400 – Anatomy of a Solar Eclipse

A photograph of the total eclipse seen from Tokyo in 2012, featuring the Sun's corona and the famous "diamond ring".Orbiting Spheres

Right on cue, day turned into a sudden eerie twilight as a great swathe of the Earth’s surface quickly plunged into transient darkness.  The magic number is 400.  For many observers, weather conditions were far from ideal.  Clouds obscured the much awaited spectacle of the 2015 eclipse.  Thankfully, alternatives were available to astronomers keen not to miss the big event… 

A frame from the American series, The Simpsons. A newspaper headline: "Old Man Yells at Cloud".
Weather conditions did not play nice in Central Scotland…
A photograph from the solar eclipse of 20th March 2015. Image: NaturPhilosophie
The Sun finally emerges from the clouds and rain at the end of the eclipse.  Image: NaturPhilosophie

On the day of the partial eclipse, weather conditions did not play nice… but we are in Scotland after all.  And thanks to the Omni-present worldwide web, it now takes mere seconds to travel from the comfort of one’s sofa to even remote locations and be where the astronomical ballet of our familiar celestial spheres was at its most spectacular.


What is the Fuss about a Total Solar Eclipse?

A labelled photograph showing a total solar eclipse, with its accompanying features: the diamond ring, the corona and Baily's beads.Why do so many people get excited about watching the Moon photo-bombing the SunAs the Earth’s lunar companion comes between us and the Sun, astronomers have a unique opportunity to study its characteristics first-hand, so to speak, without the use of special telescopes and coronagraph equipment.

A photograph showing a solar eruptive prominence, compared to the relative size of Earth.
A solar eruptive prominence as seen in extreme UV light on March 30, 2010 with Earth superimposed for a sense of scale. Credit: NASA/SDO

A total solar eclipse provides a rare chance to see the Sun’s Corona – the solar outer atmosphere.

Prominences – large, bright, gaseous features extending outward from the Sun’s surface or photosphere, often in a loop shape – also become visible.

The Diamond Ring – a fleeting visual phenomenon that occurs during a total solar eclipse – is seen from Earth when standing in the umbra of the Moon’s shadow.

It occurs as part of Baily’s beads – glimmers of the Sun’s brilliant photosphere.


The Geometry of a Solar Eclipse

A diagram explaining the geometry of a total solar eclipse. It shows the orbits of the Earth and the Moon around the Sun, along with the zones of penumbra and umbra.
The Geometry of a Solar Eclipse

Once in a lifetime, at any given location, you get a chance to experience a full solar eclipse.  Nowhere else in the Solar system would this be possible.  This awe-inspiring phenomenon is due to an extraordinary cosmic set-up, the perfect coincidence which brings the Earth, the Moon and the Sun in an ideal alignment.  It does not end here.


An animation showing the shadow of the Moon travelling on the Earth during the Solar eclipse of 20th March 2015.

The magic number is 400.  For although the Moon is roughly 400 times smaller than our host star, the Sun is also around 400 times further away from than the Earth’s satellite.  This “accident” of cosmic proportions means that the Sun and the Moon’s angular sizes are virtually the same as seen from the Earth.


First Contact

During the public broadcast, you may have heard a media commentator refer to “1st contact” at the very start of the eclipse – ingress phase – or “4th contact” at the very end – egress phase.

Two diagrams showing the differences between a total and a partial eclipse of the Sun.
The key differences between a Total Solar Eclipse and a Partial Solar Eclipse.

As stellar discs appear limb darkened, with a maximum light intensity at their centre, the four contact points of a transit by a moon or planet across a star’s visible surface (in the present case, a solar eclipse) occur when one of the limbs of the planet or orbiting body crosses one of the limbs of the host star.


Transit Light Curves

The duration of the ingress phase, t1-2 (or egress, t3-4) depends on the radius of the occulting object and its orbital inclination relative to the plane of sight.

The impact parameter is the closest approach to the centre of the orbiting body’s visible disc to the centre of the disc of the star being occulted.  For central transits, the motion of the planet is along the normal to the limb of the star.  So the distance moved between first and second contact is a minimum.  For larger impact parameters, the motion of the orbiting body is at an angle to the normal to the stellar limb, and thus both the distance travelled and the elapsed time between first and second contacts are longer.

A graph showing the theoretical light curve of the Solar eclipse of 1999.
Theoretical light curve of the 1999 total solar eclipse. The brightness during totality is set to approx. 1/20000 of the full sunlight, the observed brightness during totality. Source: Wikimedia.org

Due to limb darkening, transit light curves are not generally flat-bottomed.

A transit light curve cannot alone help determine the absolute size of any orbiting bodies, such as that of distant variable stars, but it can provide useful ratios.  Combining Kepler’s third law with knowledge of the binary system’s total mass with values of a star’s mass and radius – inferred from the host star’s spectral type – allows for the period of rotation and the orbiting bodies’ separation to be deduced.

During the 2015 event, the total eclipse, as observed from the Faroe Islands and Svalbard, lasted almost three minutes.


Impact on European Power Grids

Solar energy is on the rise.  Over the past decade, the amount of solar photovoltaic (PV) capacity in the United States has increased more than 120-fold – from 97 megawatts in 2003 to over 12,000 megawatts at the end of 2013.  In the first quarter of 2014, solar energy accounted for 74% of all the new electric generation capacity installed in the United States.

Last October, we caught a glimpse of how a solar eclipse can affect a region teeming with solar panels.  The Western United States includes several of the top solar states in America – Arizona, California, Colorado, Delaware, Hawaii, Massachusetts, Nevada, New Jersey, New Mexico and North Carolina. Its Sun-fuelled energy portfolio continues to expand, including large-scale solar arrays as well as customer rooftops. So when a partial eclipse obstructed 30% to 50% of the Sun on the afternoon of 23rd October 2014, the Western power grid was significantly impacted. Utility-generated solar electricity production plunged between the hours of 1:45 pm and 4:30 pm, before returning to a typical late-afternoon pattern.

Rooftop solar systems responded similarly. Electric usage data from a sample of 5,000 solar homes in Opower’s database shows that their shipment of excess power to the grid – indicated by negative electricity usage in the chart below – rapidly contracted during the eclipse. Solar customers exported 41% less electricity than usual between 1:45 pm A graph showing the effect of a solar eclipse on the US power grid on 23rd October 2014. The average grid electric use by western US solar homeson day of partial eclipse: Actual electric use versus Projected electric use in kilowatt-hours per household. During the eclipse, solar homes sent 41% less electricity than normal to the grid.and 4:30 pm

As the electricity produced by renewables like solar and wind continues to grow, the grid will inevitably see larger swings in power production.  That is why flexibility measures like fast-ramping power plants, adjustments to customer energy behaviour, dynamic power pricing, energy storage, and a range of other strategies represent a critical dimension of the power grid’s evolution to meet the needs of the 21st century.

Although Germany is no bigger than the state of Montana, it boasts more than a quarter of all the solar electric capacity installed on Earth.  Its 1.4 million solar energy systems produce nearly 7 percent of the nation’s electricity.  In the U.S., solar provides only about 0.5 percent.  And during the sunniest hours of the year, photovoltaic systems have satisfied up to half of Germany’s power demand.

A graph showing the expected solar electric output in gigawatts in Germany on 20th March 2015. Germany's eclipse is poised to cause a rapid decrease in solar power supply, followed by a rapid increase.
Modelled values assume clear sky conditions. Edited from Source: www.greentechmedia.com

Between 9:30 am and noon on 20th March 2015, Germany’s 1.4 million solar power systems were predicted to be in for a wild ride.  In the span of 75 minutes, the Moon went from occluding 1% of the Sun’s glow to 73%.  Solar production fell fast – up to 2.7 times faster than it normally does, according to an analysis by the University of Applied Sciences in Berlin.  The effect was similar to turning off a medium-sized power plant in Germany every minute for a full hour.

The reverse was also true.  As the Moon receded from blocking 73% of the Sun to blocking none of it, solar power output sky-rocketed by as much as 18 gigawatts in just over an hour – up to 3.5 times faster than usual.

If you missed it, for whatever reason, here is the total eclipse of the Sun, in all its glory, as seen from Svalbard…

What’s Next?

The next total eclipse of the Sun will be visible next year on 9th March 2016.  And I have been led to believe that one of the best places to observe it will be the Yosemite National Park, in California.

Should any one of my regular readers – most of whom are based in the United States – wish to invite me over for such a momentous occasion, I’ll be sure to get organised!

Hey!  You don’t ask, you don’t get… right?