Unexpectedly Intriguing!
04 May 2018
NASA/Solar Dynamics Observatory - HMI Intensitygram - colored - 20180502 - Courtesy of NASA/SDO and the AIA, EVE, and HMI science teams - https://sdo.gsfc.nasa.gov/assets/img/latest/latest_1024_HMIIC.jpg

"Sunspots are becoming scarce. Very scarce."

That's how Dr. Tony Phillips of Spaceweather.com introduced an article earlier this week on the approaching solar minimum, the point of the sun's average 11-year cycle when the number of sunspots visible on the surface of the star typically falls to their lowest levels when compared to other points of time during its cycle. 2018 has been somewhat unusual in that the sun's surface has been nearly entirely clear of sunspots during a large portion of the year-to-date.

So far in 2018 the sun has been blank almost 60% of the time, with whole weeks going by without sunspots. Today’s sun, shown here in an image from NASA’s Solar Dynamics Observatory, is typical of the featureless solar disk.

The fact that sunspots are vanishing comes as no surprise. Forecasters have been saying for years that this would happen as the current solar cycle (“solar cycle 24”) comes to an end. The surprise is how fast.

“Solar cycle 24 is declining more quickly than forecast,” announced NOAA’s Space Weather Prediction Center on April 26th.

When the number of sunspots declines to the low levels associated with solar minimums, the sun's irradiance, or energy output, also declines and the sun dims, which might at first seems counterintuitive. How can the absence of comparatively dark spots on the sun's surface lead to a decrease in the sun's light output?

The answer is because when the sun's surface is pockmarked with sunspots, it is also pockmarked with "faculae", which are bright spots on the sun's surface whose increased light output more than offsets the effects of the relatively darker sunspots on the sun's overall luminosity, making the sun brighter overall.

During a solar minimum however, the number of both sunspots and faculae decline, where the sun's energy output declines by about one tenth of one percent below the amount of light that the sun emits during solar maximums, when the number of sunspots and faculae are at the highest levels of the 11-year solar cycle.

We wondered just how much less energy that would mean arriving at the Earth. So, we built a tool to find out!

The key parameters that we need to do the math is the sun's total power output (or luminosity, which is 3.828 x 1026 watts) and the average distance from the Sun to the Earth (149,587,000,000 meters). We've plugged those values as the default values into the tool below, where we've also added a percentage adjustment factor to account for changes in the sun's luminosity, which we've set at 0.0%. Let's run the numbers (if you're accessing this article on a site that republishes our RSS news feed, please click here to access a working version of the tool at our site).

Solar and Astronomical Data
Input Data Values
Total Solar Power Output, or Luminosity [1026 Watts]
Percentage Adjustment for Solar Output [%]
Distance from Sun to Planet [109 meters]

Solar Energy Irradiance (or Insolation)
Calculated Results Values
Solar Energy at Distance from Sun [Watts/square meter]

For the default values, we find that the maximum amount of insolation, or solar irradiance, that can reach the Earth at its average distance from the is 1,361.4 Watts per square meter [W/m²]. That's not the same as the amount of solar energy that will actually reach a given square meter on the Earth's surface, where factors like the atmospheric conditions, the curvature of the Earth's surface, where the Earth is in its orbit, the tilt of the Earth's axis, et cetera, will directly impact that value, but this is a decent reference value for considering the amount of total solar energy that can make it out to the Earth from the Sun.

If we change the Percentage Adjustment for Solar Output to -0.1%, we find that the Earth's insolation value drops to 1,360.0 W/m². That may not seem like very much, but Phillips puts that small change into perspective:

A change of 0.1% may not sound like much, but the sun deposits a lot of energy on the Earth, approximately 1,361 watts per square meter. Summed over the globe, a 0.1% variation in this quantity exceeds all of our planet’s other energy sources (such as natural radioactivity in Earth’s core) combined.

That 1,361 W/m² figure assumes that the Earth is at its average distance from the sun. Because the Earth's orbit is elliptical however, it can be as close as 147.1 billion meters to the Sun (as it was on 3 January 2018), or as far away as 152.1 billion meters from the Sun (as it will be on 6 July 2018).

Earth Distance to Sun During Year - Source: TimeandDate - https://www.timeanddate.com/astronomy/perihelion-aphelion-solstice.html

Changing the distance between the Sun and the Earth has a bigger effect on the maximum amount of solar energy that might reach the Earth. Resetting the percentage adjustment back to 0.0% and entering the Earth's minimum distance from the sun boosts the amount of solar irradiance up to 1,407.8 W/m², while entering the Earth's maximum distance from the sun sends it plunging to 1,316.1 W/m².

Of course, because we now have a tool to do this math, we can also do it for any planet in the solar system, where we've listed the minimum, average and maximum distances for the terrestrial planets orbiting the Sun below for your entertainment, if you choose to run those numbers!

Distance from Sun to Terrestrial Planets in Meters
Planet Shortest Distance Longest Distance Average Distance
Mercury 46,000,000,000 70,000,000,000 57,909,200,000
Venus 107,000,000,000 109,000,000,000 108,208,900,000
Earth 147,100,000,000 152,100,000,000 149,598,000,000
Mars 205,000,000,000 249,000,000,000 227,940,600,000

While we stopped at Mars, that doesn't mean that you have to - here's a link to where you can get the average distances from the sun to the solar system's major points of interest all the way out to Pluto!

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About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations.com

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