Photographing the Sun at Aphelion and Perihelion
(with thanks to Art Camosy for his help in acquiring these images)
Presented here are two photographs of the sun, taken approximately six months apart. The first image was when the Earth was close to aphelion - the point when Earth is farthest away from the sun during its year-long orbit. The second was taken within a few days of perihelion - when Earth is closest to the sun.
Our goal was to use these images to supplement a unit taught to high school freshman science students on the seasons: an attempt to help dispel the common misconception that summer occurs when the Earth is closest to the sun, etc.
1. July 4, 2002, approximately noon Madison time.
2. December 31st, 2002, approximately noon Madison time.
Photo #2 was more than 50 hours prior to perihelion but our hands were forced - the weather forecast for the week was dismal, and December 31st was a clear and nearly perfect day. We decided to shoot now as insurance against bad weather.
Here are the two images side by side, where the size difference is subtle, but unmistakable. The image on the right, perihelion, is clearly larger. Carefully measuring the two images reveals that the aphelion (July) sun is about 96.38% of the diameter of the perihelion (January) sun. Calculations carried out using predicted differences in the distance to the sun at aphelion and perihelion (using Starry Night Pro) give a predicted change of 3.28%.
Incidently, this measurement, and some basic math, can be used to calculate a value for the eccentricity of the Earth's orbit. Eccentricity is a measure of how much an orbit deviates from that of a perfect circle. If Earth's orbit around the sun were a perfect circle, there would be no size difference in the two images above. Save the two images to disk and open them in a photo-editing program that allows some type of measurement (see Photoshop example below). Carefully measure the two images (number of pixels, inches, centimeters, etc.) and compare the two. Calculate the percentage of the difference between the photos. Expressed as a decimal and divided by two, should be a decent approximation of the eccentricity of Earth's orbit (compare with value given here).
My careful Photoshop measurement of the sun images resulted in a July sun that was 96.38% the size of the January sun, or a difference in size of 3.62%. Expressed as a decimal, this would be 0.0362. Divided by two gives 0.0181. This value is respectably close to the accepted value for Earth's orbital eccentricity of 0.017.
This is a considerable simplification mathematically, and eccentricity is never calculated by measuring the angular size of one of the foci of the elipical orbit, but it works very well as an approximation. For more info on orbital eccentricities, see this site.
Animating the two photographs is the clearest way to visualize the size change. It is unmistakable visual evidence that the Earth is closer to the sun in January than it is in July. This image was selected as the Earth Science Picture of the Day for July 4, 2004.
Measuring the Size of the Sun's Image in Photoshop
Photoshop's ruler tools provide very precise measurement potential for digital images, but my sun pics came with a problem: blurry edges.
Zooming in on the sun's limb with unmodified view. The blurred limb makes measuring the diameter of the disk subjective and imprecise. Same zoom level after the contrast has been adjusted to extreme maximum, creating a distinct border. Measurements were taken of the sharp yellow border.
All images copyright John Rummel, 2003. If you make use of this material, please contact me and provide a link on your web site to this page.
Equipment: Celestron C8 telescope, Nikkormat 35mm SLR, Kodak color slide film, Thousand Oaks solar filter. All images were shot with slide film to avoid any measurement errors that could be traced to unknown manipulations during processing of prints. The slides were mounted in Wess glass slide mounts and then projected onto a screen for initial measurement. The slides were then scanned into Adobe Photoshop where the above measurements were conducted using Photoshop's rulers.
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