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SOLAR SYSTEM HISTORY

By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
This web page shows how gravitational interactions between Earth and other planet size bodies passing close to Earth cause mass extinctions on Earth.
 

THE PLANETS WITHIN THE SOLAR SYSTEM:
One of the major issues regarding solar system history is that the element mix comprising the rocky planets is different from the element mix comprising the sun. Unlike the sun, the planets contain a large fraction of heavy elements. It appears that the solar system planets are the result of orbital capture by the sun of reminants of at least one super nova. The fact that the planets largely share the same orbital plane suggests that the planets are of common origin.
 

The planets appear to be formed from molecules that gravitationally aggregated into bodies that were later captured by the sun. Initially the planetary bodies had linear momentum which caused them to deflect past the sun. Somehow these bodies lost kinetic energy, perhaps by interacting with the edge of the sun or something else, which energy loss trapped these bodies in an orbit around the sun.

The issue is that planet formation requires:
1. Aggregation of planetary molecules to form a body;
2. Movement of that body into proximity of the sun;
3. Loss of kinetic energy so that the body is captured in the sun's gravitational potential energy well.

In order to form a stable orbit generally there must be a third body involved that subsequently leaves the scene, possibly by direct collision with the sun, taking part of the body's original kinetic energy with it, so that the body is trapped as a planet in the sun's gravitational potential energy well.
 

AGGREGATION OF PLANETARY BODIES:
If stars form by gravitational aggregation of molecules, then planet size bodies will form the same way, especially in the vicinity of a super nova. Initially these bodies will have a high surface area to volume ratio and hence will radiate away the heat acquired by gravitational aggregation. Hence these bodies will have the same surface temperature as the cosmic back ground and will not be detectable via a radio telescope. If the bodies are far from a radiating star then they are also not detectable via an optical telescope. However, these bodies will move through space due to gravity.
 

DEFINITIONS:
Ru = radius of local universe
= 16.3 light years
 
N = number of stars in the local universe
= 51
 
G = Newtons gravitational constant;
= 6.674 X 10^-11 m^3 kg^-1 s^-2
 
Ms = mass of sun (assumed to be typical of other stars);
= 1.98892 X 10^30 kg
 
Rho = average density of matter in the universe before gravitational aggregation.
 

GRAVITATIONAL AGGREGATION TIME:
Consider the volume of space from which the sun acquired hydrogen via gravitational aggregation.
Newton's law of gravitation gives:
Ek = G Ms Mh / R
where R is the radius from the center of the sun to the hydrogen atom.

For speeds much less than the speed of light:
Ek = (Mh / 2) (dR / dT)^2
where:
T = time.

Combining these two equations gives:
G Ms / R = (1 / 2) (dR / dT)^2
or
dR / dT = - (2 G Ms / R)^0.5
or
- (R / 2 G Ms)^0.5 dR = dT
and integrating from state a to state b gives:
- [(Rb^1.5 - Ra^1.5) 2] / [3 (2 G Ms)^0.5] = (Tb - Ta)

In this case:
Rb = Rs
where Rs is the solar radius.
For Ra >> Rb this equation simplifies to:
(Tb - Ta) = [(Ra^1.5) 2] / [3 (2 G Ms)^0.5]
or
(Tb - Ta)^2 = [4 (Ra^3)] / [9 (2 G Ms)]

The average initial matter density in space was:
Rho = Ms / [(4 / 3) Pi Ra^3]
or
(4 Ra^3 / Ms) = (3 / Rho Pi)

Hence:
(Tb - Ta)^2 = [4 (Ra^3)] / [9 (2 G Ms)]
= (3 / Rho Pi)(1 / 18 G)
= 1 / (6 Rho Pi G)

Hence the time required to aggregare a body such as the sun is given by:
(Tb - Ta) = 1 / (6 Rho Pi G)^0.5

There are N = 51 known visible stellar systems within Ru = 16.3 light years from the Earth. Hence Ra is approximately given by:
4 Pi (16.3 light years)^3 / 3 = 51 (4 Pi Ra^3) / 3
or
Ra (51)^0.333 = 16.3 light years
or
Ra = 16.3 light years / 3.7084
= 4.395 light years

One light year is:
1 light year = 3 X 10^8 m / s X 8760 h / year X 3600 s/ h X 1 year
= 94.608 X 10^14 m

Hence:
Ra = 4.395 light years X 94.608 X 10^14 m / light year
= 4.1584 X 10^16 m

Thus:
(Tb - Ta) = [(Ra^1.5) 2] / [3 (2 G Ms)^0.5]
= [8.4798 X 10^24 m^1.5 X 2] / [3 (2 X 6.674 X 10^-11 m^3 kg^-1 s^-2 X 1.98892 X 10^30 kg)^0.5]
= (16.9597 X 10^24 s) / [3 X 16.293 X 10^9]
= 0.3469 X 10^15 s
= 0.3469 X 10^15 s / (3600 s / h X 8766 h / year)
= .01099 X 10^9 years
= 10.99 million years.
= aggregation time for the Sun.

Since the Earth is much smaller than the Sun the aggregation time for a body comparable in size to the Earth is small compared to 11 million years.
 

DARK MATTER AND DARK ENERGY:
Astronomical observations of the structure of galaxies indicate that the amount of non-luminous dark matter exceeds the amount of luminous matter by a considerable margin. The non-luminous bodies are likely gravitational "black holes". There is also an unexplained acceleration in the apparent rate of expansion of luminous matter which is currently attributed to unexplained "dark energy". However, there is no indication of either dark matter or dark energy within our solar system.
 

ORBITAL CAPTURE AND FAILED ORBITAL CAPTURE:
Consider a body moving towards the sun under the influence of gravity. This body will have an initial velocity component perpendicular to the line between it an the sun. If the body does not hit anything it will slingshot around the sun and head off into deep space.

However, if the body hits something or skins the edge of the sun, the body will lose kinetic energy and hence will be trapped in orbit by the sun's gravitational potential energy well. The kinetic energy lost will be absorbed by the sun and over time converted into solar radiation which is emitted into deep space.
 

TIDAL INTERACTION AND EXTINCTIONS:
The normal tidal interactions between Earth, the Moon and the Sun cause a twice daily tidal ocean level change of about 5 m as Earth rotates. Assume that millions of years ago Earth was in a stable orbit around the Sun. Now assume that another body of comparable mass to Earth passed sufficiently close to the Earth to cause a tidal interaction much stronger than the normal Earth-Moon tidal interaction.

Gravitational tidal interactions between the Earth and passing planet size bodies seem to explain many of the mass extinctions in the Earth's geologic record. All that is necessary for a mass extinction is a gravitational interaction that causes ocean tides that sweep over populated areas. Life forms located on high mountains or in suitably constructed ships might survive, but most crops and livestock would be wiped out. An Earth sized body passing at the same distance as the moon is more than sufficient to cause a massive tidal wave.

The astronomical evidence and the geological record both support the general theme of the biblical story of a massive flood during which Noah and the contents of his arc survived. Likewise, the biblical story of the parting of the Red Sea might have been due to another close passage of a planet sized body. There is an observational trick that a naked eye observer could use to determine that a planet size body is on a near collision course with the Earth.
 

PETM:
Carbon and oxygen isotope analysis of sediments shows that about 55 million years ago, during the Paleocene Eocene Thermal Maximum (PETM), the atmospheric CO2 concentration suddenly increased due to massive combustion of carbohydrates and fossil fuels. Much of this excess CO2 was absorbed by the oceans within a century. However, the atmospheric and ocean CO2 concentrations and the atmospheric temperature remained unusually high for over 200,000 years. The excess CO2 concentration in the oceans then gradually decayed over the next 300,000 years.

The PETM may have be triggered by a another star passing within 4 astronomical units of the sun or may have been the result of the brief emergence of a dominant life form, analogous to humans, that extracted fossil fuels for energy generation.
 

This web page last updated November 18, 2015.