A new model showing the Solar System has expanded by 50% since its formation
and what it means for Mars, the Moon, and the Faint Young Sun paradox.

The Universe has been physically expanding for 13.8 billion years (the half-life of Thorium-232). The Solar System has been physically expanding for 4.6 billion years (the half-life of Uranium-238). For the purpose of this presentation let's refer to this Solar System Birth as the (SSB), which began when the Universe was 2⁄3 of its current size. Is the expansion of the Universe all‑encompassing? Let us consider what would happen if the Solar System expanded in the same way, increasing at the same rate. We can refer to it as the Local Hubble Expansion.

Won't the force of gravity override any expansion? Isn't our Solar System "gravitationally bound"? The "truly bound" structures are kept together by the electromagnetic force.
And no, gravity is not a force; it is a curvature of spacetime, and as the Universe expands, so does the curvature of spacetime. Note that the very small, photons themselves, obey the expansion of the Universe. Their wave packet length would also have lengthed by 50% since the creation of the Solar System.

SolarSystem Credit:Physics Astronomy

At the time of the formation of the planets, Mars was in the true Goldilocks zone as its semi-major axis was then 1.0 au. This is now Earth's orbit, when the Sun was 70% as bright as it is today. How does the Sun's distance affect each planet's sunlight? They would have received 1.52 = 2¼ more sunlight per area falling on the planet.

The following table shows the amount of solar energy that currently reaches the outer atmosphere of each planet. Consider the solar energy at the SSB. There are two factors to consider. The smaller size of the Solar System by one third as well as the faint young sun(fys) hypothesis. For example, Mars now gets 605 watts/m² but at the SSB the solar energy was 953 watts/m².

The planets of the Solar system

planet
 semi‑major axis
at the
SSB in au		 solar energy in watts/m² at the SSB adjusted for fys hypothesis solar energy in watts/m² at the SSB semi‑major axis
now
in au		 semi‑major axis
now
in log10 of au (linear)		 solar energy now in
watts/m²		 Increase of semi-major axis each year in metres
Mercury 0.258 20,446 14,312 0.387 -0.412 9,087 4
Venus 0.482 5,858 4,101 0.723 -0.141 2,604 8
Earth 0.667 3,062 2,144 1.000 0.000 1,361 11
Mars 1.0 1,361 953 1.5 0.176 605 16
Asteroids 1.83 405 283 2.75 0.439 180 30
Jupiter 3.469 113 79 5.203 0.716 50 56
Saturn 6.358 34 24 9.537 0.979 15 103
Uranus 12.794 8.3 5.8 19.191 1.283 3.7 208
Neptune 20.0 3.4 2.4 30.0 1.477 1.5 325

The Earth-Moon distance is now 384,400 km. At the Solar System Birth (SSB) it was at a distance of 256,267 km. Universe Expansion has increased it by 2.78 cm ⁄year. The observed increase of the Earth‑Moon distance is now 3.78 cm⁄year; The other 1.00 cm⁄year is due to gravitational interactions from Earth's ocean tides. This suggests that the increasing Earth‑Moon distance is ¼ tidal forces and ¾ universe expansion. Note that these computed values are not the result of a simulation, but use values widely accepted for universe expansion.

EarthMoonTides Credit:NASA

This Earth table goes back to the SSB describing the amount of sunlight reaching the planet.

The initial column shows certain events, such as when the Jovian planets form.

The second column shows how far back in time the period that we examine.

The third column shows the length of planet's semi-major axis in billions of metres.

The fourth column is the amount of calculated sunlight received with an increasing output from the Sun. According to the Faint Young Sun hypothesis, it is assumed to have a value of 70% at the SSB, and now has a value of 100%. Over this range we are assuming a linear increase in luminosity.

The fifth column is the amount of sunlight reaching the planet based on the increasing distance of the Sun due to the expansion of the Solar System.

The sixth column is simply multiplying the third and fourth columns to produce the effective sunlight. This shows that the effective sunlight was 57% greater at the SSB than it is today. That includes Mars as well.

The seventh column is the sunlight reaching the planet if the Sun's output was constant.

The eighth column has been adjusted, allowing for the amount of sunlight being emitted from a cooler Sun to a warmer Sun.

The ninth column has not been adjusted due to tidal forces, showing the Earth-Moon distance in millions of metres.

The tenth column has been adjusted due to tidal forces, showing the Earth-Moon distance in millions of metres.

Earth in an physically expanding Solar System

Earth Events Millions of years ago
 au in Gm (linear) Faint Young Sun hypothesis (linear) Expansion Factor (quadratic) Effective Sunlight Solar Energy with expansion and no Faint Young Sun Solar Energy with expansion and a Faint Young Sun Earth Moon distance in Mm ignoring tidal effects Earth Moon distance in Mm including tidal effects
Solar System Birth 4.6 100 0.700 2.25 1.575 3,062 2,143 256.3 210.2
Jovian planets form 4.59 100 0.701 2.245 1.574 3,056 2,142 256.5 210.1
Sun fuses Hydrogen 4.55 101 0.703 2.226 1.565 3,029 2,129 257.7 212.1
Hadean Terrestrial planets form 4.5 101 0.707 2.202 1.557 2,997 2,119 259.1 214.0
Hadean HCN arrives on Earth 4.4 102 0.713 2.155 1.537 2,933 2,091 261.9 217.8
Hadean LUCA appears on Earth 4.2 104 0.726 2.066 1.500 2,812 2,042 267.4 225.3
Archean Continents form 3.9 108 0.746 1.943 1.449 2,644 1,972 275.8 236.7
Archean Stromatolites 3.2 115 0.791 1.695 1.341 2,307 1,825 295.3 263.2
Archean Cyanobacteria 2.6 122 0.830 1.518 1.260 2,066 1,715 312.0 286.0
Archean Oxidation Events 2.4 124 0.843 1.465 1.235 1,994 1,681 317.5 293.5
Proterozoic Photosynthesis 1.75 131 0.886 1.312 1.162 1,785 1,582 335.7 318.2
Proterozoic Mitochondria 1.5 134 0.902 1.259 1.136 1,713 1,545 342.6 327.6
Proterozoic Snowball Starts 0.72 142 0.953 1.113 1.061 1,515 1,444 364.3 357.1
Proterozoic Snowball Ends 0.64 143 0.958 1.1 1.054 1,497 1,434 366.6 360.2
Phanerozoic Cambrian explosion 0.54 144 0.965 1.083 1.045 1,474 1,422 369.4 364.0
Phanerozoic The Present 0.00 150 1.000 1.000 1.000 1,361 1,361 384.4 384.4

The above table shows the solar energy under three scenarios.

The orange line graph shows what the solar energy would be if there was
Solar Energy with expansion and no Faint Young Sun.

The green line graph shows what the solar energy would be if there was
Solar Energy with expansion and a Faint Young Sun.

The blue line graph shows what the solar energy would be if there was
Solar Energy with no expansion and no Faint Young Sun.

The Mars table also goes back to the SSB describing the effects of the amount of sunlight reaching the planet, with different event points.

Mars in an physically expanding Solar System

Mars Events Billions of years ago
 au in Gm (linear) Faint Young Sun hypothesis (linear) Expansion Factor (quadratic) Effective Sunlight Solar energy watts/m² (cubic) Solar energy
Adjusted by Faint Young Sun hypothesis
Solar System Birth 4.6 150 0.700 2.25 1.575 1,328 930
Jovian planets form 4.59 150 0.701 2.245 1.574 1,325 929
Sun fuses Hydrogen 4.55 151 0.703 2.226 1.565 1,313 923
Terrestrial planets form 4.5 152 0.707 2.202 1.557 1,299 918
Extensive volcanism 4.0 160 0.739 1.983 1.465 1,170 865
Extensive water outflow 3.7 165 0.759 1.867 1.417 1,101 836
Slow iron‑oxidation 3.5 168 0.772 1.795 1.386 1,059 818
Loss of atmosphere 3.0 176 0.804 1.633 1.313 963 774
The Present 0.0 225 1.000 1.000 1.000 590 590

These are extraordinary claims. Yet, they acknowledge basic questions.

First, about the late start of life on Earth. At the time of genesis, the Earth was then closer to the Sun than Venus is now, possibly too hot for life to begin. Some theories suggest very cold, even freezing, conditions might have been beneficial for concentrating key precursors such as hydrogen cyanide (HCN) and promoting their polymerization into nucleic acid bases. Earth may have had to move further from the Sun so that the needed cooler temperatures could support life.

Second, this explains why Mars had a warmer and wetter atmosphere. It has features, such as riverbeds, lakebeds, and even ocean beaches, as well as a newly located vast underground reservoir of liquid water deep below its surface. This indicates a past climate in which temperatures were above freezing, allowing liquid water to exist on its surface.

Third, the no-expansion hypothesis does not match the historical increase of the Earth-Moon distance, whereas the expansion hypothesis gives exceptional agreement. The current rate of the Moon's recession is considered unusually high. Earth's geological past calculates the recession primarily through the analysis of tidal rhythmites and growth patterns in ancient fossils, which provide physical evidence for a shorter day length and a closer moon in the distant past.
This 1.00 cm/year figure is an estimate for the average recession rate of the Moon.

Fourth, this solves the Faint Young Sun paradox, first introduced in 1972 by Carl Sagan and George Mullen. As the Sun evolved, its brightness was 70% of what it is today. So, why was Earth not frozen? The expansion hypothesis resolves the paradox. It shows that the early Earth was closer to the Sun and actually received 1.575 times more solar energy per square metre hitting the Earth's upper atmosphere than today. This may have been too hot for a snowball Earth. As for Mars it started losing its atmosphere three billion years ago when its solar radiation was 30% higher than it is today.

Fifth, this is the reason for the outward migration of the planets. There is no need to explain the migration of Uranus and Neptune by postulating "gravitational attraction" by unspecified masses. There is also the Nice Model:The leading model for our solar system's evolution suggests the gas giants started in a more compact configuration (true). Jupiter, Saturn, Uranus and Neptune migrated significantly outward to their current positions, scattering a disk of planetesimals in the process. This model assumes that the inner rocky planets (Mercury, Venus, Earth and Mars) have also migrated outward at the same rate. That rate is the current(and constant) expansion of the Universe(the speed of light). The speed of light is not a speed limit. It is a direct consequence of universe expansion.

Citation
Leslie King, Heikki Sipilä 2022
Cosmological expansion in the Solar System

Citation
J.A.M. Green, M. Huber, D. Waltham, J. Buzan, M. Wells
Explicitly modelled deep-time tidal dissipation and its implication for Lunar history