Calculating Sun-Earth Distance
Name: rick a cazzato
Date: 1993 - 1999
How can one calculate the distance from earth to the sun using high
school mathematics and high school sciences? Is this possible?
Yes it is possible.
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 to 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.
If you want any clarifications you can send me a mail.
Here's the way the Greeks did it:
Around the 20th of the 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 trig problem that let's you calculate the earth-s un 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.
Click here to return to the Astronomy Archives
Update: June 2012