[Bill S]

Can we say that any two objects in relative motion are accelerating relative to each other?

My understanding is that acceleration requires a change of speed or direction.  One or both of these would be necessary in order to say that "two objects in relative motion are accelerating relative to each other".

Presumably, two objects that were circling each other at constant speed would qualify. (?)

[Colin2B]

I'm surprised it's used in science. if the amount of stuff 4.24 light years away becomes so insignificant it should be regarded as nothing,  then we shouldn't be able to see other stars,  the photons would be negligible. ...no?

Here we are talking about 2 different things, the visibility of photons and the transfer of momentum. The eye can see even a few photons, but the momentum they transfer is negligible. They won’t push you over.
Negligible is an important word in physics, no use spending time calculating something you can ignore. Take a car, you know it’s weight (hence mass) and speed so you can calculate its momentum. If a fly lands on the car the effect on the momentum is negligible, no need to recalculate. If an elephant lands on the car .........

Key rule of science, recognise what is significant.

Can we say that any two objects in relative motion are accelerating relative to each other?

Not any, only some. The relative motion has to be an acceleration.

Can we say that photons are emitted by electrons, and are traveling at the speed of light when emitted?

We can

[geordief]

Not any, only some. The relative motion has to be an acceleration.

Just semantics to say that all motion is acceleration to a greater or lesser degree and that unaccelerated  motion is an idealization ,a mathematical limit?

Like your fly on the car it may be  true but is of no consequence? 

[raf21]

I somewhat like the car analogy. ....perhaps I could pose a few stipulations to said scenario. ....
1)said car is driving in a vacuum
2)car has a set of alien technology frictionless tires.
3)the fly is immortal,  is able to fly inn a vacuum,  and lands oon car with same velocity or impact every time.
4)fly is very determined and lands oon car one million times over the next 10000 years.
5) fly weight is .01 grams.

does the accumulating impacts add up to the same impact a 22lb turkey hitting a vehicle one time?

[Bogie_smiles]

...
does the accumulating impacts add up to the same impact a 22lb turkey hitting a vehicle one time?

I can't speak for geordief, but I will try to test my understanding of his point: the fly has a tiny mass relative to the mass of the car. There is a mutual gravitational attraction between the fly and the car, but the effect of the presence of the fly on the motion of the car is inconsequential.


I'm not sure of the physics involved with the fly leaving and returning multiple times, but if the departure is not a push off, and if the return is a soft landing, hmm, maybe someone can explain the accumulative effect on the path of the car in space as a result of multiple tiny gravitational attractions from the repeated close proximity of the fly, in comparison to the collision with the turkey.

[raf21]

assume fly falls off, and flies a long loop Aaron's to land on car in had on collision approach

[Bogie_smiles]

Can we say that any two objects in relative motion are accelerating relative to each other?

Not any, only some. The relative motion has to be an acceleration.

There is always a gravitational potential between two objects, though often it is negligible? Can we say that the gravitational potential between two bodies would be the mutual effect they have on each other’s spacetime curvature, i.e., their geodesics?

If so, am I right to think that their mutual gravitational attraction qualifies as an acceleration, and is included in the calculation of the geodesics that they will follow?

[Bill S]

does the accumulating impacts add up to the same impact a 22lb turkey hitting a vehicle one time?

Is the turkey frozen? 

Apparently, one aircraft manufacturer, using chickens for impact tests, forgot to thaw the birds before firing them at the aircraft.  Their results were quite different from anyone else's.  OK, that's off topic, but I like it.

[raf21]

i had not considered if the turkey was frozen. .... I would think that would be a slight,  but, "negligible" density change.  Although definitely a hardness change.  I'm not sure how off subject that could be considered,  I'm the one talking about flies and turkeys flying around in a vacuum hitting alien cars.
I understand that the single fly impacting the car would have thus said negligible effect. .... what can
drop of water do? nothing (negligible) ..... yet over time things like the grand canyon,  and probably even our oceans them selves are created.  I have no interest in what one or 2 photons do to an object far away.  I'm going with the notion that millions of years of an endless barrage of photons,  however inversely squared,  must amount to something.  I'm sure the math could be done by someone much smarter then me.  I'll attempt to explain,  but practically guarantee I'm probably not going too use the correct terms,  so I'll take the liberty to try to think like someone smarter then i and create terms i think might be close enough.
example,  the light sail,  theoretically able to use light to get pushed,  need a relatively high "photon density " striking it to operate in a usable manner.  I'll make up a number,  let's say out needs 1 million photons per second per centimeter striking its surface to created 1g acceleration (I know those numbers are probably way off )
each photon has same impact energy,  correct? then could it not be said that 1 photon per second per centimeter would create 1 millionth of a g of thrust?  would the inverse square law balance the gravity of the two different light sails from a single light source so the both will accelerate,  one just taking a million times longer to accelerate?

[raf21]

on a cosmic scale,  a million of anything is probably a negligible number

[Kryptid]

I'll make up a number,  let's say out needs 1 million photons per second per centimeter striking its surface to created 1g acceleration (I know those numbers are probably way off )
each photon has same impact energy,  correct? then could it not be said that 1 photon per second per centimeter would create 1 millionth of a g of thrust?

Yes, assuming you meant "square centimeter".

would the inverse square law balance the gravity of the two different light sails from a single light source so the both will accelerate,  one just taking a million times longer to accelerate?

I'm not quite sure what you mean here. Are you asking if the gravitational attraction between the two solar sails would significantly impact how much acceleration the light gives the sails? That would depend on the mass and distance between the sails, as well as the energy of the light hitting them.

[raf21]

my apologies for my vagueness,  yes,  I meant square centimeter.  also,  I didn't describe sails and conditions very well.  assume sails are identical in all aspects except distance from light source.  assume the further sail is so far away it only receives 1 photon per square centimeter.  I realize these numbers only work for an instant,  as soon as the sail moves any distance,  acceleration will decrease,  and probably proportionally according to inverse square law. .....and I'm assuming that gravitational attraction will behave the same.  but I'm am just a primitive guessing at this.

[Kryptid]

my apologies for my vagueness,  yes,  I meant square centimeter.  also,  I didn't describe sails and conditions very well.  assume sails are identical in all aspects except distance from light source.  assume the further sail is so far away it only receives 1 photon per square centimeter.  I realize these numbers only work for an instant,  as soon as the sail moves any distance,  acceleration will decrease,  and probably proportionally according to inverse square law. .....and I'm assuming that gravitational attraction will behave the same.  but I'm am just a primitive guessing at this.

If you are considering the light source to be a star and the gravity is coming from that same star, then yes, the force of gravity and the acceleration caused by the light pressure will fall off at the same rate. They both follow the inverse-square law.

[raf21]

then am I way off base asking what effect light has 4.24 light years away from an object,  over millions of years,  multiplied by trillions of stars,  combined with the process repeating for billions of years with new stars replacing dying stars? 4.24 ly is distance to nearest star.  granted,  each photons effect is negligible,  but the accumulated effect must amount to something.  if we can see a photon,  then it must affect an object,  however miniscule.  surely this must add up to a phenomenal amount of "light pressure"........ and if light has mass as some theorize,  could this be the missing mass needed to make the models of the universe work correctly?  ..........perhaps this material is not so dark after all. .....

[Kryptid]

then am I way off base asking what effect light has 4.24 light years away from an object,  over millions of years,  multiplied by trillions of stars,  combined with the process repeating for billions of years with new stars replacing dying stars? 4.24 ly is distance to nearest star.  granted,  each photons effect is negligible,  but the accumulated effect must amount to something.  if we can see a photon,  then it must affect an object,  however miniscule.  surely this must add up to a phenomenal amount of "light pressure"........ and if light has mass as some theorize,  could this be the missing mass needed to make the models of the universe work correctly?  ..........perhaps this material is not so dark after all. .....

I'll see what I can come up with calculation-wise, but first I'd like to point out that (as shown by E=mc²) that energy already has an associated mass and therefore a gravitational field all its own. I'm sure scientists would have taken into consideration this fact when calculating how galaxy rotation curves should look. The anomaly remains.

Just for fun, let's see how much radiation pressure Proxima Centauri exerts on Earth. The power flux of the Sun at 1 AU is 1,360.8 watts per square meter. Proxima Centauri has a bolometric (total) luminosity of only 0.0017 times that of the Sun, resulting in a power flux of 2.31336 watts per square meter 1 AU away from it. Proxima Centauri is 4.246 light-years away, which is equal to 268,521.61 AU. Using the inverse-square law:

1/(268,521.61)² = 1/(72,103,855,037) = 1.3868884 x 10^-11

Multiply this by the power flux:

(1.3868884 x 10^-11)(2.31336) = 3.2083721 x 10^-11 watts per square meter

There are two different pressure equations that could be used now: one that assumes all the light is absorbed and one that assumes all the light is reflected. Reflecting all of the light doubles pressure. Earth, however, neither absorbs nor reflects all electromagnetic radiation. So instead, I will assume that the Earth reflects 30.6% of all radiation back into space (based on its bond albedo of 0.306). So to put that into equation form:

P = ((1.306)(I))/c
P = ((1.306)(3.2083721 x 10^-11))/299,792,458
P = 4.190134 x 10^-11/299,792,458
P = 1.3976783 x 10^-19 pascals (a very small pressure)

Since the Earth's mean radius is 6,371,000 meters, that would make its total cross-sectional area:

A = π(6,371,000)²
A = π(4.0589641 x 10¹³)
A = 1.2751612 x 10¹⁴ square meters

Multiply that by the pressure to get the total force on the Earth:

F = (1.2751612 x 10¹⁴)(1.3976783 x 10^-19)
F = 0.00001782265 newtons

To find the acceleration this force gives the Earth, we divide this force by the mass of the Earth:

Acceleration = 0.00001782265/(5.97237 x 10²⁴)
Acceleration = 2.984184 x 10^-30 meters per second squared

To get the total increase in velocity that this would have given the Earth over its entire 4.5 billion-year (1.42 x 10¹⁷ second) lifespan, we multiply the acceleration by the age:

Velocity = (1.42 x 10¹⁷)(2.984184 x 10^-30)
Velocity = 4.2378158 x 10^-13 meters per second (extremely slow)

So even after 4.5 billion years of shining on the Earth, Proxima Centaur's light still has a negligible effect on Earth's speed.

[Colin2B]

There is always a gravitational potential between two objects, though often it is negligible? Can we say that the gravitational potential between two bodies would be the mutual effect they have on each other’s spacetime curvature, i.e., their geodesics?

If so, am I right to think that their mutual gravitational attraction qualifies as an acceleration, and is included in the calculation of the geodesics that they will follow?

Depends what you are considering.
In SR the assumption is flat spacetime far away from gravitational influence and small objects far enough apart for the gravitational attraction to be negligible. So non-accelerating motion is possible.
GR considers spacetime under the influence of gravitational forces including bodies where there is significant mutual attraction, so as you say, there will be relative acceleration included.

then am I way off base asking what effect light has 4.24 light years away from an object,  over millions of years,  multiplied by trillions of stars,  combined with the process repeating for billions of years with new stars replacing dying stars? 4.24 ly is distance to nearest star.  granted,  each photons effect is negligible,  but the accumulated effect must amount to something.  if we can see a photon,  then it must affect an object,  however miniscule.  surely this must add up to a phenomenal amount of "light pressure"........ and if light has mass as some theorize,  could this be the missing mass needed to make the models of the universe work correctly?  ..........perhaps this material is not so dark after all. .....

EDIT: while I was typing @Kryptid posted the one above, so this is to be read with what he wrote.

There are 2 things to consider, the ability of an object to move and the ability of something to move it.
Elsewhere there is a question about whether a rocket taking off from the moon can change the moon’s orbit and the same principles apply if we consider some examples.

- Starlight falling on the earth is of very low intensity due to inverse square law. However, the earth has a large surface area and so can collect a lot of starlight, but each photon of starlight carries an unbelievably small amount of momentum and the earth’s inertia is phenomenal - even large asteroids won’t kick it off orbit. So the earth does not move.
- a solar sail has a very large surface area, so can collect a lot of photons, it also has a very low mass (inertia) so near a large source of light eg the sun, it will move. As it gets further away the effect diminishes and the drive will stop working, also there comes a point where the sail is equidistant from 2 stars and the pressure from both would cancel out.
- take interstellar dust and gas. Very low mass, easy to move, but small cross sectional area so it won’t collect many photons and even then their momentum is minuscule compared to the inertia of the particles. Yes, over time they might move, but remember, wherever you are in the universe you are surrounded by stars so the net pressure on this interstellar material is zero. Question: would that, over time, lead to any form of gas/dust clumping and can it be detected? Would that clumping force be greater than the ability of gravity from nearby stars to attract the dust/gas, I suspect not.

[Bill S]

The thought that came to mind when reading #68 has probably been adequately covered, but I’ll add it to the mix.

If you assume that the number of photons per sec, per sq cm required to overcome the inertia of the sail is 1,000,000; then 1 per sq cm per sec will not move the sail.  Presumably the energy of the photon will be dissipated as heat.

Therefore there is a reciprocity failure between 1,000,000 photons per sec, and 1 photon per sec x 1,000.000 secs.

[raf21]

wow,  very informative. .....I'm way out of my league here,  obviously.
after reading the responses to my post,  I did wonder about something else.  do photons traveling in opposite directions in the same space affect each other? can they collide?  it doesn't seem like it should,  but I'm confident I've already proven my limited understanding of things.  one other thing. .... if two photons travel next to each other for millions of years,  will they remain on a parallel path? or could the tiny mass draw them closer to each other? or does a photon carry a charge,  and being identical,  repel each other?

[Kryptid]

wow,  very informative. .....I'm way out of my league here,  obviously.
after reading the responses to my post,  I did wonder about something else.  do photons traveling in opposite directions in the same space affect each other? can they collide?  it doesn't seem like it should,  but I'm confident I've already proven my limited understanding of things.

In most cases, they will pass through each other and keep going on their merry way. Every once in a long while, though, they can scatter off each other: https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.111.080405

one other thing. .... if two photons travel next to each other for millions of years,  will they remain on a parallel path? or could the tiny mass draw them closer to each other? or does a photon carry a charge,  and being identical,  repel each other?

The photons will slowly approach each other over time, since their energy produces a tiny gravitational field. They do not have any charge.

[raf21]

interesting that they attract each other. ... should I assume the effect has negligible impact on the inverse squire law?