There exist people that doubt or doesn't believe or simply don't know that Earth orbits Sun. This web-site is done for those people.

My binocular visual observations of RZ Cas show movement of the Earth

RZ CAS is famous variable star, eclipsing binary or fotometric double star, in constellation of Cassiopeia. It is double star so that they orbit each other at about 1.195252 days period. RZ CAS rounds 305.6 cycles in one Earth's year. Eclipsings are easily observable visually by typical 10x50 binoculars. Minima are deep and fast which makes it possible to get reasonable minute-accurate minima even without special expensive equipments.

All you need are : eyes, watch, binoculars, star chart with magnitudes, ephemerides(predicted approx. minima times),notebook, pencil, CAREFUL PATIENCE and calculator.

I have been observing double star RZ Cas for over four years since 3 May 1997. Personally observed 39 single geocentric minima show such regular variation that man can get only one conclusion: Earth is moving.

Heliocentric point of view: Light time effect

The Earth orbits the Sun. Distance between the Earth and the Sun is 150 million kilometers (92 million miles). Light is not infinite fast but it has finite speed of light 0.3 million kilometers/s. So it takes (150/0.3/60) 8.31 minutes for light to travel from the Sun to the Earth.

RZ Cas is never behind the Sun but high up at about 50 degrees angle compared to Earth's orbit level. So light travel difference time between Earth and Sun is never greater than cos(50)*8.3 min = approx 5.3 minutes.

Situation can be visualized this way:

Fig.1. On 28 May every year the Earth is on the farthest point from RZ CAS point of view. Light pulses get to the Sun 5.3 minutes earlier than to the Earth.

Fig.2. On 28 November every year the Earth is on the closest point from RZ CAS point of view. Light pulses get to the Sun 5.3 minutes later than to the Earth. It means Observed values should be 5.3 less (O-C=-5.3) than expected from Earth citizen's point of view.

Respectively on 25 February and 30 August every year the Sun and the Earth are at the same distance from RZ Cas's point of view and light time difference is 0.

In fact if heliocentric hypothesis is right then minima times should be heaving back and forth approx. at 5.3 amplitude according to sine wave when someone observes RZ Cas minima on the Earth. On the other hand if geocentric hypothese is right and heliocentric hypothesis is wrong then minima times should not be waving on such yearly period at all. Only "small" random variation.

Observed-Calculated Values

Here we can see my personally observed 40 minima O-C values of RZCAS. Observed-Calculated (O-C) means observed versus (linearly) predicted. I have used 1.195252d as predicted period (Source was Kari Kaila: Tahtitaivaan opas, URSA (Finnish)). And On 3 May 1997 heliocentric minimum HelioJudianDate 50571.422971 was as starting zeropoint O-C for my graphs.
If minima happens for ex. 4.6 minutes later than predicted then it is marked O-C=+4.6 min.

TABLE1. Personally Observed Minima of RZ Cas in May 1997-Apr 2000
Date [ddmmyy] Time[hh.mm.des]+-acc[min] FINTIME (UT+2h) GeoJulianDate Geocentric O-C [min] Light-time delay [min] Heliocentric O-C [min] Cycles from first minimum
03.05.199700.14.0+-6m50571.426389+4.92-4.92 0.000
09.08.199700.25.0+-2m50669.4340 +0.64-1.84-1.2882
14.08.199723.49.6+-3m50675.4094 -0.65-1.32-1.9787
26.08.199722.41.5+-4m50687.3622 -0.38-0.25-0.6397
19.02.199820.14.4+-4m50864.2600 +0.41+0.50+0.91245
27.02.199800.23.4+-4m50871.4329 +2.44-0.17+2.27251
05.04.199801.42.1+-2m50908.4876 +5.09-3.34+1.75282
22.09.199823.41.6+-6m51079.4039 -1.70+2.12+0.42425
04.10.199822.33.0+-4m51091.3563 -1.93+3.07+1.14435
09.11.199819.07.6+-4m51127.2136 -2.22+4.99+2.77465
22.12.199819.52.3+-1m51170.2446 +0.62+4.78+5.40501
24.12.199800.28.1+-2m51171.4362 +4.72+4.73-0.01502
09.01.199918.08.6+-4m51188.1726 -0.52+3.86+3.34516
10.01.199922.46.7+-2m51189.3658 -3.58+3.78+0.20517
28.01.199921.06.6+-3m51207.2963 -1.13+2.46+1.33532
11.02.199900.40.3+-2m51220.4447 -0.22+1.32+1.10543
17.02.199900.06.1+-2m51226.4209 -0.24+0.78+0.54548
06.03.199922.26.6+-4m51244.3518 +2.82-0.87+1.95563
12.03.199921.53.2+-2m51250.3286 +3.61-1.42+2.19568
14.03.199902.32.0+-2m51251.5222 +1.24-1.52-0.28569
26.03.199901.25.2+-2m51263.4758 +2.81-2.54+0.27579
12.04.199923.45.2+-2m51281.4064 +5.37-3.86+1.51594
24.04.199922.40.2+-4m51293.36125 +8.74-4.55+4.19604
26.08.199901.13.4+-3m51416.4676 +2.17-0.38+1.79707
07.09.199900.01.7+-5m51428.4178 -1.17+0.71-0.46717
12.09.199923.29.5+-3m51434.39548 +0.82+1.24+2.06722
06.10.199921.13.8+-4m51458.30125 +1.87+3.19+5.06742
18.10.199920.01.6+-4m51470.2511 -1.97+3.99+2.02752
02.12.199901.24.7+-2m51514.4755 -1.89+5.25+3.36789
08.12.199900.48.6+-3m51520.4504 -3.80+5.19+1.39794
30.12.199917.48.2+-2m51543.1585 -6.30+4.44-1.86813
18.01.200020.53.1+-2m51562.28687 -0.01+3.26+3.25829
24.01.200020.08.8+-7m*51568.25611 -10.12+2.80-7.32834*
14.02.200003.59.5+-2m51588.58299 +0.81+1.06+1.87851
24.02.200022.09.3+-5m51599.33979 +0.15+0.07+0.22860
26.02.200002.52.0+-3m51600.53646 +2.18-0.04+2.14861
03.03.200002.17.7+-2m51606.51229 +1.57-0.59+0.98866
21.03.200000.35.2+-3m51624.44111 +1.62-2.19-0.57881
27.03.200000.03.0+-4m51630.41875 +3.61-2.68+0.93886
01.04.200023.29.8+-4m51636.39569 +4.60-3.15+1.45891

I omitted one point(*) from graphs. It was very cloudy sky and accuracy very poor. Normally man should not observe variable stars on such poor weather but I tried to look if it affects accuracy. It did.

These are not just my personal data anymore. First 10 minima points are reported to AAVSO, the rest are reported in Swiss Astronomical Society and appeared (and to appear) in BBSAG Bulletins. Closer look to my observations and links to my scientific observations of variable stars can be found at astrov.html.

Observed-Calculated Curves of RZ CAS minima

Here we can see observed minima in cycles vs O-C graphs. Blue spikes mark approximate typical (95%-)accuracy (+-3 minutes) of my minima observations.

Fig.3.Geocentric plot. Observed points (yellow dots) are plotted as they are seen from Earth. The blue sine wave is theoretical heliocentric light-time model to explain varying dots. Blue spikes show +-3 minute accuracy borders.

Remark how well dots fit to heliocentric explanation curve. Earth is really moving and minima pulses are really waving according to light time effect as it should.

Fig.4.Heliocentric plot. Points are plotted from Sun's (calculated) point of view. Light time effect is mathematically decreased from points and we can see here that dots fit reasonable well to mildly increasing line(slope). And most of them fit to the slope within 3 minutes accuracy. Slightly increasing slope means that RZ Cas has in recent years shown little longer period (1.195270d) than was predicted (1.195252d) in literature.

Some refinements: Actually you can see that arc of parabole would fit better than straight line. RZ CAS is making some very long period O-C. Fortunately it stayed quite constant for 4 years. Perhaps later I analyse for accurate, fit parabola and get good estimate of speed of light of distant star from my 39 measurements !

Doupter of heliocentricity should explain me how come it is possible:

  • -Light time effect period is about 365 days long
  • -Phase is about the same as heliocentrist would predict (On 28 Nov GeocentricO-C in minimum)
  • -Amplitude is about +-5 min


    My personal observations seem really show that
  • Light has finite speed.
  • The Earth is moving yearly orbit around the Sun.
  • Heliocentricity is right.

  • This article was written by Mr. Kari A.Tikkanen with Emacs-editor on 9 October 2000 in Oulu.
    (c) K.A.T. 2000.