OBSERVATION OF THE JUPITER SATELLITES



OBSERVATION OF THE JUPITER SATELLITES

In the year 1610 Galileo Galilei set his telescope to Jupiter and discovered four of its satellites (Io, Europa, Ganymede and Callisto). Later on Jupiter cloud pattern was recognized and observed with more advanced telescopes.

View of Jupiter through a telescope leaves a great impact and stimulates to observe Jupiter clouds or motion of its satellites by oneself. It is possible to observe the motion of Jupiter satellites even with a small telescopes or good binoculars. That is enough for estimate of the orbital periods of the satellites. With small instruments it is possible to record only the largest angular distance of the satellite from the planet. With larger telescopes (~60–80 mm diameter) and in good weather conditions it is possible to observe satellite transits across the disk of Jupiter and their eclipses. Satellites hide and come out from the shadow in a certain order. In order to achieve better accuracy observations have to be made with the same telescope. It is advised to set magnification of the telescope to be twice as big as the lens diameter measured in millimetres. The accuracy of observation time should be better than 10 seconds, and the reference frame must also be registered as possible precise.

By observing the Jupiter satellites it is possible to calculate speed of light, in a similar way like it was done by Dane O. Remer in the year 1676. He noticed the eclipse of Jupiter satellites and calculated that Io comes out from the shadow every 42h 28min. When he calculated time of eclipse for several months in advance, he observed and noticed that the satellites every time were late for 22 min. When he measured the difference of time he calculated the speed of light.

Scientists calculate the rotation periods tracing the planet (or satellite) surface features. But if they can’t see the surfaces features, they measure Doppler shift of the signal reflected from surface. Scientists calculate precise positions of the satellites for several hundred years in advance. Mass of the Jupiter and its density were also calculated by observing the Jupiter satellites.

For Jupiter disk observations it is better to have a telescope of larger diameter, about 150 mm and high magnification. With such telescopes amateurs can observe Jupiter clouds and register them. It is also possible to make their photos or just draw the clouds. In order to draw the clouds faster and easier it is necessary to prepare for the observation in advance. It is recommendable to cut 47 mm and 50 mm oval, and mark the surface details on it. View of the planet changes in 15 min. significantly, because of different speed of rotation of different zones and because of the fast planet rotation, therefore, estimated time for the sketch should be less than 10 min.

Once in 6 years, inclination of the orbits of four biggest Jupiter satellites coincides, and they are seen edge on from Earth. Then it is possible to observe satellites eclipsing each other. This phenomenon is very interesting for amateurs.

Amateur calculations of the orbital periods are not very important for science but facilitate increase of the observer skills.


MY OBSERVATIONS

I have carried out observations of the Jupiter satellites: Io, Europa, Ganymede and Callisto. Observations have been performed with the reflector “Alkor” (diameter of the mirror, 8 cm; magnification, 15 X ). I have carried out 40 observations in total. Each observation was documented and pictures of the satellite positions were drawn. Drawing of the positions of the Jupiter satellites was performed at the moments when location of the satellite is about the same. Then I calculated the time interval among the observations and derived a period. The orbital period, absolute and relative errors of calculations as well as final accuracies of the parameters were derived by averaging all available observations.

       Figure 1. Successive positions of the Ganymede observations. I-Io: G-Ganymede: C-Callisto.

In Figure 1 Ganymede is shown during two successive observations. It is nearly in the same position with respect to the Jupiter. First of all I calculated time interval which passed between these two observations of similar position of the Ganymede, and then derived a period. Then I improved average orbital period taking into account my previous observations of the Ganymede. At the second step I estimated absolute and relative errors of calculation. Finally, I evaluated an average accuracy, i.e. determined average period and its absolute error. Then I compared derived periods with the real periods. As it is shown below derived periods of all satellites coincide with the real periods within the error bars.


Observations performed in February 2001

Io observations were carried out:

from 2001.02.25, 21:50 to 2001.02.27, 21:11 (local time).

Europa observations were carried out:

from 2001.02.23, 20:06 to 2001.02.27, 19:25 (local time).

Ganymede observations were carried out:

from 2001.02.20, 21:06 to 2001.02.27, 21:11 (local time).

Callisto observations were carried out:

from 2001.02.10, 17:57 to 2001.02.27, 22:25 (local time).

Satellite

Calculated orbital period in days,     T cal.

Real orbital period in days,

T real

Absolute error of calculation in days, ΔT

Relative error of calculation,

εT (%)

Io

Europa

Ganymede

Callisto

1.89

3.97

7.04

17.0

1.77

3.55

7.16

16.69

0.12

0.42

0.12

0.31

6.3

10.6

1.6

1.8

1)       ΔT 1 =|T cal.1 -T real1 |=0.12 (days)         1)  εT 1 = ΔT 1 / T cal1. 100%=6.3 %

2)       ΔT 2 =|T cal.2 -T real2 |=0.42 (days)         2)  εT 2 = ΔT 2 / T cal2. 100%=10.6 %

3)       ΔT 3 =|T cal.3 -T real3 |=0.12 (days)         3)  εT 3 = ΔT 3 / T cal3. 100%=1.6 %

4)       ΔT 4 =|T cal.4 -T real4 |=0.31 (days)         4)  εT 4 = ΔT 4 / T cal4. 100%=1.8 %

Note. ΔT - absolute error of calculation; εT - relative error of calculation.

Observations performed in November 2001

Io observations were carried out:

from 2001.11.15, 7:05 to 2001.11.16, 20:23 (local time).

Europa observations were carried out:

from 2001.11.13, 6:56 to 2001.11.16, 22:23 (local time).

Ganymede observations were carried out:

from 2001.11.01, 6:45 to 2001.11.08, 6:45 (local time).

Callisto observations were carried out:

from 2001.11.13, 21:54 to 2001.11.30, 23:30 (local time).

Satellite

Calculated orbital period in days,     T cal.

Real orbital period in days,

T real

Absolute error of calculation in days, ΔT

Relative error of calculation,

εT (%)

Io

Europa

Ganymede

Callisto

1.50

3.56

7.00

16.9

1.77

3.55

7.16

16.69

0.27

0.01

0.16

0.21

18

0.3

2.3

2.4

1)       ΔT 1 =|T cal.1 -T real1 |=0.27 (days)         1)  εT 1 = ΔT 1 / T cal1. 100%=18%

2)       ΔT 2 =|T cal.2 -T real2 |=0.01 (days)         2)  εT 2 = ΔT 2 / T cal2. 100%=0.3%

3)       ΔT 3 =|T cal.3 -T real3 |=0.16 (days)         3)  εT 3 = ΔT 3 / T cal3. 100%=2.3%

4)       ΔT 4 =|T cal.4 -T real4 |=0.21 (days)         4)  εT 4 = ΔT 4 / T cal4. 100%=1.2%

Accuracy of measurements

Europa    T average =(T 1 +T 2 +T 3 +T 4 )/4=                

=(3.97+3.9+3.56+3.7)/4=3.78 (days)

ΔT E1 =|T average -T 1 |=|3.78-3.97|=0.19 (days)

ΔT E2 =|T average -T 2 |=|3.78-3.90|=0.31 (days)

ΔT E3 =|T average -T 3 |=|3.78-3.56|=0.22 (days)

ΔT E4 =|T average -T 4 |=|3.78-3.70|=0.08 (days)

ΔT averige =( ΔT E1 + ΔT E2 + ΔT E3 + ΔT E4 )/4=

=(0.97+0.90+0.14+0.70)/=0.70 (days)

T real =3.55 (days)

T averige ± ΔT averige =3.78±0.43 (days)

Io   T averige =(T 1 +T 2 +T 3 +T 4 )/4=                                                                                         

=(1.5+1.98+1.89+1)/4= 1.59 (days)

∆T I1 =|T average -T 1 |=|1.59-1.50|=0,09 (days)     

∆T I2 =|T average -T 2 |=|1.59-1.98|=0.39 (days)     

∆T I3 =|T average -T 3 |=|1.59-1.89|=0,30 (days)

∆T I4 =|T average -T 4 |=|1.59-1.00|=0,59 (days)

∆T averige = (∆T I1 +∆T I2 + ∆T II3 +∆T I4 )/4=

=(0,09+0,39+0,30+0,59)/4=0.3 (days)              

T real =1.77 (days)

T averige ± ∆T averige =1.59± 0,3 (days)

Ganymede  T averige =(T 1 +T 2 +T 3 +T 4 )/4=

=(7.00+7.04+7.90+7.90)/4=7.46 (days)

ΔT G1 =|T average -T 1 |=|7.46-7.00|=0.46 (days)                    

ΔT G2 =|T average -T 2 |=|7.46-7.04|=0.42 (days)                    

ΔT G3 =|T average -T 3 |=|7.46-7.90|=0.44 (days)                    

ΔT G4 =|T average -T 4 |=|7.46-7.90|=0.44 (days)                    

ΔT averige =( ΔT G1 + ΔT G2 + ΔT G3 + ΔT G4 )/4=                    

=(0.46+0.42+0.44+0.44)/=0.44 (days)                          

T real =7.1 (days)                                                              

T averige ± ΔT averige =7.46±0.44 (days)                               

Callisto  T averige =( T 1 +T 2 +T 3 +T 4 )/4=

  =(17.1+14+17+16.9)/4=16.25 (days)

ΔT C1 =|T average -T 1 |=|16.25-17.1|=0.85 (days)

ΔT C2 =|T average -T 2 |=|16.25-14.0|=2.25 (days)

ΔT C3 =|T average -T 3 |=|16.25-17.0|=0.75 (days)

ΔT C4 =|T average -T 4 |=|16.25-7.00|=0.65 (days)

ΔT averige =( ΔT C1 + ΔT C2 + Δ GC3 + ΔT C4 )/4=

=(0.85+2.25+0.75+0.65)/4=1.12 (days)

T real =16.69 (days)

T averige ± ΔT averige =16.25±1.12 (days)

T averige - calculated average orbital period.

ΔT - absolute error of period calculation.

ΔT averige - absolute error of calculated average orbital period.

T 1 ;T 2 ;T 3 ;T 4 - calculated orbital periods from different observations.

CONCLUSIONS

The orbital periods of the four Jupiter satellites determined from my observations coincide within errors of a method with real orbital periods. Therefore, I have proved that even with a small telescope and during a short period of observation accurate orbital periods of Jupiter’s satellites can be derived easily. Very interesting coherence of the Jupiter satellite motion is noticed: while Ganymede revolves one time around Jupiter, Europa does two times, and Io - four times.

Used literature :

CD: Red Shift 3

Book: Astronomija 1995m.; Vytautas Straizys, Aloyzas Pucinskas, Algimantas Azusienis.

Made by: Paulius Klyvis

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Lithuania Panevezys 2002