How to Find the Distance From the Earth to the Sun Using an Eclipse

You can calculate the distance from the Earth to the Sun by using triangulation relationships and the concept of parallax. Parallax is defined as the perceptible displacement of an object when it is viewed from two different lines of sight. The parallax is measured by the angle of the inclination of the two lines of sight. An example of parallax is observed when two people riding in the same car (one in the back seat, the other driving) view the same dial speedometer at the same time, both observe two different speeds. Parallax is also proportional to distance; objects closer have a larger parallax than distant objects. This method of using parallax was used to determine the sun's distance from Earth when Venus had a solar eclipse. This eclipse is commonly known as Transit of Venus.

Things You'll Need

• Theodolite
• Calculator
• Eclipse shades

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Instructions

1. • 1

     Track Venus's path as it travels across the Sun. You need two observers on Earth at two different latitudes ("A" and "B"). The two observers track Venus as it crosses in front of the Sun. They should see the planet at different points on the Sun because of parallax. This relationship is illustrated in Figure 1. Using a theodolite, the observers should track Venus and give its coordinates at the same exact time.

   • 2

     Measure the angle between the two lines of sights, or paths. This angle, called "E," is required to determine the distance of Earth from Venus as shown in Figure 2.

   • 3

     Using Kepler's Third Law to determine the angle between the two paths as seen from Venus. Kepler's Law states that Venus's distance to the Sun is 0.72 times the distance of the Sun from the Earth.

   • 4

     Use basic trigonometry to calculate the distance from Venus to Earth:
     tan (v/2) = 1/2 D (distance between observers) / D (distance of Earth to Venus)

   • 5

     Calculate the distance between the Earth and the Sun. Using Kepler's Third Law, which states the distance between the Earth and Venus is 0.28 times the distance between the Sun and the Earth, this is what the calculation looks like:
     D (between Earth and Sun) = D (distance of Earth to Venus) / 0.28 = 93,000,000 miles.