Chris Peterson wrote:neufer wrote:Chris Peterson wrote:
The gravitational effect of the Earth on light is incredibly small.
The focus of light frequencies from the sun as they deferentially refract passing around the earth
due to gravity is ~15,000 AU away!
I was thinking of doing that calculation, but was feeling too lazy yesterday. Glad you did it (but I'm surprised it's actually so close... I was thinking it would come out in light years).
- If the Earth were only as dense as the Sun the minimal focus
would scale inversely with the Earth's size or ~ 109 x 550 AU.
Because the Earth is denser than the Sun the minimal focus is proportionately closer.
----------------------------------------------------------------------
- Newtonian Gravitational focus = b2/rs
Einsteinian Gravitational focus = 0.5 x b2/rs
Where b is the
impact parameter (which is greater than or equal to the body's radius)
And r
s is the
Schwarzschild radius (which roughly scales with the body's radius cubed)
----------------------------------------------------------------------
Chris Peterson wrote:
Were you considering light rays that are tangent to the surface? Those will be refracted much more strongly by Earth's atmosphere than by gravity, of course. The presence of an atmosphere adds a fair bit of complication to a ray tracing problem for sunlight around the Earth.
I was considering light rays tangent to
the Kármán line
where atmospheric refraction effects
quickly start to drop below the gravitational effects for light rays.
--------------------------------------------------------------------------------------
The average amount of
atmospheric refraction at the Earth's surface is 2x34 arcminutes.
The
average air density at 100 kilometers altitude
(i.e., the Kármán line) is about 1/2,200,000 the density on the surface.
Hence a simple estimate of atmospheric refraction at 100 kilometers altitude
(i.e., the Kármán line) is 1.85mas for a focus at ~5,000 AU.
--------------------------------------------------------------------------------------
Chris Peterson wrote:neufer wrote:
A better 'alternative gegenschein theory' might involve a possible concentration of particles at the
L2 Earth–Sun Lagrangian point.
I'm not sure I'd call that an alternative, though. The diameter of the gegenschein is much too large for L2 dust alone to explain it, and it clearly is part of the zodiacal light band structure. The nature of the scatter is well understood, as is the size distribution for the particles involved. The only real question around the effect of L2 is the degree to which captured dust in that region enhances the dust concentration and therefore slightly alters the brightness distribution of the gegenschein.
All five Earth–Sun Lagrangian points are just the centers of
broad relatively stable potential wells.
The L2 potential well is particularly broad (not to mention unstable) as viewed from Earth.
https://en.wikipedia.org/wiki/Lagrangian_point#L2 wrote:
A contour plot of the effective potential due to gravity and the centrifugal force of a two-body system in a rotating frame of reference. The arrows indicate the gradients of the potential around the five Lagrange points—downhill toward them (red) or away from them (blue). Counterintuitively, the L4 and L5 points are the high points of the potential. At the points themselves these forces are balanced.
(OTOH, any focusing of sunlight by the Earth's atmosphere would, indeed, be quite localized as demonstrated by the Moon's ability to generally avoid that particular dark red spot.)
An Airplane Glory
