The orbital eccentricity change of the Earth ?

[Bjarne]

Can someone answer one, some or all these questions;

• Is the orbit of the Earth right now getting more circular or more elliptical?
• How much?
• How can we be sure?

 

[Janus]

The eccentricity of the Earth's orbit is decreasing at a rate of ~-0.00004292/century.

 

[Drakkith]

Can someone answer one, some or all these questions;

• Is the orbit of the Earth right now getting more circular or more elliptical?
• How much?
• How can we be sure?

We can be sure based on observations and measurements coupled with predicted effects based on physics.

 

[Bjarne]

We can be sure based on observations and measurements coupled with predicted effects based on physics.

We can so far I know not measure the distance to the Sun because the Sun does not reflect radar.

So how accurate is “observation” ?

 

[lpetrich]

Very accurate, actually. The trick is not to observe the Sun directly, but to observe the other planets, and to find a self-consistent orbital solution from these observations that agrees with General Relativity. One can even test for departures from GR and for unmodeled mass.

Once one does that, one can extrapolate the planets' motions several million years both forward and backward. When one does that, one finds that the planets' orbit orientations do loop-the-loops, and that their eccentricities and inclinations oscillate quasiperiodically. This leads to Milankovitch climate cycles on the Earth and likely also on Mars.

In particular, I've plotted

Eccentricity / Runge-Lenz vector: {e*cos(w), e*sin(w)}
Inclination / north-pole vector: {sin(i)*cos(W), sin(i)*sin(W)}

for the last several million years.

I've made videos for YouTube:
http://www.youtube.com/my_playlists?p=D0825FC30A2F00A6
http://www.youtube.com/my_playlists?p=86F2CCA7F3F677ED

I got the numbers from here:
J. Laskar
"Secular evolution of the Solar System over 10 million years"
Astronomy and Astrophysics, 198, 341-362 (1988).
http://adsabs.harvard.edu/abs/1988A&A...198..341L

I had to OCR the numbers and then painstakingly correct the OCRing, so there might still be some typos.

 

[Drakkith]

We can so far I know not measure the distance to the Sun because the Sun does not reflect radar.

So how accurate is “observation” ?

There are direct observations that can be made to determine the distance to the sun. We don't need to reflect radar off of it.

See here for more info. http://curious.astro.cornell.edu/question.php?number=400
(Further down is how the 1st astronomers measured the distance to the sun)