"Earth Resident" writes:

How did scientists calculate the distance between earth and moon, earth
and sun etc.

This is really a question for 'sci.astro.research', but I will answer it.

The earliest estimates of the distance to the moon was by the ancient
Greek astronomer Aristarchus [310--230 BC], who determined that the
Sun had to be at _least_ 19 times further away than the Moon,
http://galileoandeinstein.physics.virginia.edu/lectures/gkastr1.html,
http://www.astro.queensu.ca/~waugh/fallterm/qlecture5.html,
http://www.eas.purdue.edu/eas105/geos105/lecture3.html;
since the true distance ratio is about 400, this was not very accurate ---
but it was considerable better than the previously accepted value of "3."

The ancient Greek astronomer Hipparchus [190--120 BC] was able to deduce a
more accurate estimate for the distance to the Moon of 59 to 67 Earth radii
(the true value is about 60 Earth radii), from observations of lunar eclipses,
and from the Earth's diameter determined by Eratosthenes [276--195 B.C.]
(which was only about 1% off!), and observations of solar eclipses,
Hipparchus was able to estimate the diameters and distances of both the
Sun and Moon.

Later, more accurate measuremeents of the distance to the Moon used
parallax (change in apparent angle with viewpoint) to determine the
distance through trigonometery,
http://www.ifa.hawaii.edu/~barnes/ASTR110L_S03/lunardist.html;
for a high-school astronomy lab exercise that replicates this method,
see: http://www.math.wisc.edu/~rushton/scopes_kti/northstar/main.html.

Once Newton's Laws of Motion and Law of Gravitation were discovered and
Cavendish measured the Gravitational Constant, it was possible to deduce
the distances to the Sun, Moon, and all the planets from measurements of
their orbital periods plus celestial mechanics.

Moderne methods use the laser retroreflectors left by the Apollo astronauts
to measure the distance to the Moon to an accuracy of about three centimeters
(a bit more than an inch), radar can measure the distances of planets to within
a fraction of a kilometer, and the distances to space-probe transponders can be
determined to a few meters.


-- Gordon D. Pusch

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