Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 4Q
To determine
An epicycle and it’s important on Ptolemy’s explanation of the retrograde motions of the planets.
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I. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius.
Average
Radius of
Orbit
Times of
Planet
R3
T2
T?/R3
Revolution
Mercury
5.7869 x 1010
7.605 x 106
Venus
1.081 x 1011
1.941 x 107
Earth
1.496 x 1011
3.156 x 107
1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?
II. Solve the given problems. Write your solution on the space provided before each number.
1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the
following:
a) Speed
b) Period
c) Radial Acceleration
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion.
Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU.
Does this make physical sense? Explain why or why not.
How long (in Earth-Years) does it take Saturn
to orbit the Sun? Use these values of
(average) distance to the Sun.
Venus: .72 A.U.
Saturn: 9.5 A.U.
Give your answer in (Earth) years to the
correct number of significant figures.
Chapter 4 Solutions
Universe: Stars And Galaxies
Ch. 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. 10Q
Ch. 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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- In Ptolemys model, how do the epicycles of Mercury and Venus differ from those of Mars, Jupiter, and Saturn?arrow_forwardIf you lived on Mars, which planets would describe retrograde loops? Which would never be visible as crescent phases?arrow_forwardWhich major planet has the largest . . . A. semimajor axis? B. average orbital speed around the Sun? C. orbital period around the Sun? D. eccentricity?arrow_forward
- Which of Keplers laws gives the most direct indication of the shape of the orbit of a planet? (16.1) (a) law of elliptical orbits (b) law of equal areas (c) harmonic lawarrow_forwardList some reasons that the study of the planets has progressed more in the past few decades than any other branch of astronomy.arrow_forwardScientists at NASA announced the discovery of a new solar system containing four planets. The average distance of each planet from its sun is given in AU. Sort the planets from the shortest orbital period to the longest orbital period. 1. Maroon V 1.2 AU 2. Autumn III 11 AU 3. Aquarius 7.1 AU 4. Planetius 0.54 AUarrow_forward
- Until recently, the term "planet" had no clear-cut definition. In August of 2006, leading astronomers established new guidelines and declared that Pluto is no longer a planet. Which of the following is either false or least consistent with the new guidelines? Group of answer choices Pluto is by far the largest known object in the Kuiper belt, while Eris is the largest known object in the asteroid belt. A planet must have cleared the neighborhood around its orbit. Pluto is automatically disqualified from being a planet because its oblong orbit overlaps with Neptune's. A planet must have sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a nearly round shape. Pluto and the asteroid Ceres are both now classified as dwarf planets.arrow_forwardCongratulations! You just derived a version of Kepler's Third Law for Mars! Using the mass of Mars in kilograms and converting the 4.5 hours to seconds, calculate the distance from the center of the planet. GM kg 4π² ]s)² 3 = And then determine the distance (in km) from the surface. r = rm + rs rs km = kmarrow_forwardBetween mars and Jupiter the asteroid ceres orbits the sun at an average radius of 2.766 AU. Use kelpers third law to calculate the time in earth it takes for ceres to make one complete orbit. Round up your answer to the correct number of significant digits.arrow_forward
- Saturn's mass is M= 5.69 x 1026 kg and its radius R=60,300 km. If a moon orbits Saturn at a distance equal to 5 times its planetary radius, what is its period of orbit? (Hint, use Newton's version of Kepler's 3rd law, and you can neglect the mass of the moon) Express your answer in days to three significant figures.arrow_forwardMeasure the periods for each planet. Measure the orbital radius of each planet. Calculate the ratios of square of the periods and cubed of the radii for the planets. Compare the results and comment if your result confirms Kepler's Third Law. (Pic1 has the yellow and bluw planets points plotted. Pic2 has the grey and red planet plots listed.)arrow_forwardWhat is retrograde motion? How did the geocentric theory explain these motions? How did the heliocentric theory explain these motions?arrow_forward
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