<p>Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 years for Earth to undergo a full cycle. In periods of high eccentricity, radiation exposure on Earth can accordingly fluctuate more wildly between periods of perihelion and aphelion. Those fluctuations are likewise far milder in times of low eccentricity. Currently, the Earth's orbital eccentricity is at about 0.0167, which means its orbit is closer to being at its most circular.</p>

CC BY-SA 3.0
2018-04-07T07:08:15.730Z
I've just asked [Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?](https://astronomy.stackexchange.com/q/25806/7982)
uhoh
CC BY-SA 3.0
2015-08-14T05:18:44.543Z
2015-08-14T05:18:44.543Z
AnonDCX
<p>Since the late heavy bombardment, the Earth's orbit couldn't have changed much. After all, life has been here ever since. Most scientists think that the answer to the faint young sun paradox is a thicker CO2 atmosphere and not the Earth being closer in. In earlier solar system history, the Earth may have been "shepherded" in by Jupiter when it migrated closer.</p>

CC BY-SA 3.0
2015-09-15T05:17:04.640Z
2015-09-15T05:17:04.640Z
Jack R. Woods
<p>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. Further possibilities are: (c) Tidal torques from the Sun have increased the angular momentum of the Earth; (d) Radiation pressure from the Sun changes the orbit; (e) drag from the interplanetary medium slows the Earth.</p>
<p>Of these I think only (a) (in the early lifetime of the Earth) and (b) (again, mainly in the first hundred million years or so, but with some effect afterwards) are important.</p>
<p><strong>Early Collisions</strong></p>
<p>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.</p>
<p><strong>Solar Mass Loss</strong></p>
<p>It seems, from observations of younger solar analogues, that the mass loss from the early Sun was much greater than the modest rate at which it loses mass now via the solar wind (or by solar radiation). A review by <a href="https://arxiv.org/abs/0712.1763" rel="nofollow noreferrer">Guedel (2007)</a> suggests a mass loss rate over the last 4.5 billion years that increases as <span class="math-container">$t^{-2.3}$</span> (with considerable uncertainty on the power law index), where <span class="math-container">$t$</span> is time since birth, and suggests an initial solar mass between 1% and 7% larger than it is now.</p>
<p>Conservation of angular momentum a
means that <span class="math-container">$a \propto M^{-1}$</span> and Kepler's third law leads to <span class="math-container">$P \propto M^{-2}$</span>. <strong>Therefore the Earth's orbital period was 2-14% shorter in the distant past</strong> due to solar mass loss, but has been close to its current value for the last few billion years.</p>
<p>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.</p>
<p><strong>Tidal Torques</strong></p>
<p>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 &quot;bulge&quot; induced by the Earth applies a torque that increases the orbital angular momentum, much like the effect of the Earth on the Moon.</p>
<p>Quantifying this is difficult. The tidal torque on a planet from a the Sun is
<span class="math-container">$$ T = \frac{3}{2} \frac{k_E}{Q} \frac{GM_{\odot}^{2} R_{E}^{5}}{a^6},$$</span>
where <span class="math-container">$R_E$</span> is an Earth radius and <span class="math-container">$k_E/Q$</span> is the ratio of the tidal <a href="https://en.wikipedia.org/wiki/Love_number" rel="nofollow noreferrer">Love number</a> and <span class="math-container">$Q$</span> a tidal dissipation factor (see <a href="https://arxiv.org/abs/1206.0334" rel="nofollow noreferrer">Sasaki et al. (2012)</a>.</p>
<p><a href="http://astro.cornell.edu/academics/courses/astro6570/Tidal_evolution.pdf" rel="nofollow noreferrer">These lecture notes</a> suggest values of <span class="math-container">$k_E/Q\sim 0.1$</span> for the Earth and therefore a tidal torque of <span class="math-container">$4\times 10^{16}$</span> Nm. Given that the orbital angular momentum of the Earth is <span class="math-container">$\sim 3\times 10^{40}$</span> kgm<span class="math-container">$^2$</span>s<span class="math-container">$^{-1}$</span>, then the timescale to change the Earth's angular momentum (and therefore <span class="math-container">$a$</span> and <span class="math-container">$P$</span>) is <span class="math-container">$&gt;10^{16}$</span> years and thus this effect is <em>negligible</em>.</p>
<p>Edit:</p>
<p>Further effects that can be ignored are a changing radiation pressure from the Sun and drag from the interplanetary medium.</p>
<p><strong>Radiation Pressure</strong></p>
<p>The outward force on the Earth is roughly the solar flux at the Earth multiplied by <span class="math-container">$\pi R^2$</span> and divided by the speed of light. However, since the radiation flux is, like gravity, obeying an inverse square law, this simply reduces the effective strength of the solar gravity. Because the Sun is getting more luminous with time, by about 30% since it's early youth, then this should result in a weaker effective gravity and the Earth's orbit behaving like it orbits a correspondingly less massive star.</p>
<p>This is a 1 part in <span class="math-container">$10^{16}$</span> effect so can safely be neglected.</p>
<p><strong>Drag from the Interplanetary Medium</strong></p>
<p>The density at the Earth is of order 5 protons per cubic centimetre (though I can't immediately locate a reference for this much quote figure) and thus a mass density <span class="math-container">$\rho \simeq 10^{-20}$</span> kg/m<span class="math-container">$^{3}$</span>. The drag force is about <span class="math-container">$0.5 \rho v^2 \pi R^2$</span>, where <span class="math-container">$v$</span> is the velocity of Earth's orbit and <span class="math-container">$\pi R^2$</span> is the cross-sectional area presented by the Earth. The torque is then this multipled by <span class="math-container">$a$</span> and if assumed constant over billions of years would decrease the angular momentum of the Earth's orbit by 1 part in a billion - so this can safely be neglected.</p>

CC BY-SA 3.0
2018-04-07T09:37:53.247Z
Thank you.  Very nice detailed answer.  I didn't see this until today.
userLTK
CC BY-SA 4.0
2017-01-25T19:36:20.920Z
2022-11-16T20:19:46.573Z
2022-11-16T20:19:46.573Z
ProfRob
<p>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.   <a href="http://www.nasa.gov/topics/solarsystem/features/young-jupiter.html" rel="noreferrer">Article</a></p>

<p>and Uranus and Neptune may have switched spots <a href="http://news.nationalgeographic.com/news/2007/12/071219-planet-swap.html" rel="noreferrer">Article</a></p>

<p>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.</p>

<p>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?</p>

<p>Or any good summaries, also encouraged.    Thanks.</p>

<p>I also found this article, but it seems more theoretical than evidence based.   <a href="http://www.futurity.org/did-orbit-mishap-save-earth-from-freezing/" rel="noreferrer">http://www.futurity.org/did-orbit-mishap-save-earth-from-freezing/</a></p>

CC BY-SA 3.0
2015-07-13T13:50:10.473Z
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.
Andy
<orbital-migration>
How has the Earth's orbit changed over hundreds of millions or billion of years?
userLTK
# How has the Earth's orbit changed over hundreds of millions or billion of years?

(Asked by: username_0 on 2015-07-10)

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](http://www.nasa.gov/topics/solarsystem/features/young-jupiter.html)

and Uranus and Neptune may have switched spots [Article](http://news.nationalgeographic.com/news/2007/12/071219-planet-swap.html)

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/>

**Tags:** orbital-migration

> **Comments:**
> **username_1**: 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.  

---

## 3 answers

### Answer by username_5 on 2017-01-25. Score: 14 | Accepted answer

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. Further possibilities are: (c) Tidal torques from the Sun have increased the angular momentum of the Earth; (d) Radiation pressure from the Sun changes the orbit; (e) drag from the interplanetary medium slows the Earth.

Of these I think only (a) (in the early lifetime of the Earth) and (b) (again, mainly in the first hundred million years or so, but with some effect afterwards) are important.

**Early Collisions**

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.

**Solar Mass Loss**

It seems, from observations of younger solar analogues, that the mass loss from the early Sun was much greater than the modest rate at which it loses mass now via the solar wind (or by solar radiation). A review by [Guedel (2007)](https://arxiv.org/abs/0712.1763) 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 a
means that $a \propto M^{-1}$ and Kepler's third law leads to $P \propto M^{-2}$. **Therefore the Earth's orbital period was 2-14% shorter in the distant past** due to solar mass loss, but has been close to its current value for the last few 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.

**Tidal Torques**

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](https://en.wikipedia.org/wiki/Love_number) and $Q$ a tidal dissipation factor (see [Sasaki et al. (2012)](https://arxiv.org/abs/1206.0334).

[These lecture notes](http://astro.cornell.edu/academics/courses/astro6570/Tidal_evolution.pdf) 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*.

Edit:

Further effects that can be ignored are a changing radiation pressure from the Sun and drag from the interplanetary medium.

**Radiation Pressure**

The outward force on the Earth is roughly the solar flux at the Earth multiplied by $\pi R^2$ and divided by the speed of light. However, since the radiation flux is, like gravity, obeying an inverse square law, this simply reduces the effective strength of the solar gravity. Because the Sun is getting more luminous with time, by about 30% since it's early youth, then this should result in a weaker effective gravity and the Earth's orbit behaving like it orbits a correspondingly less massive star.

This is a 1 part in $10^{16}$ effect so can safely be neglected.

**Drag from the Interplanetary Medium**

The density at the Earth is of order 5 protons per cubic centimetre (though I can't immediately locate a reference for this much quote figure) and thus a mass density $\rho \simeq 10^{-20}$ kg/m$^{3}$. The drag force is about $0.5 \rho v^2 \pi R^2$, where $v$ is the velocity of Earth's orbit and $\pi R^2$ is the cross-sectional area presented by the Earth. The torque is then this multipled by $a$ and if assumed constant over billions of years would decrease the angular momentum of the Earth's orbit by 1 part in a billion - so this can safely be neglected.

> **Comments:**
> **username_0**: Thank you.  Very nice detailed answer.  I didn't see this until today.  

---

### Answer by username_2 on 2015-08-14. Score: 6

Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 years for Earth to undergo a full cycle. In periods of high eccentricity, radiation exposure on Earth can accordingly fluctuate more wildly between periods of perihelion and aphelion. Those fluctuations are likewise far milder in times of low eccentricity. Currently, the Earth's orbital eccentricity is at about 0.0167, which means its orbit is closer to being at its most circular.

> **Comments:**
> **username_3**: I've just asked [Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?](https://astronomy.stackexchange.com/q/25806/7982)  

---

### Answer by username_4 on 2015-09-15. Score: 4

Since the late heavy bombardment, the Earth's orbit couldn't have changed much. After all, life has been here ever since. Most scientists think that the answer to the faint young sun paradox is a thicker CO2 atmosphere and not the Earth being closer in. In earlier solar system history, the Earth may have been "shepherded" in by Jupiter when it migrated closer.


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