### How has the Earth's orbit changed over hundreds of millions or billion of years?

• First, I know that modeling orbital mechanics of 8 planets is hard, but there are some theories out there, for example, Jupiter is thought to have moved in towards the sun then started moving away. Article

and Uranus and Neptune may have switched spots Article

Is there any pretty good evidence on how the Earth's orbit has changed over time. I remember reading some geological evidence that a year used to be longer, implying that the Earth used to be farther form the Sun, but I've since been unable to find that article, and for purposes of this question, lets count a day as 24 hours even though a day used to be quite a bit shorter hundreds of millions or billions of years ago. - footnote, I've still not been able to find that article but it occurs to me, it could have been counting shorter days, not longer years - so, take that part with a grain of salt.

Are there any good studies out there on how many 24 hour days were in a year, 100, 300, 500, 800 million years ago? or 1 or 2 billion years ago? Either geological or orbital modeling? Preferably something a layman can read, not something written by and for PHDs?

Or any good summaries, also encouraged. Thanks.

I also found this article, but it seems more theoretical than evidence based. http://www.futurity.org/did-orbit-mishap-save-earth-from-freezing/

A comment to clarify: I believe the usually quoted geological evidence is that the day length has increased, i.e. slower rotation of the Earth caused by tidal effects. (This evidence comes from daily growth marks in fossilised corals - there were around 400 days per year in the Devonian period.) So that particular part doesn't relate to Earth orbit changes.

6 years ago

What governs the Earth's orbital period is its orbital angular momentum and the mass of the Sun. Two events have certainly changed the Earth's orbital period (a) whatever collision formed the Moon and (b) the continuous process of mass loss from the Sun. A third possibility (c) is that tidal torques from the Sun have increased the angular momentum of the Earth.

Given that (a) probably happened sometime in the first tens of millions of years and likely did not alter the Earth's angular momentum greatly - it depends on the speed, mass and direction of the impactor and the amount of mass lost from the Earth-Moon system - I will ignore it.

(b). It seems, from observations of younger solar analogues, that the mass loss from the early Sun was much greater thanthe modest rate at which it loses mass now via the solar wind. A review by Guedel (2007) suggests a mass loss rate over the last 4.5 billion years that increases as $t^{-2.3}$ (with considerable uncertainty on the power law index), where $t$ is time since birth, and suggests an initial solar mass between 1% and 7% larger than it is now.

Conservation of angular momentum and Kepler's third law means that $a \propto M^{-1}$ and $P \propto M^{-2}$. Therefore the Earth's orbital period was 2-14% shorter in the past due to solar mass loss, but has been close to its current value for the last 2-3 billion years.

If the solar wind power law time dependence is very steep, then most of the mass loss occurred early, but the total mass loss would have been greater. On the other hand, a lower total mass loss implies a shallower mass loss and the earth spending a longer time in a smaller orbit.

(c)
The tidal torque exerted by the Sun on the Earth-Sun orbit increases the orbital separation, because the Sun's rotation period is shorter than the Earth's orbital period. The Sun's tidal "bulge" induced by the Earth applies a torque that increases the orbital angular momentum, much like the effect of the Earth on the Moon.

Quantifying this is difficult. The tidal torque on a planet from a the Sun is
$$T = \frac{3}{2} \frac{k_E}{Q} \frac{GM_{\odot}^{2} R_{E}^{5}}{a^6},$$
where $R_E$ is an Earth radius and $k_E/Q$ is the ratio of the tidal Love number and $Q$ a tidal dissipation factor (see Sasaki et al. (2012).

These lecture notes suggest values of $k_E/Q\sim 0.1$ for the Earth and therefore a tidal torque of $4\times 10^{16}$ Nm. Given that the orbital angular momentum of the Earth is $\sim 3\times 10^{40}$ kgm$^2$s$^{-1}$, then the timescale to change the Earth's angular momentum (and therefore $a$ and $P$) is $>10^{16}$ years and thus this effect is negligible.

Thank you. Very nice detailed answer. I didn't see this until today.