Stellar and Planetary aberration Working Model

Transcription

1 Stellar and Planetary aberration Working Model Bart Leplae Updated on 2-Dec-2011 (Org. 7-Apr-2011) This paper describes why we can observe stars that are actually behind the moon and provides an alternative interpretation of stellar and planetary aberration. 1

2 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 2

3 Stellar aberration true position (or geometric position) apparent position of a star Source: Wikipedia 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. 3

4 Stellar aberration Light appears to come from a location that is slightly ahead of the direction of movement of the Earth Diagram illustrating aberration of a star at the north ecliptic pole Source: Wikipedia 4

5 Stellar aberration 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) Source: Wikipedia Stellar aberration is the same for every star in a given region, regardless of its distance to the Earth 5

6 Stellar aberration 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) 6

7 Paradox Apparent position = 10 arcsec separated from the moon While True position = 10 arcsec behind the moon 7

8 Paradox How can a star that is behind the moon be visible? 8

9 Watch the paradox Search Google for Video s using the keywords: moon star occultation 9

10 Anomaly 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 Moves with speed of Earth 10

11 Explanation True position apparent position 1. Stellar aberration must be taking place, far before the light reaches the moon. static Medium Medium moves with speed of Earth Aberration due to difference in speed 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) Moves with speed of Earth 11

12 apparent position Rotating Medium Model True position Model introduced in paper: Working model Magnetism Gravity on: Bart Leplae Medium above and below the orbit of the Earth has the same angular speed as the Earth 12

13 Rotating Medium Model Stellar aberration is no different for the other planets (but is more pronounced for the inner planets) Medium rotates around the sun with the same speed as the planets 13

14 Rotating Medium Model In reality, this is a curve as the speed is lower for the outer planets True direction apparent direction Border of Solar System 14

15 Rotating Medium Model Border of Solar System The light goes in a curve. The curve is a function of the progressive difference in orbital speed while moving through the 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. 15

16 Rotating Medium Model 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) 16

17 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). 17

18 Planetary Aberration 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) 18

19 Planetary Aberration 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. 19

20 Planetary Aberration The calculation described on the previous page is elaborated in more detail on: The effect of planetary aberration examined for Jupiter occultation by the moon on 7-Dec-2004:

21 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. 21

22 Michelson Morley experiment Conceptual model used by MM: 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 Conceptual model with rotating medium: Through the MM experiment, the speed of light was observed to be the same from any direction Earth Sun 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. 22

23 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 23