### Re: How are distances between earth and sun/moon found in the 18th cent.?

Date: Wed Sep 15 19:16:18 1999
Area of science: Science History
ID: 933266727.Sh
Message:
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Hello, Julia.

First, I apologize that it has taken us so long to answer your
question.  It isn't polite to keep a lady waiting.

Measurements of the distance between the earth and the sun, and
the earth and the moon, have gotten much more accurate as time has passed.
Today, very precise measurements between the earth and moon are made by
aiming a laser at a mirror on the moon, and counting the time it takes
until the laser is reflected back to earth.  We know the distance between
the laser on earth and the mirror on the moon within a few centimeters.  Of
course, things weren't always so precise.

No one person can be credited with figuring out the distances in
the 18th century.  Many people learned different truths which helped us
know how to solve the problem.  Here's a few of them, when they lived or
worked, and what they discovered.

Nicolaus Coupernicus (who published his findings in 1540) discovered that
all the planets travel around the sun, not the earth.

Johannes Kepler (1571-1630) discovered that planets travel around the sun
in elliptical orbits, not perfect circles.  He also showed that there is a
fixed relationship between the time it takes a planet to revolve around the
sun and its average distance from the sun.

Isaac Newton (whose book "Philosophiae Naturalis Principia Mathematica" was
published July 5, 1686) invented calculus, which is the math we still use
today to describe motion.  He also showed that it was gravity that caused
the planets to move around the sun.  He also showed that the gravity of the
planets affected other planets.

So before 1700, we know that the distance between the sun and moon is
always changing, because of the elliptical nature of their orbits, and we
have the math necessary to calculate how far planets are from the sun by
how long it takes them to complete a revolution around it.

All that was really needed after that was more accurate measurements of the
time it took for the moon to revolve around the earth, and the earth around
the sun.  But even in 1700 those times were known quite accurately.  It
takes exactly one solar year (about 365 1/4 days) for the earth to revolve
around the sun.  We knew this long before Isaac Newton, by comparing the
positions of the stars in the sky night after night.  Every 365 1/4 days,
the stars were in the same place in the sky.

One last thing, Julia.  Imagine a baseball connected by a string to a golf
ball.  If you throw them high into the air, they will spin around each
other.  Because the baseball is heavier, it will not be moved out of its
trajectory as much as the golf ball will.  This is similar to the earth and
the moon orbiting one another.  Sometimes the moon is between the earth and
the sun, and the earth is then farther from the sun than when it is between
the sun and the moon.  We're nearer to the sun during full moons than new
moons.  And yes, even this was known in the 18th century.

Layne Johnson

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