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In celestial mechanics, mean anomaly is a parameter relating position and time for a body moving in a Kepler orbit. It is based on the fact that equal areas are swept in equal intervals of time by a line joining the focus and the orbiting body (Kepler's second law).
The mean anomaly increases uniformly from 0 to radians during each orbit. However, it is not an angle. Due to Kepler's second law, the mean anomaly is proportional to the area swept by the focustobody line since the last periapsis.
The mean anomaly is usually denoted by the letter , and is given by the formula:
where n is the mean motion, a is the length of the orbit's semimajor axis, and m are the orbiting masses, and G is the gravitational constant.
The mean anomaly is the time since the last periapsis multiplied by the mean motion, and the mean motion is divided by the duration of a full orbit.
The mean anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. If the mean anomaly is known at any given instant, it can be calculated at any later (or prior) instant by simply adding (or subtracting) where represents the time difference. The other anomalies can hence be calculated.
Formulas[edit]
The mean anomaly M can be computed from the eccentric anomaly E and the eccentricity e with Kepler's Equation:
To find the position of the object in an elliptic Kepler orbit at a given time t, the mean anomaly is found by multiplying the time and the mean motion, then it is used to find the eccentric anomaly by solving Kepler's equation.
It is also frequently seen:
 ,
Again n is the mean motion. However, t, in this instance, is the time since epoch, which is how much time has passed since the measurement of M_{0} was taken. The value M_{0} denotes the mean anomaly at epoch, which is the mean anomaly at the time the measurement was taken.
See also[edit]
References[edit]
 Murray, C. D. & Dermott, S. F. 1999, Solar System Dynamics, Cambridge University Press, Cambridge.
 Plummer, H.C., 1960, An Introductory treatise on Dynamical Astronomy, Dover Publications, New York. (Reprint of the 1918 Cambridge University Press edition.)






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RealClimate 
RealClimate
Tue, 06 Jan 2015 07:02:18 0800
That means you need fewer data points to make a good estimate of the global value. The 2 \sigma uncertainty in the global mean anomaly on a yearly basis are (with the current network of stations) is around 0.1ºC in contrast that to the estimated ...
 The Guardian (blog) 
The Guardian (blog)
Mon, 05 Jan 2015 18:13:58 0800
... above average. This general trend is in line with preliminary estimates for global temperatures for 2014 from the World Meteorological Organisation, which suggest 2014 is likely to be the warmest year on record: Global temperature mean anomaly ...
 
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Mon, 01 Sep 2014 08:40:12 0700
The Mail on Sunday reports that Arctic summer ice is on the increase, disproving the "myth of Arctic meltdown". But the article, by journalist David Rose, acknowledges a declining trend in summer Arctic seaice. And scientists tell us the increase in ...
 Washington Post (blog) 
Washington Post (blog)
Fri, 02 May 2014 08:22:30 0700
April 2014 was a very variable month over the MidAtlantic region. We had periods of protracted dryness and wetness along with very cool weather including a trace of snow, while also reaching up into the middle 80s. For National Airport, it was the ...
 
Climate Central
Sun, 10 Nov 2013 10:04:36 0800
The Montreal Protocol, a treaty enacted in 1987 to protect the Earth's thinning ozone layer, has had the unintended benefit of helping to slow the rate of global warming since the mid1990s, according to a new study published Sunday. The study ...
 
Ecology Global Network
Fri, 26 Oct 2012 18:03:55 0700
We can see that in 1955, 1965, and 1975 temperatures throughout most of the globe were normal and the global mean anomaly was small: 0.09, 0.11, and 0.08 ºC. The situation between 20062011 is completely different. The maps are dominated by ...
 
The Conversation
Mon, 05 Aug 2013 06:40:08 0700
Michael Burrows receives funding from the UK Natural Environment Research Council. He is affiliated with the Scottish Association for Marine Science. Pippa Moore has received funding from UK Research Councils, the EU Marie Curie Actions, and ...

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