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Earth's perihelion passed about nine hours ago. How accurately do we know the moment of closest approach of the Earth to the center of the sun? How do we make this measurement?

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Two things that we are really good at measuring in astronomy: time and angles. With respect to the sun and other planets, we can measure our relative orientation in the solar system to better than a milliarcsec ($8\times 10^{-10}$ of a circle). A year is $3\times 10^7$ sec, so we know passage of pericenter to about 0.02sec. This precesion can be built up even more by observations over many years (the greeks knew the average length of a month to much better than a second by comparing eclipse times separated by hundreds of years). Of course, all our atomic clocks keep absolute time much better than this, and in practice we know (because of these accurate astronomical measurements) that the earth rotation is not nearly so constant, so we often have to add or subtract leap-seconds.

EDIT: from radar ranging, we can actually measure our instantaneous location in the solar system to within 3m. With an orbital velocity of about 4.7km/s, that gives pericenter passage to better than a millisecond!

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I'm not sure about this 0.02sec figure. Measuring where we are would only give us that much precision if we also knew exactly where the pericenter is. My question isn't about how we measure the length of a year or measure our position relative to the other planets. It's about how we know where in our orbit we're closest to the sun. –  Mark Eichenlaub Jan 4 '11 at 17:50
    
Well, they all go into the same fit. If we don't know our orbit perfectly, the positions of the planets will be wrong, so by measuring the planets, we constrain our own orbit. I just looked up in Murray&Dermott the SS orbital elements. They list all longitudes of pericenter to 8 digits, so I bet I'm not far off. –  Jeremy Jan 4 '11 at 22:27
    
Okay. Thanks for the reference and info! –  Mark Eichenlaub Jan 5 '11 at 5:27
    
We know the Earth's orientation to .001 as, but the Earth's orientation has no effect on the time of perihelion. –  Nick Dec 13 '12 at 21:02

The time of perihelion is not measured by radar. The Sun is not a solid body, there is no single surface to reflect a signal. Radar measures the distance to the surface of a body, not to its center of mass, so the accuracy of radar is limited by our knowledge of the topography of the body. In practice, ephemerides are used.

An anomalistic year is the mean duration between two periapsis (or apoapsis) events. It is about 365.2596358 days. The Earth is offset from the Earth-moon barycenter by about 4674.9 kilometers, this causes the actual time of perihelion to vary by a few minutes compared that predicted by simple Keplerian motion. The relative orientation of the Sun and Jupiter is another significant perturbation.

The current JPL ephemeris predicts the Earth-Sun distance to within one kilometer. Given the velocity of the Earth at perihelion is 30286 m/s, that would imply the moment of perihelion is predictable to within 34 milliseconds.

After perihelion has occurred, measurements taken during the event, including radar ranging (of the inner planets), and VLBI, can be used to improve the accuracy.

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I'm pretty sure the current method of measuring solar-system scale distances is radar ranging. I don't know enough about the details of this for measuring the Earth-Sun distance. A first order estimate of the error in measuring the moment of closest approach would have to be something of the order of the 16 minute delay time in sending a signal from Earth and receiving a response on the Earth's surface from the reflection event at the Sun's surface. There might be subtle problems tied to the fact that the Sun doesn't have a solid surface, but we could certainly do radar ranging with several planets--triangulating the Earth-Sun distance using Mercury and Venus, for example.

and like Jeremy said, we could probably improve this time by using several years' worth of data.

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I think this is right--radar ranging is even better than astrometry. –  Jeremy Jan 4 '11 at 22:31

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