Stellar and Planetary aberration Working Model

Bart Leplae

Updated on 2-Dec-2011 (Org. 7-Apr-2011)

bartleplae@hotmail.com

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This paper describes why we can observe stars that are actually behind the moon and provides an alternative interpretation of stellar and planetary aberration.

Introduction • Bradley’s discovery of Stellar aberration explains:

– why stars appear up to 20.5 arc seconds from their true position

– how this displacement can be calculated as a function of the Earth’s orbital velocity

• Bradley assumed stellar aberration to occur near the observer, but this does not explain why we can observe stars that are actually behind the moon.

• An alternative explanation resolves the anomaly while maintaining the validity of the calculations

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Stellar aberration

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Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light, a phenomenon known as the aberration of light. Angle between apparent and true position is determined by the Earth's speed, divided by the speed of light, times the sine of the angle between the direction to the star, and the direction of the Earth's motion.

apparent position of a star

true position (or geometric position)

Source: Wikipedia

Stellar aberration

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Diagram illustrating aberration of a star at the north ecliptic pole

Light appears to come from a location that is slightly ahead

of the direction of movement of the Earth

Source: Wikipedia

Stellar aberration

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Diagram illustrating the effect of annual aberration on the apparent position of three stars at ecliptic longitude 270 degrees, and ecliptic latitude 90, 45 and 0 degrees, respectively Star appears to be up to 20 arcseconds “ahead” of true position. (adding up to 40 arc seconds over the course of a year) Stellar aberration is the same for every star in a given region, regardless of its distance to the Earth

Source: Wikipedia

Stellar aberration

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The apparent position of all stars surrounding the moon is displaced with the same amount and in the same direction (relative their true positions)

BUT the Moon is NOT Subject to stellar aberration. (because the Moon is moving with the Earth in nearly the same direction and at nearly the same speed)

Paradox

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Apparent position = 10 arcsec separated from the moon

While True position = 10 arcsec behind the moon

Paradox

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How can a star that is behind the moon be visible ?

Watch the paradox …

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Search Google for Video’s using the keywords: moon star occultation

Anomaly

10 Moves with speed of Earth

True position

Apparant position

A star that is behind the moon cannot become visible as a result of stellar aberration that would take place near the observer

Explanation

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Medium moves with speed of Earth

Moves with speed of Earth

True position

apparent position

1. Stellar aberration must be taking place, far before the light reaches the moon.

2. The location where stellar aberration occurs is where a medium that has the same speed as the Earth comes is in contact with a medium having a different speed (because the formula’s for stellar aberration prove to be valid and include the orbital velocity of the Earth)

“static” Medium

Aberration due to difference in speed

Rotating Medium Model

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Medium above and below the orbit of the Earth has the same angular speed as the Earth

apparent position

True position Model introduced in paper:

Working model Magnetism Gravity on:

Bart Leplae

Rotating Medium Model

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Medium rotates around the sun with the same speed as the planets

Stellar aberration is no different for the other planets (but is more pronounced for the inner planets)

Rotating Medium Model

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Border of Solar System In reality, this is a curve as the speed is lower for the outer planets

apparent direction

True direction

Rotating Medium Model

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The light goes in a curve. The curve is a function of the progressive difference in orbital speed while moving through the Solar System.

Border of Solar System

From the perspective of an observer on Earth, the difference between apparent and true position does not depend on this complex curve=> only the oribtal velocity of the Earth needs to be accounted for.

Rotating Medium Model

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The apparent direction of a star depends on the orbit and is different for every planet.

Apparent direction (observed from Earth) Apparent direction

(observed from Saturn)

Planetary Aberration

• Wikipedia: Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to the object's motion and distance). Both are determined at the instant when the moving object's light reaches the moving observer on Earth. It is so called because it is usually applied to planets and other objects in the solar system whose motion and distance are accurately known.

• More precisely: planetary aberration depends on the relative motion between source (planet) and observer (Earth). As a specific example, if the source and observer move with the same relative transverse velocity (e.g. moon), the aberration term is zero (and only light-time correction remains).

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Planetary Aberration

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Images of Planets don’t overlap with the moon ... Neither do they show a gap with the moon … So the same paradox applies. (according to Bradley’s model)

Planetary Aberration

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Planetary aberration depends on the relative motion between source (planet) and observer (Earth).

Apparent direction of Uranus (as observed from Earth) = Apparent direction of any star behind Uranus (as observed from Earth) minus (vector operation) Apparent direction of the same star (as observed from Uranus) In other words: to calculate the aberration for Uranus as seen from the Earth, the curve already described by the light travelling between boundary of Solar System and Uranus needs to be substracted.

Planetary Aberration

The effect of planetary aberration examined for Jupiter occultation by the moon on 7-Dec-2004:

http://www.gsjournal.net/Science-Journals/Research%20Papers/View/3802

The calculation described on the previous page is elaborated in more detail on:

Diurnal Aberration

• Wikipedia: Diurnal aberration is caused by the velocity of the observer on the surface of the rotating Earth. It is therefore dependent not only on the time of the observation, but also the latitude and longitude of the observer. Its effect is much smaller than that of annual aberration, and is only 0".32 in the case of an observer at the equator, where the rotational velocity is greatest.

• Diurnal Aberration is a ‘local / apparent’ effect (as described by Bradley) that adds upon the effect of annual Aberration which is causing a true displacement of the path followed by light coming from stars.

• In contrast with Stellar Aberration: Diurnal Aberration also applies to the light reflected by the moon. As a consequence: diurnal aberration will not allow an observer to see more stars that are actually behind the border of the moon since the observed star and border of the moon displace with exactly the same amount.

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Michelson Morley experiment

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Earth

Sun

According to Wikipedia: Light traveling along with the motion of the Earth would have a different speed than light traveling backward, as they would both be moving against the unmoving aether. Even if the aether had an overall universal flow, changes in position during the day/night cycle, or over the span of seasons, should allow the drift to be detected

Sun

Earth

If the medium rotates around the sun with the same speed as the planets, the speed of light is expected to be the same when measured from any direction.

Through the MM experiment, the speed of light was observed to be the same from any direction

Conceptual model used by MM:

Conceptual model with rotating medium:

Summary

• Stellar Aberration does not occur near the observer

• Stellar Aberration occurs while light propagates through of the solar system.

• Diurnal Aberration is a local effect adding upon the effect of Stellar Aberration.

• This Model of Stellar Aberration is consistent with the outcome of the Michelson Morley experiment

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