Reference: Disturbance Theory
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Problem: Celestial objects have apparent motion. (See https://en.wikipedia.org/wiki/Aberration_of_light )
What is true position of the celestial objects?
Mean Equator and Equinox of J2000.0: This coordinate system is oriented with its xy-plane parallel to the mean Earth equator at epoch J2000.0, and its z-axis pointing toward the mean north celestial pole of J2000.0. The x-axis points toward the mean equinox of J2000.0. This coordinate system is used for expressing the positions of stars in catalogs and planets in basic solar system ephemerides.
Right Ascension: Angular distance on the celestial sphere measured eastward along the celestial equator from the equinox to the hour circle passing through the celestial object.
Declination: Angular distance on the celestial sphere north or south of the celestial equator. It is measured along the hour circle passing through the celestial object.
Distance: The distance from the center of the Earth to the Solar System object, given in astronomical units (kilometers for the Moon). Distance is not calculated for stars.
Celestial Sphere: An imaginary sphere of arbitrarily large radius, concentric with Earth. All objects in the observer’s sky can be thought of as projected upon the inside surface of the celestial sphere, as if it were the underside of a dome or a hemispherical screen. The celestial sphere is a practical tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant.
Shouldn’t there be a motion?
The celestial sphere does not rotate with the earth. But it moves around the sun with earth. This may affect the observation of true position.
Annual aberration — a deflection caused by the velocity of the Earth’s motion around the Sun, relative to an inertial frame. This is independent of the distance of the star from the Earth.
Light-time correction is a displacement in the apparent position of a celestial object from its true position (or geometric position) caused by the object’s motion during the time it takes its light to reach an observer.
Is the aberration of light constant for all celestial objects?
It appears to be so for stars. For objects in the solar system their speeds become relevant.
Why is James Bradley’s (1729) explanation not adequate for the aberration of light?
Bradley conceived of an explanation in terms of a corpuscular theory of light in which light is made of particles that do not require a medium. His classical explanation appeals to the motion of the earth relative to a beam of light-particles moving at a finite velocity, and is developed in the Sun’s frame of reference. However, once the wave nature of light was better understood, a medium needed to be accounted for.
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.
Let a star be at distance ‘d’ from earth. Light takes time = ‘d/c’ to reach earth from the star. If earth is moving at velocity ‘v’, then it has moved a distance ‘v.d/c’ during the time star light reaches earth. The ratio of these two distances is ‘v/c’. This is the angle of aberration.
In SRF, the only motion visible is acceleration. Uniform motion is indistinguishable from ‘rest’. Earth is always accelerating toward the sun, so this motion shall be visble in SRF. Earth’s velocity ‘v’ is the result of balanced acceleration.
Light’s velocity ‘c’ is also the result of balanced acceleration. It is a limiting velocity. Light has velocity ‘c’ because it cannot be accelerated anymore.
The motion visible in SRF is balanced acceleration. So, the explanation given above for angle of aberration based on ‘v’ and ‘c’ shall be valid in SRF.
In SRF, the motion of planets shall be perceived as if they are moving in a groove carved in space. Light is moving, similarly, in a groove carved in space.
Conclusion:
James Bradley’s (1729) explanation for aberration of light became unacceptable in 1804 because light was established to be a wave. It was no longer looked upon as corpuscular as was assumed earlier by Newton. So, the medium of light (aether) became an issue.
In SRF (space reference frame), the aether is the space itself. From SRF point of view, the change in view of light from corpuscular to wave would not have created an issue in 1804 with the earlier 1729 explanation for aberration of light.
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