## sabato 15 dicembre 2018

### Philosophia Naturalis : A possible new proof of Earth's revolving motion around the Sun? by P. Pasqualucci

Philosophia  Naturalis :  A possible new proof of Earth’s revolving motion around the Sun?
by  Paolo  Pasqualucci

We all know the traditional proofs of Earth’s revolving motion around the Sun.  The scope of this short paper is to present the following hypothesis:  when the slightly elliptical orbit of the Earth is at perihelion (i.e. at its nearest point to the Sun), the Sun, as seen from the Earth, must appear slightly bigger than when the Earth is at aphelion, that is, at its farthest point from the Sun.  This difference in the apparent size of the Sun as seen from us, can be explained as proof of the fact that our Earth revolves around the Sun in a slightly elliptical orbit?
It might be useful  to recall the traditional proofs of Earth’s revolving motion.

1. Traditional proofs of Earth’s revolving motion around the Sun.

1. The measurement of the stellar  aberration ( 1725).
2. The measurement of the stellar parallax (1838).
3. The Doppler effect in measuring the line of sight velocities in stars.

Further evidence is also offered by the occasionally suggested following considerations:

a. The enormous disproportion between the mass and the radius of the Sun and the mass and the radius of the Earth.  The mass of the Sun amounts to :  1, 991030  Kg = 1,990 million of billions of billions of tons =  333,000  terrestrial masses. Its radius amounts to : 6, 96105 km = 0, 696 million of km = 109 terrestrial radiuses; that is, 696,000 km.  The radius of the Earth is :  6, 370 km; its mass: 6,000 billion tons.[1]  So we have that the diameter of the Sun measures 1,392,000 km while the diameter of  the Earth measures 12, 740 km only.
Compared to the mass and size of the sun, the earth is but a small dot.  Given these measurements, sizes and proportions, how could the much heavier and bigger body (the Sun) revolve around the incomparably lighter and smaller one (the Earth)?  How could a flea like the earth attract the colossal giant that’s the Sun so as to provoke the latter’s rotation around that flea?  A revolving motion of this type would be against the known laws of nature, which show, since Galileo’s time, that the little Venus revolves around the Sun and four little moons revolve around the massive Jupiter: they show that it is the small celestial body that revolves around the much bigger one, not the opposite.

b. The 23.5 degree t i l t  of the Earth’s rotation axis with respect to the plane of the ecliptic, main cause of the changing of seasons.  These two related phenomena would not be possible if the Earth were not revolving around the Sun.

c.  The trajectory of orbiting satellites.  The orbital motion of the Earth around the Sun is regularly used  as a parameter to successfully calculate the trajectory of the satellites launched by the earth.

d. The proven total absence of celestial spheres believed in the past to carry Sun and Planets embedded in them above and around the Earth.  Already the correct interpretation of the eccentric periodic motion of comets made this hypothesis untenable. In our times, we have seen that Space Probes launched from the Earth, like Voyager 1 for instance, though crossing the entire solar system and continuing to travel beyond it at a speed of 17.46 km/s, have never found trace of something like a celestial sphere or crashed into it.  Voyager 1 was launched on September 5, 1977 and is still operating after 41 years, 3 months and 6 days as of December 11, 2018.  On August 25, 2012 it left the Solar System advancing into the “interstellar medium”. As of June 4, 2018 it was at a distance of 142.31 astronomical units (21.289 billion km) from the Sun.[2]

2. Another proof could also result from the apparent difference in size between the two images of the Sun, as seen from the Earth, at perihelion and at aphelion?

We know that the orbit of the Earth around the Sun is almost a circle – an oblate ellipsoid the orbital mean eccentricity of which is 0.017 – so that its distance from the Sun isn’t always the same, as it should be if the orbit were a perfect circle.[3]  The mean distance of the Earth from the Sun is: 149.600 million km.  More specifically, it consists of about 147 million  km at its nearest point (perihelion, 1 to 5 January) and of about 152 million km at its farthest point (aphelion 2 to 5 July). The Earth’s mean velocity is calculated at 108,000 km/h, resulting in a mean velocity of 29.78 km/s: 30.29 km/s at the perihelion, 29.29 km/s at the aphelion.  Between the two mentioned  orbital points there is a difference of about 5 million km.  This fact should affect our image of the Sun. I mean, its size as it appears to us: at aphelion the globe of the Sun should appear to us slightly smaller than at perihelion.
Indeed, the difference is clearly shown by the accurate comparison of two photos of the sun, taken by dr. Peter Lowenstein, retired geochemist and skillful photographer, respectively at perihelion and at aphelion. From this ascertained fact we might conclude perhaps that the visual difference in the apparent size of the Sun from our standpoint, can be explained only admitting that the Earth revolves around the Sun. Such a further evidence of the motion of the earth, would confirm once more  Kepler’s first law (“All planets move in elliptical orbits, with the Sun at one focus”).
If the two images of the Sun were to appear perfectly equal in size, this might imply that the Earth’s orbit is perfectly circular and that Kepler’s first law does not apply to the Earth.
On the other hand, if the Sun were to revolve around the Earth, its image (I think) would equally appear to us to be always the same size:  there would not  be any perigee and ipogee, the equivalent of perihelion and aphelion applied to the (supposed) different positions of a Sun revolving around the Earth.   Indeed, given the enormous difference in their respective masses, we ought to exclude any gravitational attraction from the Earth to the Sun.  Therefore, the only possible hypothesis would be here that of the celestial sphere of the ancient cosmology: a sphere embedding the Sun and carrying it in its rotation around a totally motionless Earth, positioned at the centre of this same cosmic sphere.  As a consequence of such a motion, the image of the Sun, as seen from the Earth, should appear always the same in size because the rotational motion of such a cosmic sphere would not admit to any  inclination  on its axis, either towards the earth (perigee) or away from it (apogee).  But a resurrection of the ancient cosmological ethereal spheres is not possible, against the vast theoretical and empirical knowledge we now have of our heliocentric solar system and of the universe.
Dr. Peter Lowenstein has taken two photos, because of wheather conditions just few days from a perihelion, in January 2016, and from an aphelion, in July 2017.  Then he has created a “composite image” superimposing one photo to the other. The composite image shows “unmistakably” the size difference of the sun as viewed from Earth, across our yearly orbit.  You notice a “grey rim around the sun”, actually the perihelion photo on which the aphelion one has been superimposed.  The presence of the rim shows that, as seen in our sky, “the sun is about 3.6 per cent bigger at perihelion than aphelion, a difference impossible to be detected with the eye”.[4]

Paolo  Pasqualucci

Saturday, Dec 15, 2018

[1] Ester Antonucci, Dentro il sole [Inside the Sun], il Mulino, Bologna, 2014, pp. 16-17.
[2] Voyager 1, en.wikipedia.org/wiki/Voyager_1, p. 1/16.  The “astronomical unit” (AU)  is “a unit of length, formerly the mean distance of the Earth from the Sun, but now defined more tecnically”(Oxford Dictionary of Astronomy, 2nd ed. revised, 2012, entry: Astronomical Unit (AU), containing the more technical definition).
[3] “Eccentricity (e)  A measure of the shape of an orbit, or how far it diverges from a circle.  If e = 0, the orbit is a perfect circle. If e is less than 1 the orbit is an ellipse, and the nearer  e is to 1, the more elongated the ellipse.  If e = 1 exactly, the orbit is a parabola, and if e is greater than 1 the orbit is a hyperbola.  The orbit of the planets and major satellites are ellipses of small eccentricity.  Eccentricity is one of the elements of an orbit”(Oxford Dcitionary of Astronomy, entry: Eccentricity (e)).  The eccentricity of Earth’s orbit is very small, less than 0.02.  It is measured  at around  0.017 (Oxford Dict. of Astr., entry:  Earth).  For the data on the Earth, see also, among other popular science sources: Earth’s Orbit.en.wikipedia.org/wiki/Earth;  windows2universe.org/[…]eccentricity; How do we know that the earth revolves around the sun?/scienceline.ucsb.edu/getkey etc.(Question Date: 1998-01-08).

[4] Here’s how much smaller the sun looks at aphelion/Today’s Image, published by earthsky.org/todays-image/composite-image-size-of-sun- aphelion-perihelion,  two pages, published on July 9, 2018.  In the site www.eyes-on-the-skies.org/ Solar Robotic Telescope Oservatory, I have found the caption: Comparison of the Sun’s apparent size on our orbit far (aphelion) and near (perihelion) points, dated Jul 13, 2006, but the access to the content was denied to my old lap-top.