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Name:  Rick A Cazzato and Burbank School
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Question:
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?



Replies:
The average distance is 92 million miles, or, more precisely, 1 AU = 1.495978706 x 10^11 meters.

Hawley



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.

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 distance.

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.

J Lu


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