface. Even at the equator the spin speed is a very small fraction of the speed of light, so the redshift/blueshift effect has to be very small. (If all this radiation was directed East, the effect would be some 650,000 times greater)

 

2. Any difference would be much more due to absorption/dissipation/re-radiation of solar energy hitting the Earth...still related to v/c for momentum, but the energy exchange of solar is (50,000 times if my sources are contextually correct) many times greater than tidal.

 

So I am thinking the Earth would lose some angular momentum anyway, the angular momentum robbed by the moon is a much greater effect, but the angular momentum loss from dissipating tidal energy is almost insignificant in comparison.

 No, again you are trying to attribute a slowing of the Earth's rotation as being caused by the emission process.  It doesn't work that way.   The Sun warms the Earth, raising it temperature until the net radiation of the Earth matches that the Sun is supplying.  Ergo. the Sun, by warming the Earth, increases its momentum and the Earth in turn sheds that momentum by radiating heat away. This results in a state of thermal equilibrium. (Climate change is caused by a change in the atmospheric composition that raises the temp at which this occurs.)

 

The loss of angular momentum not transferred to the Moon is caused by tidal friction converting rotational energy into heat. Which is then radiated away.  In this process rotational kinetic energy of the Earth is being converted to electromagnetic radiation. The act of radiating does not slow the Earth, it just carries away that portion of that energy that was converted to heat by the process that did slow it down.

 

With the Sun, it is incoming radiation being converted to outgoing radiation and there is no involvement of the Earth's rotational kinetic energy.


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