For a published version of this work see the Paper:

The diagram at left shows the orbit of Mercury about the Sun. This diagram is not to scale and is cropped to bring out the elliptical nature of the Mercury orbit. In reality the orbit is closer to a circle.

Also, it should be noted that the precession of the ellipse orbit about the Sun is not shown. This is because it is very small at 0.43 arc sec per year.

The thing that puzzled astronomers in the past is that the Mercury ellipse rotated with respect to the earth (deviating from Kepler’s law). This phenomena was termed precession. Eventually, Einstein provided an explanation for this precession via his theory of general relativity which postulated that mass curves space-time. See this link for a general relativity accounting of the precession of Mercury.

I believe that there is another way to account for the precession of Mercury using the dark energy connecting Mercury and the Sun (see section 17 and section19) for more about dark energy and dark matter).

Basic ideas concerning the precession of Mercury’s orbit about the Sun:

1.  The concept of gravitons and dark energy mass are developed in section 17 and section 19 of this
website. This section will not make much sense without this background.

The mass of a single graviton connecting two masses is: h/dc
where h is the Planck constant, c is the speed of light, and d is the distance of separation.

The number of gravitons that connect two masses M1 and M2 is N:  N = M1M2/(PM2)

where PM is the Planck mass, c is the speed of light, and d is the distance of separation.

The amount of dark energy between two masses is MDE:  MDE = (h/dc)[M1M2/(PM2)]

2.  One orbit of Mercury about the Sun (360 deg) would be a constant (no precession) if there was no
dark energy present.

3.  The fundamental premise of this calculation is:
The dark energy between Mercury and the Sun causes an increase of the angular velocity of
Mercury. It now orbits the Sun at a slightly increased speed, causing an slight increase in the

orbit beyond the preceding 360 deg orbit. This action causes the orbit ellipse of Mercury to rotate
as a whole about the Sun at what has been measured as 42.99 arc sec for every earth century.

Here is a visualization: Mercury has a weight (the dark energy) tied to it with a string. The center
of gravity of this weight is positioned half way between Mercury and the Sun. This extra weight
wants to force Mercury inward increasing its velocity. This action unbalances the perfect ellipse
and causes a little more rotation of that ellipse that is seen as precession.

4. The equation to find the precession of Mercury about the Sun due to dark energy:

ΔDeg  =  Speed of MDE       =  (d/2)(Angular Velocity of MDE)

360        Speed of MMercury     (d)(Angular Velocity of MMercury)

Since the angular velocity of both MDE and MMercury are the same we get:

ΔDeg  =  (0.5)MDE    OR      ΔDeg = 180(MDE)/MMercury

360         MMercury

From step 1 above we have MDE = (h/dc)[MSunMMercury/(PM2)]

and ΔDeg = 180(MDE)/MMercury becomes  ΔDeg = 180(h/dc)[MSunMMercury/(PM2)]/MMercury
We can simplify further: ΔDeg = 180(h/dc)[MSun/(PM2)] = (180)(h)(MSun) / (d)(c)(PM2)

5. Putting numbers into the equation ΔDeg = (180)(h)(MSun) / (d)(c)(PM2)

“h” Planck constant:                                           6.62607 × 10-34

“MSun” Mass of Sun:                                           1.989 × 1030 kg

Perihelion (closest approach to sun):                 4.60 × 1010 m.
Aphelion (farthest distance from sun):                6.982 × 1010 m.

“d” Average distance of Mercury from the Sun:  5.791 × 1010 m.
“c” Speed of light:                                                2.99 × 10
8 m/s
“
PM” Planck mass:                                               2.176 471 × 10−8 kg
“
PM2” Planck mass squared:                                4.737 × 10−16

ΔDeg = [(180)(h)(MSun)] / [(d)(c)(PM2)]

= [(180)(6.62607 × 10-34)(1.989 × 1030)] / [(5.791 × 1010)(2.99 × 108)(4.737 × 10−16)]

= [2361.53 × 10
-4] / [82.0215 × 102] = 28.791 × 10-6

ΔDeg = 2.8791 × 10-5  deg for each orbit of Mercury     (We can convert degrees to arc sec and get)
ΔDeg = 0.10365 arc sec for each orbit of Mercury

ΔDeg = 0.10365 (365/88) arc sec for each orbit of Earth

ΔDeg = 0.4229 arc sec for each orbit of Earth

ΔDeg = 42.29 arc sec for each Earth century.

This is in close agreement with experiment and with Einstein’s calculation (42.98 arc sec).

6. So, is the concept of dark energy equivalent to Einstein’s curvature of Space-Time?

These two concepts seem so different. Yet, as demonstrated by this calculation of Mercury’s
precession they give the same result.

The dark energy concept has the advantage of having the quantum mechanical underpinnings of
the graviton as demonstrated in this section. It also can explain the accelerated expansion of the
universe as seen in section 19 as well as curving the path of Mercury. However, it remains to be
proven that this dark energy theory can account for the Eddington experiment showing that mass
curves the path of light.

General relativity has a lot of experimental evidence going for it. However, it has a two
shortcomings:

a. It is not connected to quantum mechanics. And so we have two major physical theories of reality
that are not connected. Many think this is esthetically unpleasing.
b. General relativity at present does not account for the accelerating universe that we are
observing.

It is the author’s belief that in the future the theory of dark energy presented here and the general
relativity curving of space-time theory will be shown to be identical. This will probably inspire
physics for many years to come.