Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 2, Problem 3E
Explain, according to both geocentric and heliocentric cosmologies, why we see retrograde motion of the planets.
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Explain the geocentric view of the universe.
Use a distance of R = 1.48x10^11 meters for the distance between the earth and the sun.
Use a mass of 1.99x10^30 kg to be 1 solar mass.
For each of the different sun masses (as values of solar mass, aka 0.5 solar masses = 1x10^30 kg), as outlined in the lecture, calculate the period of the earth's orbit in days using Kepler's law for circular orbits (I double-checked it with these values and it works) and also calculate the corresponding orbital velocity of the earth.
Questions:
1.) Using these values, and 6x10^24 kg for the mass of the earth, what is the strength of the gravitational force between the earth and the sun?
2.) If the earth were twice as far from the sun, what would be its period of orbit?
3.) Mars orbits the sun at a distance of 2.18x10^11 meters. How long is a Martian year, using Kepler's law for circular orbits?
Given that a geocentric universe is (mathematically) only a matter of the choice of a reference frame, explain why the Ptolemaic model of the universe was able to survive scrutiny for such a long period of time.
Chapter 2 Solutions
Astronomy
Ch. 2 - From where on Earth could you observe all of the...Ch. 2 - Give four ways to demonstrate that Earth is...Ch. 2 - Explain, according to both geocentric and...Ch. 2 - In what ways did the work of Copernicus and...Ch. 2 - What were four of Galileo’s discoveries that were...Ch. 2 - Explain the origin of the magnitude designation...Ch. 2 - Ursa Minor contains the pole star, Polaris, and...Ch. 2 - How many degrees does the Sun move per day...Ch. 2 - How many degrees does the Moon move per day...Ch. 2 - Explain how the zodiacal constellations are...
Ch. 2 - The Sun was once thought to be a planet. Explain...Ch. 2 - Is the ecliptic the same thing as the celestial...Ch. 2 - What is an asterism? Can you name an example?Ch. 2 - Why did Pythagoras believe that Earth should be...Ch. 2 - How did Aristotle deduce that the Sun is farther...Ch. 2 - What are two ways in which Aristotle deduced that...Ch. 2 - How did Hipparchus discover the wobble of Earth’s...Ch. 2 - Why did Ptolemy have to introduce multiple circles...Ch. 2 - Why did Copernicus want to develop a completely...Ch. 2 - What two factors made it difficult, at first, for...Ch. 2 - What phases would Venus show if the geocentric...Ch. 2 - Describe a practical way to determine in which...Ch. 2 - What is a constellation as astronomers define it...Ch. 2 - Draw a picture that explains why Venus goes...Ch. 2 - Show with a simple diagram how the lower parts of...Ch. 2 - Parallaxes of stars were not observed by ancient...Ch. 2 - Why do you think so many people still believe in...Ch. 2 - Consider three cosmological perspectives-the...Ch. 2 - The north celestial pole appears at an altitude...Ch. 2 - What were two arguments or lines of evidence in...Ch. 2 - Although the Copernican system was largely correct...Ch. 2 - During a retrograde loop of Mars, would you expect...Ch. 2 - The Great Pyramid of Giza was constructed nearly...Ch. 2 - Explain why more stars are circumpolar for...Ch. 2 - What is the altitude of the north celestial pole...Ch. 2 - If you were to drive to some city south of your...Ch. 2 - Hipparchus could have warned us that the dates...Ch. 2 - Explain three lines of evidence that argue against...Ch. 2 - What did Galileo discover about the planet Jupiter...Ch. 2 - What did Galileo discover about Venus that cast...Ch. 2 - Suppose Eratosthenes had found that, in...Ch. 2 - Suppose Eratosthenes’ results for Earth’s...Ch. 2 - Suppose you are on a strange planet and observe,...
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- One year on Planet AAA is 5 time the length of one earth year and it orbits its sun at an average distance 4.38 AU. Planet ZZZ orbits the same sun at an average distance of 2.53 AU. Determine the length of one year on Planet ZZZ in earth days.arrow_forwarddiscuss some of the cultural and philosophical implications related to the geocentric modelarrow_forwardKepler'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.arrow_forward
- A 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_forwardWhile the Earth spins around its axis and orbits around the sun, then suppose we remove the sun from its location, will Earth continue to spin around its axis and orbits around the point where the sun used to be? Why or why not?arrow_forwardwhat is Retrograde-motion and the failure of the geocentric universe model?arrow_forward
- If the semi-major axis, a, is measured in AU and the orbital period, p, is measured in years, then Kepler's 3rd law allows us to calculate the mass of the object they are orbiting using the following equation: M = a3/p2 Furthermore, the mass that is calculated by this equation is given in solar masses (MSun) where, by definition, the Sun's mass is 1 MSun. Now, suppose I were to tell you that the mass of Jupiter is equal to 4.5e7 MSun. Does the stated mass of Jupiter make sense? it is to big or to small or makes sensearrow_forwardIf the semi-major axis, a, is measured in AU and the orbital period, p, is measured in years, then Kepler's 3rd law allows us to calculate the mass of the object they are orbiting using the following equation: M = a3/p2 Furthermore, the mass that is calculated by this equation is given in solar masses (MSun) where, by definition, the Sun's mass is 1 MSun. Now, suppose I were to tell you that the mass of Jupiter is equal to 4.5e7 MSun. Does the stated mass of Jupiter make sense? Group of answer choices - Yes - No, it's too big. - No, it's too smallarrow_forwardSuppose, hypothetically, that the Earth orbited the Sun at half its current distance. (That is, at 1/2 AU instead of 1 AU). What would be the length of the year? What else would be different?arrow_forward
- How Do We Know? Why is it important that a theory make testable predictions?arrow_forwardHow Do We Know? Why is astrology a pseudoscience?arrow_forwardDraw a picture that explains why Venus goes through phases the way the Moon does, according to the heliocentric cosmology. Does Jupiter also go through phases as seen from Earth? Why?arrow_forward
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