Are there any exact data about Earth's orbit?

Wikipedia says that the Earth's orbit's axis is $a=149\ 598\ 000\ \mathrm{km}$ and its eccentricity is $e=0.016\ 7086$, but if we use these values to find distance at aphelion and perihelion we get

• $A = 149\ 598\ 000 \times (1+e) = 152\ 097\ 753$, and
• $P = 149\ 598\ 000 \times (1-e) = 147\ 098\ 426$, whereas wiki says respectively:

• $A = 151\ 930\ 000$ and

• $P = 147\ 095\ 000$.

The reported figures are different and, also, the ratio of the figures is greater at

• A: 0.0166 than at
• P: 0.000023

Can you, please, explain this difference? what are the exact (current) values?

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• Maybe I'm being fussy, but to me the words accurate, precise and exact mean three different things... – Beta Nov 1 '15 at 18:10
• @Beta whats the difference? – bubakazouba Nov 2 '15 at 23:25

I generally regard NASA as authoritative, and they report the orbital parameters on their Earth Fact Sheet. I note that they disagree with Wikipedia about the aphelion though they agree on the perhelion, semi-major axis and eccentricity:

NASA    Wikipedia
Aphelion       152.10    151.93
Perhelion      147.09    147.095
Semi-major     149.60    149.598
Eccentricity   0.0167    0.0167086

Since the NASA figures are consistent I assume there is an error on the Wikipedia page.

Are there any exact data about Earth's orbit?

No. There are always measurement errors. There are however very good estimates. The best estimates come from three competing organizations, the Jet Propulsion Laboratory (the Development Ephemeris models), the Russian Institute for Applied Astronomy (the Ephemerides of the Planets and Moon), and the IMCCE (the INPOP models).

None of these use a Keplerian model. The eccentricity of the Earth's orbit varies from nearly zero to 0.06 thanks to perturbations from other planets.

If you want a good approximate model, I suggest you use the values from http://ssd.jpl.nasa.gov/?planet_pos , which for J2000.0 has the orbit of the Earth-Moon barycenter having a semi-major axis of 1.00000261 AU (149598261 km) and an eccentricity of 0.01671123.

The elements you give describe an idealised orbit that does not exist in reality. Those numbers are parameters to an approximate model. Earth's closest distance to the sun is different each and every year, by a lot (about 20,000 km in fact).

Are there any exact data about Earth's orbit?

There are certainly far better models than the 6-parameter elliptical one. Your best bet for very accurate positioning is an ephemeris like the JPL DE or VSOP. These models provide very long series with literally thousands of terms, which you must compute at a given point in time to get the value of a parameter. They supply such series for a wide range of orbital parameters in various coordinate systems and reference frames.

In particular, VSOP87 claims an accuracy of around ± 4 km for Earth – and this is one of the older ones. A basic elliptic approximation cannot come close to this, no matter what parameters you choose. I happen to have an implementation lying around, so I ran some numbers spanning the years 2001-2010, using the "Barycentric rectangular variables J2000" series. The code computes X, Y and Z for both the Sun and the Earth and then finds the distance between them. The numbers are:

Observe how variable these are. A perfectly elliptical orbit would have the same min and max every year, but the solar system is quite far from that.

Having said this, the average min/max distance agrees with NASA's values as provided by John Rennie, and not Wikipedia. If you wish to use the elliptical model, those are the better numbers to go by.