This paper considers the planets Neptune, Uranus, Earth, Venus, and Mercury.

If all the masses of the planets and satellites are added together and placed at an orbit distance of 5.3 AU from the Sun, then the force exerted by the sum of the masses at this distance equals the sum of the forces exerted on the Sun by the individual planets and satellites in their present orbits. The orbital velocity at 5.3 AU equals 12.9 km.sec^-1. An original single body would have had to have been at this orbit distance, moving at 12.9 km.sec^-1, at the commencement of its breakup if the Solar System as we know it came about solely from that body. That is, the Solar System has been a closed force system throughout its life.

Assume that at one stage of the breakup of the body there was Saturn and a body - protoJupiter - which contained all the masses and volumes of the other planets and satellites. Further, assume that the masses and volumes of the terrestrial planets formed one sphere within protoJupiter and the masses and volumes of Neptune and Uranus formed another, with the two internal spheres touching at the protoJupiter centre. Then the mass of the terrestrial sphere would have been 11.82x10²⁴ kg and its radius 8116 km, while the mass of the gaseous sphere would have been 189.6x10²⁴ kg and radius 32089 km. The ratio of the force exerted by sphere_gas to the force exerted by sphere_terrest. at their touching point can be shown to be 1.0261:1, i.e. the forces are in equilibrium.

If none of the six planets have since been impinged upon by any external force then the forces of the same bodies in their present orbits, when on a common radius from the Sun, must show the same force ratio within calculation error on a point at 5.3 AU from the Sun as determined above while lying within protoJupiter. And in fact a calculation will show the ratio of the sum of the forces of Neptune and Uranus to that of the sum of the forces of the terrestrial planets is 1.0046:1. That is to say, the assumption of internal breakup is supported.

Without explanation, I shall state here that the breakup of the two internal spheres being considered was as shown below after the removal of Mars and at the commencement of ejection of Uranus and Earth, i.e. from left to right Earth, Venus, Mercury, point X, Neptune, and Uranus; with point X at the centre of protoJupiter.

That the distribution shown in the figure was probable can be shown by again applying the argument of the Solar System being a closed force system. The ratio of the force of Earth to that of Uranus exerted on point X can be simply calculated and is 0.722. This is the same as the ratio of the force of Earth to that of Uranus on a point at 5.3 AU from the Sun when the three objects lie on the same radius from the Sun. And it should be if the force field of the developing Solar System has remained closed from formation.

How did the bodies move from 5.3 AU to their present distances from 5.3 AU? With fairly rapid separation of the internal bodies and movement outwards of the parts there would have been a partial void formed around the centre of protoJupiter. This would have been filled by inward collapsing material and an impulse force would have been created, acting outwards along the diameter on which the internal bodies lay. That such occurred is indicated by the following.

If such an impulse force developed then the impulse pressure exerted along the diameter should have decreased outwards closely as a straight line variation. This means that it is possible to determine the ratio of the impulse pressures for various distances measured from the centre of protoJupiter. The distances considered here are:

Uranus = (2x24750 + 26150) = 75650 km

Earth = (2x(2439 + 6050) + 6378) = 23356 km

Neptune = 24750 km

Venus = (2x24329 + 6050) = 10928 km

so ratio Uranus to Earth is 3.23900 and ratio Neptune to Venus is 2.26482.

M and R are known. The impulse velocity would have been very nearly the positive value of the present orbit velocity of the planet less the orbit velocity of protoJupiter (12.9 km.sec^-1), so that the impulse velocities were:

Neptune, 7.5 km.sec^-1; Venus, 22.1 km.sec^-1.

Here it is important to realise that there were at least two impulses at this stage of breakup, the first ejecting Uranus and Earth and the second (and greater) ejecting Neptune and Venus - followed almost immediately by Mercury.

The impulse pressures exerted on the four planets, calculated using the formula, are:

Uranus, 2.4589770x10¹⁷; Earth, 7.9080423x10¹⁷kg.km.sec^-1;

Neptune, 4.0141926x10¹⁷; Venus, 9.3596716x10¹⁷kg.km.sec^-1.

and the ratios required (the reciprocals of the previous) are:

Earth/Uranus = 3.2159887, Venus/Neptune = 2.3316449.

These are within 0.72% and 2.95% respectively of the distance ratios. The result thus supports the contention that a protoJupiter broke up as postulated to give the present lesser planets.

There is supporting evidence. Should the impulse direction have been at an angle to the diameter along which the internal bodies lay, no matter how slight the angle, then an impulse component would have been applied to the bodies in the plane containing the rotation axes. As a result, the rotation axes of the bodies would have begun to rotate in this plane until stopped by surface friction of the surrounding fluid body. It can be shown that the angle of rotation in this plane (the obliquity of the rotation axis) is proportional to the planet radius so that:

obliquity_A/obliquity_B = radius_A/radius_B for any impulse.

In the case of Uranus/Earth the radii ratio is 4.10003. Thus the inclination of Uranus should be closely 23.45^o x 4.10003 equals 96.15^o and this compares with a measured value of 97.92^o relative to the planet’s orbit plane. Various corrections can be made to the measured values but the final result, whatever obtained, still gives a near 4.1: 1 ratio as required.

Neptune/Venus is not so simple. The radii ratio is 4.09091 and the inclination of Venus’s rotation axis is given in the literature as 177.33^o = (180 - 2.67 )^o. But this value cannot be differentiated by observation from (180 + 2.67)^o = 182.67^o . Multiplying this latter figure by 4.09091 gives a value of 747.29^o , which is two whole revolutions plus 27.29^o. This compares with a value of 28.48^o measured from Neptune’s orbit plane and thus the radii ratio relationship is obeyed.

The tests given strongly support the contention that the lesser planets formed by the internal breakup of a larger body; that the origin of the planets Mercury, Venus, Earth, Uranus, and Neptune probably originated by internal breakup of a protoJupiter, which was internally differentiated and originally orbiting the Sun at a distance of 5.3 AU.