Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 3, Problem 50Q
To determine
To explain: The method that Aristarchus used for the estimation of the diameters of the Sun and Moon.
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"Aristarchus' Method of Determining the Distance to the Sun"
At the first quarter of the Moon (at position Q), the angle (EQS) equals 90° (see the
sketch below). Modern observations show that the interval from new Moon (near position
N) to first quarter (at Q) is 35 minutes shorter than that from first quarter to full Moon
(near position F). Given that the lunar synodic period (the interval between two identical
lunar phases) is 29 days and 12.73 hours, estimate the Earth-Sun distance (ES) in terms of
the Earth-Moon distance.
F/
E
"Aristarchus' Method of Determining the Distance to the Sun"
At the first quarter of the Moon (at position Q), the angle (EQS) equals 90° (see the
sketch below). Modern observations show that the interval from new Moon (near position
N) to first quarter (at Q) is 35 minutes shorter than that from first quarter to full Moon
(near position F). Given that the lunar synodic period (the interval between two identical
lunar phases) is 29 days and 12.73 hours, estimate the Earth-Sun distance (ES) in terms of
the Earth-Moon distance.
The average Earth-Moon distance is 3.84 X 10^5 km, while the Earth-Sun is 1.496 X 10^8 km. Since the radius of the Moon is
1.74 X 10^3 km and that of the Sun is 6.96 X 10^5 km.
a) Calculate the angular radius of the Moon and the Sun, qmax, according to the following figure.
D
Bax
R
b) Calculate the solid angle of the Moon and the Sun as seen from Earth.
(c) Interpret its results; Would this be enough to explain the occurrence of total solar eclipses?
Chapter 3 Solutions
Universe
Ch. 3 - Prob. 1CCCh. 3 - Prob. 2CCCh. 3 - Prob. 3CCCh. 3 - Prob. 4CCCh. 3 - Prob. 5CCCh. 3 - Prob. 6CCCh. 3 - Prob. 7CCCh. 3 - Prob. 8CCCh. 3 - Prob. 9CCCh. 3 - Prob. 10CC
Ch. 3 - Prob. 11CCCh. 3 - Prob. 12CCCh. 3 - Prob. 13CCCh. 3 - Prob. 14CCCh. 3 - Prob. 1CLCCh. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8QCh. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - Prob. 14QCh. 3 - Prob. 15QCh. 3 - Prob. 16QCh. 3 - Prob. 17QCh. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - Prob. 21QCh. 3 - Prob. 22QCh. 3 - Prob. 23QCh. 3 - Prob. 24QCh. 3 - Prob. 25QCh. 3 - Prob. 26QCh. 3 - Prob. 27QCh. 3 - Prob. 28QCh. 3 - Prob. 29QCh. 3 - Prob. 30QCh. 3 - Prob. 31QCh. 3 - Prob. 32QCh. 3 - Prob. 33QCh. 3 - Prob. 34QCh. 3 - Prob. 35QCh. 3 - Prob. 36QCh. 3 - Prob. 37QCh. 3 - Prob. 38QCh. 3 - Prob. 39QCh. 3 - Prob. 40QCh. 3 - Prob. 41QCh. 3 - Prob. 42QCh. 3 - Prob. 43QCh. 3 - Prob. 44QCh. 3 - Prob. 46QCh. 3 - Prob. 47QCh. 3 - Prob. 48QCh. 3 - Prob. 49QCh. 3 - Prob. 50QCh. 3 - Prob. 53Q
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- In a part of Earth’s orbit where Earth is moving faster than usual around the Sun, would the length of the solar day change? If so, how? Explain.arrow_forwardHow did Aristotle deduce that the Sun is farther away from Earth than the Moon?arrow_forwardTonight you see a waning crescent in the night sky. A few (n) days later, the night is once again clear and you see a waning crescent. How many degrees did the Moon advance in its orbit during this time frame?arrow_forward
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