Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Question
Chapter 4, Problem 51Q
To determine
The sidereal period of an Earth-like planet revolving around a star with four times the mass of the Sun, given that the semi-major axis of the planet is 1 au.
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A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of
12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU
..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.]
Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer
was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]
(a)
Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result.
aIo = AU
(b)
One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result.
PIo = yr
(c)
Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result.
MJup(Io) = MSun
(d)
Based on this result, Jupiter's mass is about that of the Sun.
Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.
Consider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?
Chapter 4 Solutions
Universe
Ch. 4 - Prob. 1CCCh. 4 - Prob. 2CCCh. 4 - Prob. 3CCCh. 4 - Prob. 4CCCh. 4 - Prob. 5CCCh. 4 - Prob. 6CCCh. 4 - Prob. 7CCCh. 4 - Prob. 8CCCh. 4 - Prob. 9CCCh. 4 - Prob. 10CC
Ch. 4 - Prob. 11CCCh. 4 - Prob. 12CCCh. 4 - Prob. 13CCCh. 4 - Prob. 14CCCh. 4 - Prob. 15CCCh. 4 - Prob. 16CCCh. 4 - Prob. 17CCCh. 4 - Prob. 18CCCh. 4 - Prob. 19CCCh. 4 - Prob. 20CCCh. 4 - Prob. 21CCCh. 4 - Prob. 22CCCh. 4 - Prob. 23CCCh. 4 - Prob. 24CCCh. 4 - Prob. 1CLCCh. 4 - Prob. 2CLCCh. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10QCh. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 14QCh. 4 - Prob. 15QCh. 4 - Prob. 16QCh. 4 - Prob. 17QCh. 4 - Prob. 18QCh. 4 - Prob. 19QCh. 4 - Prob. 20QCh. 4 - Prob. 21QCh. 4 - Prob. 22QCh. 4 - Prob. 23QCh. 4 - Prob. 24QCh. 4 - Prob. 25QCh. 4 - Prob. 26QCh. 4 - Prob. 27QCh. 4 - Prob. 28QCh. 4 - Prob. 29QCh. 4 - Prob. 30QCh. 4 - Prob. 31QCh. 4 - Prob. 32QCh. 4 - Prob. 33QCh. 4 - Prob. 34QCh. 4 - Prob. 35QCh. 4 - Prob. 36QCh. 4 - Prob. 37QCh. 4 - Prob. 38QCh. 4 - Prob. 39QCh. 4 - Prob. 40QCh. 4 - Prob. 41QCh. 4 - Prob. 42QCh. 4 - Prob. 43QCh. 4 - Prob. 44QCh. 4 - Prob. 45QCh. 4 - Prob. 46QCh. 4 - Prob. 47QCh. 4 - Prob. 48QCh. 4 - Prob. 49QCh. 4 - Prob. 50QCh. 4 - Prob. 51QCh. 4 - Prob. 52QCh. 4 - Prob. 53QCh. 4 - Prob. 54QCh. 4 - Prob. 55QCh. 4 - Prob. 56QCh. 4 - Prob. 57QCh. 4 - Prob. 58Q
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