# Uncertainty in the distance between Sun and other planets

I have read about the orbit distances between Sun and the planets and have come to know for example: Earth is around 150 million km away from the Sun.

However I have seen that tht value is only an average radius of the orbit.

I however cannot find the uncertainty of this measurement.

I have considered the eccentricity of the planets and thought of using it to determine uncertainty.

So then I would have: Earth distance from Sun = $(150\times10^6\pm 2.5\times 10^6)km$. As Earth's eccentricity is around 0.017

So I am wondering if this would be the right way to determine the uncertainty of the radius of the orbit distance.

• For highly precise ephemeris information, see e.g. ssd.jpl.nasa.gov/horizons.cgi, for Keplerian elements ssd.jpl.nasa.gov/txt/p_elem_t1.txt, calgary.rasc.ca/orbits.htm. – CuriousOne Jun 12 '16 at 9:37
• This isn't quite what uncertainty means. There are basically two kinds of uncertainty in physics: measurement uncertainty and quantum uncertainty. Quantum uncertainty has to do with the fundamental limit on the accuracy with which we can know the value of certain observables, which is what the uncertainty principle, which you've used as a tag, is all about. Measurement uncertainty has to do with the finite precision of our measurement devices (or things like fitting models) and the way an error in one part of the measurement can affect the final result, calculable by error propagation. – Wouter Jun 12 '16 at 9:39
• I don't think the tag uncertainty-principle is appropriate here. – David VdH Jun 12 '16 at 9:40
• You seem to be interested in how strongly the orbits deviate from a circle. In that case eccentricity is in fact a good measure. Both the measurement and quantum uncertainties are different from what you seem to be looking for, so I would argue that not only the uncertainty-principle tag is inappropriate, so is the error-analysis one. If you do want to know what the uncertainty is on the measurements of the orbit distance, I think you should rephrase the question a little bit. – Wouter Jun 12 '16 at 9:43
• Planets do not move in circles but in elliptic orbits. Trying to find a radius will in some cases mean large deviations from the actual position - depending on where in the orbit, the planet is. You can start by googling the planet's largest and smallest distance to get a feel of how elliptical the orbit is. And then you can look at the average radius. Measurement uncertainty, then, is yet another talk... – Steeven Jun 12 '16 at 10:12

## 1 Answer

The variation in the orbital distance between aphelion and perihelion is not an "uncertainty" - it is certainly variable.

The ratio between aphelion distance and perihelion distance is $(1+e)/(1-e)$.

The NASA fact sheet http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html gives the eccentricity $e$ to 8 decimal places, so I assume (though I may be being pessimistic) that the orbital separation range is known to this sort of precision. However, it will also change from orbit to orbit depending on the positions of all the other planets, though this will be a second order effect compared with the overall eccentricity of the orbit. The bottom line is - how accurately do you need to know the number?

• I just need to know whether or not I can use eccentricity to determine the uncertainty of the distance between the Sun and the planets. Since Planets orbit in eliptical paths rather than the circular path, I would want to consider the uncertainty of the average orbital radius using eccentricity. – Itakura Jun 13 '16 at 9:21
• @KennyGuy Then yes, what you have done is ok, but it is not an "uncertainty", it is entirely predictable. – ProfRob Jun 13 '16 at 9:37