Download The effect of planetary aberration examined for Jupiter occultation by

The effect of planetary aberration examined for
Jupiter occultation by the moon on 7-Dec-2004
Bart Leplae - [email protected]
27-Nov-2011
This paper describes the planetary aberration observed during the occultation of Jupiter by the Moon
on 7-Dec-2004 and provides evidence that light follows a curved path while travelling through the
Solar System.
Table of content
Detailed images of Jupiter Occultation on 7-Dec-2004........................................................................... 2
Detailed Image taken on 9:13:24 ............................................................................................................ 3
Positions calculated with Stellarium ....................................................................................................... 4
Observed versus calculated distances..................................................................................................... 4
Planetary Aberration ............................................................................................................................... 5
Relative position of Earth and Jupiter ..................................................................................................... 6
Calculation of Planetary Aberration ........................................................................................................ 8
Stellar Aberration .................................................................................................................................. 11
Occultation of Jupiter by the Moon ...................................................................................................... 12
Summary/Conclusion ............................................................................................................................ 13
Page 1
Detailed images of Jupiter Occultation on 7-Dec-2004
The following detailed image of the occultation of Jupiter by the Moon can be found on:
http://spaceweather.com/occultations/07dec04/parker1_huge.jpg
D. Parker, Coral Gables, Florida 25°39’5”N, 80°16’41”W
Page 2
Detailed Image taken on 9:13:24
Moon
Ganymedes
Europa
Jupiter
The planets of Jupiter Europa and Ganymedes can be observed as very faint dots.
The distance between Europa and the Moon = 35 arcsec
The distance between Jupiter and the Moon = 8 arcsec
The distance between Ganymedes and the Moon = 6 arcsec
Page 3
Positions calculated with Stellarium
For the coordinates: N 25° 39' 5.00" W 80° 16' 40.99" the Stellarium software calculates the following
positions (including light-time correction):
Observed versus calculated distances
Comparing the distances as measured on the photograph with the distances as calculated with
Stellarium:
Arcseconds to Moon Observed Calculated Difference
Europa
35
44
9
Jupiter
8
16
8
Ganymedes
6
9
3
Remark:


The distances Europa <> Jupiter, Ganymedes <> Jupiter match exactly between the observed
and calculated values.
The Stellarium Software was configured to take into account light-time correction
Page 4
Planetary Aberration
Arcseconds to Moon Observed Calculated Difference
Europa
35
44
9
Jupiter
8
16
8
Ganymedes
6
9
3
When we displace Europa, Jupiter and Ganymedes with 20arcsec towards the top of the ‘calculated’
picture (along the orbit of Jupiter), then the distances with the Moon match the observed values.
In other words: the observed values correspond with an aberration of light of around 20 arcsec.
(whereby Jupiter shows behind the actual position from where light departed)
Remark: Light reflected by from our moon is not subject to aberration (or at least only to a very
limited extent).
Page 5
Relative position of Earth and Jupiter
The Gravity Simulator software provides us with the following positions for
Earth and Jupiter on 7-Dec-2004:
Page 6
The relative positions of Jupiter, Earth as obtained from Gravity Simulator rotated with 16.4 arcsec:
X (km)
Y (km)
0 -146307037
760751578
293436327
0
0
Earth
Jupiter
Sun
6,00E+08
4,00E+08
Jupiter
2,00E+08
Sun
0,00E+00
0,00E+00
2,00E+08
4,00E+08
6,00E+08
8,00E+08
Earth
-2,00E+08
Direction Earth-Jupiter
Direction Sun-Jupiter
Difference
Degrees
30.0
21.1
8.9
Page 7
Calculation of Planetary Aberration
Building upon paper : “Stellar and Planetary Aberration Working Model”
http://www.gsjournal.net/Science-Journals/Essays/View/3383
The aberration of light (stellar or planetary aberration) is not just caused by a local effect taking place
near the observer (using the ‘walking in the rain’ analogy), but is primarily occurring while light
propagates through the Solar System.
The path followed by the light reflected by Jupiter can be simulated using the following algorithm:
-
-
Divide the path from Jupiter to the Earth in equal distances and determine the coordinates
For every coordinate, determine the distance to the Sun and calculate the speed that a
‘virtual planet’ would have on that exact location ( SQRT(G x Mass Sun / Distance to Sun))
Determine the tangent speed of this ‘virtual planet’ relative to the direction looking from
Jupiter to the Earth
Determine the difference between the tangent speed and the tangent speed of the next
coordinate
Light will show an incremental aberration that is equal to the difference in tangent speed
with the prior coordinate divided by the speed of light. (in other words: the same formula
that is normally used to calculate the effect of stellar aberration)
For every coordinate, maintain the cumulative aberration by adding the incremental
aberration to the cumulative aberration value obtained for the prior coordinate
As an extra element of information, calculate for every coordinate the distance between the
curve followed by light and the straight line between the Jupiter and the Earth
Page 8
Using the above algorithm, we obtain the following curve for the positions of Sun, Earth and Jupiter
on 7-Dec-2004:
Vtan (m/s)
Distance (km)
Aberration (arcsec)
25000
10
20000
5
15000
0
10000
-5
5000
0
0,E+00
2,E+08
4,E+08
6,E+08
-10
8,E+08
-5000
-15
-10000
-20
-15000
-20000
-25
The blue line (Vtan) represents the tangential velocity of the rotating medium.
The red line (Aberration) is the direction of light relative to the direction of a straight line connecting
Jupiter with the Earth.
Light that reaches the observer on Earth needs to depart from Jupiter with an initial deflection of
0.7arcsec. So the ‘cumulative aberration’ referred to above needs to start with a value of -0.7 arscec
at Jupiter in order for light to reach the observer on Earth. This is why the Distance (green) curve
initially raises above the axis.
Page 9
Comparison of relative positions with curve followed by light departing from Jupiter:
6,00E+08
4,00E+08
Jupiter
2,00E+08
Sun
0,00E+00
0,00E+00
-2,00E+08
2,00E+08
4,00E+08
6,00E+08
8,00E+08
Earth
Vtan (m/s)
Distance (km)
Aberration (arcsec)
25000
10
20000
5
15000
0
10000
-5
5000
0
0,E+00
2,E+08
4,E+08
6,E+08
-10
8,E+08
-5000
-15
-10000
-15000
-20000
-20
-25
For an observer travelling from Jupiter to the Earth (from right to left on the above diagrams):
- the aberration initially increases (Jupiter appears ahead of the true direction from where light
departed)
- when light reaches a point around 200,000km away from the sun, the aberration starts to
decrease to ultimately become negative and reach a value of -19.7 arcsec when reaching the
Earth (whereby Jupiter appears behind its true position).
Page 10
Stellar Aberration
For an observer on Earth looking to a star right next to Jupiter (using the same coordinates as
referenced above), the stellar aberration is -10.3 arcsec (knowing that the direction of the star is at
an angle of 30.1 degrees relative to the direction of the Earth’s movement through the Solar System).
The same star observed from Jupiter shows at 81 degrees relative to the direction of
movement Jupiter: this causes a stellar aberration of 8.7 arcsec (as observed on Jupiter).
Because the Earth and Jupiter move in opposite directions relative to the orientation of
the star, the stellar aberration as observed from the Earth and Jupiter work in opposite
directions.
The following diagram shows the aberration of light coming from a star right next to
Jupiter (as viewed from the Earth). An arbitrary value has been chosen to represent the
border of the Solar System. The border of the Solar System is where we start to observe
a tangential value.
Remark: At the “true border” of the Solar System: „magnetic bubbles‟ have been
observed that could be the result of turbulence caused by the rotating medium of the
Solar System interacting with the „static‟ medium of the Galaxy:
http://www.nasa.gov/mission_pages/voyager/heliosphere-surprise.html
Vtan (m/s)
Aberration arcsec
20
Jupiter
140000
Distance (km)
120000
100000
10
80000
60000
0
40000
20000
-10
0
0
1E+09
2E+09
3E+09
4E+09
-20000
-40000
-20
Light reaching the observer on Earth needs to have an offset of 122000 km relative to the straight
line that connects Jupiter with the Earth at the moment it enters the Solar System. (for our arbitrary
chosen boundary)
An observer travelling along with the light would observe an increasing amount of stellar aberration
when approaching the center of the Solar System. At a distance of 2.2E8 (measured along the X-axis),
the aberration attains a maximum value of 13.8 arcsec after which the aberration decreases to
ultimately become negative (-10.3 arcsec) by the time it reaches the Earth. (whereby negative means
that the aberration works in the opposite direction).
Page 11
Occultation of Jupiter by the Moon
Jupiter is observed to be occulted by the moon whereas Jupiter is still right next to the moon (as per
Stellarium which includes the effect of light-time, but excludes the effect of aberration)
As we don’t see the image of Jupiter superposed on the image of the moon, the Stellar/Planetary
aberration must have occurred before the light reached the moon.
Page 12
Summary/Conclusion
The aberration of light as described in: http://en.wikipedia.org/wiki/Stellar_aberration:
“At the instant of any observation of an object, the apparent position of the object is displaced from
its true position by an amount which depends solely upon the transverse component of the velocity
of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken
by the light on its path to the observer). The result is a tilting of the direction of the incoming light
which is independent of the distance between object and observer. “
The observation of Jupiter during the Occulation on 7-Dec-2004 shows that stellar aberration cannot
be explained as just a local and ‘apparent effect’.
If stellar aberration would only take place near the observer, then:
-
planetary aberration would need to have the same value as stellar aberration.
planets and stars would need to show superposed upon the surface of the moon
(for which we know that the aberration is minimal)
The amount and direction of Stellar aberration can be calculated by just taking into account the
velocity and direction of the Earth moving around the Solar System. The result of this calculation is
exactly the same when:
-
the aberration takes place throughout the Solar System
the aberration is an effect taking place locally near the observer
The amount and direction of Planetary aberration depends on both the velocity/direction of the
Earth and the observed planet.
More precisely: the aberration depends on the velocity/direction of the medium near the observed
planet. If the aberration would depend on the velocity/direction of the observed planet, then
Ganymedes (having a significant velocity relative to Jupiter) would need to be observed with a
different amount of Planetary Aberration (which is not the case as per the photograph included in
this paper).
The aberration of light is not only occurring while light is travelling through the Solar System. Certain
aspects of aberration such as Diurnal aberration (due to the rotation of the Earth about its own axis)
are local in nature and are a smaller effect on superposed on the effect described above.
Page 13