- #36
PeterDonis
Mentor
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metastable said:For Illustration
Nobody is disputing how aberration works.
metastable said:For Illustration
metastable said:Is there still some disagreement about what the outcome would be?
Let me recap. In the scenario there is a black hole with a radius of the observable universe
and a fleet of coasting, co-moving ships with a variety of heights above the black hole and a variety of separation distances between them, but they are in a region of space roughly 2 black hole radii from the geometric center of the black hole
This parameter sets the scale of the gravitational redshift effects with respect to given distances and times traveled by the spacecraft .pervect said:Why is the radius of the black hole that of the observable universe?
pervect said:Are you imagining that this black hole is in our universe (which seems hard to analyze and also probably paradoxical), or in an idealized uiverse with nothing but the black hole?
pervect said:I think others have commented before that comoving is kind of hard to understand
I didn’t see any indications that you were using a black hole of the given mass or a pair of ships at any specified radius or any of the other pieces of this question. I am not sure in what sense you think that calculation was similar to the scenario you describe here.metastable said:I've tried something similar before:
Dale said:I didn’t see any indications that you were using a black hole of the given mass or a pair of ships at any specified radius or any of the other pieces of this question. I am not sure in what sense you think that calculation was similar to the scenario you describe here.
metastable said:^peak mechanical power is 10746.218459832w @ 8082.063923094534641801 motor rpm
A = meters per second = XX.XXX
B = drag coefficient = 0.75
C = frontal area = 0.6m^2
D = fluid density of air = 1.225kg/m^3
E = wind drag force in watts
F = sine of 5% slope = sin(atan(5/100)) = 0.04993761694389223373491
G = acceleration of gravity = 9.80655m/s^2
H = vehicle mass in kg = 90.7184kg = 200lb / 2.20462lb/kg
I = mechanical watts required for constant speed up slope with no wind drag
J = mechanical watts required for constant speed up slope including wind drag
K = H * G * F
L = (1/2) * D * C * B
E = ((1/2) * D * C * (A^2) * B) * A
I = H * G * A * F
J = E + I
J = (((1/2) * D * C *(A^2) * B) * A) + (H * G * A * F)
J = (1/2) * D * C * B * A^3 + H * G * F * A
J = (L * A^3) + (K * A)
^this can be rearranged to:
A=(sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * L) - ((2 / 3)^(1 / 3) * K) / (sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3)
we know:
J = 10746.218459832w peak mechanical
L = 0.275625 = (1/2) * D * C * B
K = 44.42622815547907982077 = H * G * F
therefore:
A=(sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * 0.275625) - ((2 / 3)^(1 / 3) * 44.42622815547907982077) / (sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3)
A=32.32551993764664323864 meters per second
Ok. So why are you unwilling to work this specific problem?metastable said:The point was I don't shy away from combining and rearranging equations...
Dale said:Ok. So why are you unwilling to work this specific problem?
metastable said:What is a "10gev + 1ev kinetic energy" electron's initial velocity in m/s from the lab frame?
10gev + 1ev kinetic electron (lab frame)-->
B = 0.5109989461MeV = electron rest mass
Z = 10000.000001MeV = initial electron kinetic energy (lab frame) = 10gev + 1ev
E = Electron Total Energy
E = B+Z
E = 10000.5109999461MeV
E = B/sqrt(1-(V^2/C^2))
can be rearranged to:
E = B/sqrt(1-A)
A = V^2/C^2
E = B/sqrt(1-A)
can be rearranged to:
A = -1*((B^2-E^2)/E^2)
A = -1*((0.5109989461^2-10000.5109999461^2)/10000.5109999461^2)
A = 0.9999999973890676149262
A = V^2/C^2
can be rearranged to:
V = C*sqrt(A)
C = 299792458m/s
V = 299792458*sqrt(0.9999999973890676149262)
V = 299792457.608631081048
10gev + 1ev Electron V=299792457.608631081048m/s from lab frame
%C = 299792457.608631081048 / 299792458
%C = 99.9999998694533806347%
10gev + 1ev Electron V = 99.9999998694533806611% C
10gev + 1ev Electron V = 0.999999998694533806611C
------------------------
Conclusion
Q: What is the 10gev + 1ev electron's initial velocity in m/s from the lab frame?
A: The 10gev + 1ev electron initially travels 299792457.608631081048m/s from the lab's rest frame, which is 0.999999998694533806611C.
metastable said:Will the relativistic aberration cause a higher and higher % of total photons to travel on vectors which increase in distance from the black hole over time, as the ships co-moving velocity increases in different scenarios?
In a given scenario (for example if 99.99999999999999% of total photons are moving away from the black hole), will the photons become redshifted from gravitational redshift during their flight times between craft?
^If yes, Will the measured gravitational redshift increase (as measured by an observer on one of the craft) as the separation distance between the craft increases in different scenarios (longer flight times between craft)?
metastable said:A = cos(motion path angle relative to the vector from the observer to the source at the time when the light is emitted)
B = V
C = C
D = cos(angle observed to source)
D = (A-(B/C))/(1-((B/C)*A))
A = -1*(((-1*B)-(D*C))/(C+(D*B)))
A = cos(motion path angle relative to the vector from the observer to the source at the time when the light is emitted)
B = 299792457.6086310810085m/s
C = C = 299792458m/s
D = cos(angle observed to source) = 0 = cos(90deg)
A = -1*(((-1*B)-(D*C))/(C+(D*B)))
A = -1*(((-1*299792457.6086310810085)-(0*299792458))/(299792458+(0*299792457.6086310810085)))
A = 0.9999999986945338064792 = cos(0.00292766)
0.00292766 degrees = motion path angle relative to the vector from the observer to the source at the time when the light is emitted
-----------------------------------------
Conclusions
The angle of the source motion path relative to the vector from the observer to the source at the time when the light is emitted is 0.00292766 degrees if the source momentum vector appears to be 90 degrees to the lab-frame-observed emission vector at the time of viewing from the lab frame
metastable said:0.00292766 / 179.99707234 = 0.0016265% of photons gravitationally blueshifted when initial V = 299792457.6086310810085m/s
100 - 0.0016265 = 99.9983735% of photons gravitationally redshifted when initial V = 299792457.6086310810085m/s
metastable said:This parameter sets the scale of the gravitational redshift effects with respect to given distances and times traveled by the spacecraft .
I'm imagining just outside the observable universe, but still within the total universe... & close & large enough to still observably affect events within the observable universe. For the idealized example the universe is simplified to just the black hole, the spacecraft , and the cosmological expansion parameter = 0 in the scenario.\
I mean comoving in the sense the vector of the spacecraft is extremely similar and the relative speed of the craft is insignificant compared to their speed with respect to the black hole. I am also "aware" of the separate astronomical definition of comoving in which all of the redshift is explained by cosmological expansion.
The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.pervect said:So, no really pressing reason, then?
That would seem to be a contradiction in terms.metastable said:The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.
Ibix said:That would seem to be a contradiction in terms.
Bandersnatch said:But yes, the observable universe is a subset of some larger universe.
So? You are describing something that's not observable (because it's not part of the observable universe), but is observable (because of its effects). So it's observable and not observable. I don't think you actually have a consistent scenario here.metastable said:
Ibix said:So? You are describing something that's not observable (because it's not part of the observable universe), but is observable (because of its effects). So it's observable and not observable. I don't think you actually have a consistent scenario here.
It's not clear to me that this is a consistent model. If the black hole is eternal, then yes you can detect its gravity at any distance (in principle). However, such a universe does not have the concept of "observable universe". The observable universe is a concept in FLRW spacetimes, in which black holes may form but are simply a kind of extreme over-dense patch. They don't have a long-range gravitational effect different from any other kind of over-dense region.metastable said:Not observable via light (and also because it's a black hole)... but still observable via its gravity.
Gravitational waves (nitpick: gravity waves are a kind of surface wave on liquids) propagate at the speed of light. If we can observe them, we can observe light emitted at the same time.We can't "see" black hole mergers but we can measure the gravity waves.
Ibix said:However, such a universe does not have the concept of "observable universe". The observable universe is a concept in FLRW spacetimes, in which black holes may form but are simply a kind of extreme over-dense patch.
metastable said:The black hole in the scenario is sized in such a way that the effects it causes in the scenario are still detectable while the black hole itself is completely outside the observable universe.