Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 4Q
To determine
The meaning of epicycle and its importance in 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.
Saturn has an angular size of 16”, and an observed Synodic Period of 1.035yrs. Saturn’s moon, Titan orbits the planet with an angular separation of 192”, with a period of 15.9days. From these observations we can determine Saturn’s mass.
Use the Sidereal Period of Saturn above to find the distance to Saturn from the Sun.
Chapter 4 Solutions
Universe
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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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- 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_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_forwardIf you lived on Mars, which planets would describe retrograde loops? Which would never be visible as crescent phases?arrow_forward
- Why did Kepler need Tycho Brahe’s data to formulate his laws?arrow_forwardWhy did Copernicus want to develop a completely new system for predicting planetary positions? Provide two reasons.arrow_forwardWhich of Keplers laws gives an indication of the semimajor axis? (16.1) (a) law of elliptical orbits (b) law of equal areas (c) harmonic lawarrow_forward
- Congratulations! 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_forwardA planet revolves around a certain star. At one point in the planet's orbit, called periapsis, it passes much closer to the star. Which of the following statements about periapsis is true? The planet's orbital period becomes shorter after every periapsis. The planet's orbital period becomes longer after every periapsis. The planet orbits with a slower speed during periapsis. The planet orbits with a greater speed during periapsis.arrow_forwardExplain why Galileo's discovery of the four Galilean moons of Jupiter helped disprove the geocentric model of the solar system.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_forwardQUESTION 10 Why does Venus take a shorter time to orbit the Sun in the heliocentric model, than to exhibit its cycle of phases? Because Venus' orbit is larger than that of Earth's. This is a trick question and the time period for Venus to exhibit its cycle of phases is the same as the time it takes to orbit the Sun. Because the Earth is also moving in that time period. Therefore Earth is no longer in the same position as at the start of the cycle, as after 225 days. Because the Sun is also moving in that time period. Therefore Earth is no longer in the same position as at the start of the cycle, as after 225 days.arrow_forward
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