Distance from the Earth to the Sun
Name: Rick A Cazzato and Burbank School
How can one calculate the distance from Earth to the Sun using high school
mathematics and high school sciences? What is the Earth-Sun distance?
The average distance is 92 million miles, or, more precisely,
1 AU = 1.495978706 x 10^11 meters.
First you can get an estimate of this distance by noting that the Sun and
the Moon subtend the same angle in the sky. This implies that the ratio of
distance to the Sun to that of the Moon is same as the ratio of their
respective sizes. Next you can assume that the Moon is moving in a circular
orbit around the Earth and estimate the distance to the Moon by using the
time period of its orbit. You will also need Earth's mass but that can be
measured by dropping a mass and observing its acceleration and knowing
Earth's radius can be measured by measuring the elevation of the Sun from
two different latitudes at the time of meridian crossing on the same day and
knowing the distance between two observatories used.
Jasjeet S Bagla
Here is the way the Greeks did it:
Around the 7th of the lunar month, you will notice that exactly 1/2 of the
Moon is lit. That means that a path from you to the Moon makes a right
angle with the path from the Moon to the Sun. Now measure the apparent
angle between the Moon and the Sun. This gives you a trigonometry problem
that let us you calculate the Earth-Sun distance in terms of the Earth-Moon
The Earth-Moon distance can be obtained in terms of the Earth's radius by
observing the apparent angle traveled by the Moon when it has traveled, say,
four hours (60 degrees as measured from the center of the Earth).
Another way to get the Earth's radius is to note the distance from a
mountain or tower of a given height when it first appears on the horizon.
This must have been known to the Greeks who, after all, knew how to build
lighthouses to guide ships at sea.
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Update: June 2012