What does this technical term, gamma, mean in solar eclipses?

Question

I am an amateur star gazer especially obsessed by solar and lunar eclipses since my childhood, and just live, by chance, in a city within the band area from where the next annular eclipse in 20/May can be observed.

I have visited NASA eclipse website in order to check the latest information or enjoy reading articles about past or future eclipses.
I am wondering what the numbers expressed as "gamma" in their eclipse tables or charts mean. It is very hard for me to understand.

As for now I guess it perhaps expresses the relationship between the center of the earth and a hypothetical axis which imaginatively penetrates the center of the sun and that of the moon, or the relative positions of those three heavenly bodies, considering the facts such as:

1) the gamma of "one of the biggest total solar eclipses" that occurred in July 1991 being very small; minus 0.0041,

2) and the gamma of any of "pure" partial eclipses -without totality or annularity at any points on the earth-, possibly observed only from each of the polar regions, being relatively large; around 1.2 or so.


Then, my questions are:

1) What is gamma?

2) Is it possible for gamma to be exact zero?

3) If gamma is exact one, what does it mean?

4) What is the maximum gamma thinkable?

5) Gamma is sometimes negative number, while it is positive in other cases. Does this relate to whether the intersection of the sun and the moon is at the ascending node or at the descending node?


Is there anybody who explains these for me?

Answer 1

The answers already here are very good. One thing that hasn't yet been mentioned is that the "radius" used in the definition of Gamma is the equatorial radius of the earth.



I'm going to quote from a book rather than the web -- "Fifty Year Canon of Solar Eclipses: 1986-2035", by Fred Espenak (NASA Reference Publication 1178 Revised). Fred Espenak is one of the foremost experts on eclipses.



"Column 7 lists the value of Gamma, which is defined as the minimum distance of the shadow cone axis from the center of the Earth in units of equatorial radii. This corresponds to the instant of greatest eclipse. The sign of Gamma indicates whether the shadow cone axis passes north (+) or south (-) of the Earth's center."



(In this answer, I'll use the term "central eclipse" to refer to a solar eclipse that is total or annular, although this usage is a bit imprecise.)



As the sun shines on the moon, it casts a shadow into space. This shadow consists of the umbra (complete shadow) and penumbra (partial shadow). The umbra is shaped like a cone. The central axis of this cone is what is referred to above ("shadow cone axis"). This axis is along the line that passes through the sun and moon.



This sun-moon line can be extended infinitely through space. Gamma expresses how close the line comes to the center of the earth. A value of 0 means that the axis passes through the center of the earth, and 1 means that it roughly grazes the edge of the earth. (I say "roughly" because the earth is not exactly spherical. Gamma is defined in terms of the equatorial radius, while the polar radius is a bit smaller.)



Roughly speaking, you'll get a central eclipse if the absolute value of Gamma is less than 1, and you won't if it's greater.



Now I'll get to your specific questions.



1) See above.



2) Gamma could certainly be very close to zero. It's probably never exactly zero, because that would require a perfect sun-moon-earth alignment. (The probability of the centers of three astronomical bodies lining up exactly is infinitesimal, but a near alignment is possible.)



3) If the earth were spherical, a value of 1 would mean that the sun-moon axis exactly grazes the edge of the earth (north of the equator) at the instant of maximum eclipse. Because Gamma is defined at the moment of maximum eclipse, a value near 1 (or -1) applies to an eclipse that is seen only in or near the polar regions. For instance, there is an annular eclipse on 29 April 2014 with Gamma= -1.00020. This is visible only near Antarctica and southern Australia. On 31 May 2003 there was an annular eclipse with Gamma= +0.9959. This was visible only in the upper northern latitudes.



Roughly speaking, you get a central eclipse (annular or total) if the absolute value of gamma is less than 1 and a non-central eclipse (partial) if it is greater than 1; but the dividing point is not exactly 1. As I just mentioned, a value of -1.00020 yielded an annular eclipse. There are two reasons that 1 is not the exact dividing point. First, the earth is not exactly spherical. Second, because the sun and moon usually have slightly different angular diameters, you don't have to be exactly on the sun-moon line to see a central eclipse.



4) For extreme values of Gamma during eclipses, see the additional information to my answer below. In principle, you could calculate Gamma at any time, without regard for eclipses. At first- or third-quarter moon, the value of Gamma is roughly plus or minus 59.5 (=238000 miles/4000 miles).



In fact, a quick-and-dirty method of eclipse-predicting would be to write a program that calculates Gamma as a function of time. An eclipse occurs whenever the absolute value of Gamma gets relatively small.



5) No. Gamma indicates where the sun-moon line lies relative to the earth.



Regarding #5: Every eclipse season (nearly 6 months apart) alternates between the moon being at the ascending or descending node for solar eclipses. Consider the following two eclipses:

25 Feb 1971 Gamma = 1.1187

22 Jul 1971 Gamma = 1.5128



These eclipses occurred in successive eclipse seasons, but both had positive values of Gamma. The sign of Gamma is independent of whether the moon is at the ascending or descending node.



On the other hand, if two solar eclipses occur in the same eclipse season, they will have opposite signs of Gamma, because one occurs well before the moon passes the node, and the other occurs well after. For instance, this happens in 2018 (July 13 and August 11).



---



Here are some extreme values of Gamma:

annular eclipse: Gamma=1.0242 in year 2485

partial eclipse: Gamma=1.5706 in year 2893



The theoretical extremes are close to 1.0260 (central) and 1.5729 (partial).

Answer 2

It was a bit difficult to track this down when you didn't provide a link to a source but I believe I have found what you are referring to and it's answer. I'm assuming you mean the gammas listed in this table:



http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros128.html



If that is the gamma you were referring to, then the answer can be found here:



http://en.wikipedia.org/wiki/Gamma_%28eclipse%29



To sum up what the article states though, gamma is a number which represents how close the focus of the umbra is to pointing at the center of the earth. When the eclipse occurs, the umbra will focus to a point and we can calculate the distance from the center of the planet (imagine we extended the focus to go right through the earth). The distance is divided by the Earth Radius.



From that, a value of zero means that the umbra is focused directly at the center of the earth. A value of say, 0.5 means its halfway between the edge and the center. A value of 1 means the umbra just hits the edge of the earth. They use negative a positive values to refer to the northern and southern hemisphere. If the number is positive, the focus is north of the equator, and south if it is negative. If you see a value which is greater than 1, that means the umbra doesn't even hit the earth.



Hope that clears it up for you.

Answer 3

There's a good article about it here:



http://en.wikipedia.org/wiki/Gamma_(eclipse)



To briefly answer your questions:



1) It's the smallest perpendicular distance from the "axis of the shadow cone" (the line joining the moon and sun) and the center of the earth, expressed as a fraction of the earth's radius. The instant when the axis reaches this minimum distance is also called "the moment of greatest eclipse."



2) Yes. That basically means the axis of shadow cone passes right through the earth's center. Equivalently, it means that some observers will experience totality/annularity when the sun/moon are at zenith (directly over their heads)



3) It means the axis of the shadow cone just misses the earth's surface. Totality/annularity is limited to observers in extreme polar regions, and can only be seen when the sun/moon are near the horizon.



4) About 1.55. At that value, the edge of the penumbra just barely touches the earth's surface. At values approaching 1.55, the eclipse is only partial, is only visible in polar regions, only while the sun/moon are near the horizon, and looks like just the tiniest of bites taken out of the upper part of the sun's disk. At values greater than about 1.55, the moon's shadow misses the earth entirely, so it doesn't count as an eclipse.



5) Positive gamma means the shadow cone's axis passes north of the earth's center; negative means it passes south of the earth's center. It's not related to the moon's ascending/descending nodes.

Answer 4

"...Gamma is the parameter that gives the minimum distance (in Earth radii) of the shadow axis from the center of Earth during each eclipse. Gamma is positive or negative depending on whether the shadow axis passes north or south of Earth's center. Looking at any of the Saros catalogs (e.g., Saros 145) one can see how the value of gamma changes with each eclipse in a series. When gamma reaches its minimum (absolute) value, the series is then at its peak. In the case of Saros 145, the peak occurs with the eclipse of 2342 Mar 08 (gamma=0.008).



Since there are two to five solar eclipses every year, there are approximately forty different Saros series in progress at any one time. For instance, during the later half of the twentieth century, there are 41 individual series and 26 of them are producing central eclipses. As old series terminate, new ones are beginning and take their places. ..."



http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html