Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 4, Problem 9P
Galileo’s telescope showed him that Venus has a large angular diameter (61 arc seconds) when it is a crescent and a small angular diameter (10 arc seconds) when it is nearly full. Use the small-angle formula to find the ratio of its maximum to minimum distance from Earth. Is this ratio compatible with the Ptolemaic universe shown in Figure 3b of the Chapter 4 Concept Art: An Ancient Model of the Universe?
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A planet's speed in orbit is given by V = (30 km/s)[(2/r)-(1/a)]0.5 where V is the planet's velocity, r is the distance in AU's from the Sun at that instant, and a is the semimajor axis of its orbit.
Calculate the Earth's velocity in its orbit (assume it is circular):
What is the velocity of Mars at a distance of 1.41 AU from the Sun?
What is the spacecraft's velocity when it is 1 AU from the Sun (after launch from the Earth)?
What additional velocity does the launch burn have to give to the spacecraft? (i.e. What is the difference between the Earth's velocity and the velocity the spacecraft needs to have?)
How fast will the spacecraft be traveling when it reaches Mars?
Does the spacecraft need to gain or lose velocity to go into the same orbit as Mars?
The table below presents the semi-major axis (a) and Actual orbital period for all of the major planets in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet.
Table of Data for Kepler’s Third Law:
Table of Data for Kepler’s Third Law:
Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet
Period (Yr) Period (Yr)
__________ ______________________ ___________ ________________
Mercury 0.39 0.24
Venus 0.72 0.62
Earth 1.00 1.00
Mars 1.52 1.88
Jupiter…
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.
Chapter 4 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 4 - Prob. 1RQCh. 4 - Why did early human cultures observe astronomical...Ch. 4 - Prob. 3RQCh. 4 - Name one example each of a famous politician,...Ch. 4 - Why did Plato propose that all heavenly motion was...Ch. 4 - On what did Plato base his knowledge? Was it...Ch. 4 - Which two-dimensional (2D) and three-dimensional...Ch. 4 - Are the spheres of Eudoxus a scientific model? If...Ch. 4 - In Ptolemys model, how do the epicycles of Mercury...Ch. 4 - Describe in detail the motions of the planets...
Ch. 4 - In Ptolemys model, which of the followingepicycle,...Ch. 4 - Why did Copernicus have to keep small epicycles in...Ch. 4 - Was the belief held by ancient astronomers that...Ch. 4 - When Tycho observed the new star of 1572, he could...Ch. 4 - Assume the night is clear and the Moons phase is...Ch. 4 - Does Tychos model of the Universe explain the...Ch. 4 - Name an empirical law. Why is it considered...Ch. 4 - How does Keplers first law of planetary motion...Ch. 4 - When Mercury is at aphelion (farthest from the...Ch. 4 - Prob. 20RQCh. 4 - What is P for Earth? What is a for Earth? Do these...Ch. 4 - Based Figure 4-13c, do planets with larger a take...Ch. 4 - How did the Alfonsine Tables, the Prutenic Tables,...Ch. 4 - Explain how each of Galileos telescopic...Ch. 4 - How did discovery of the Galilean moons disprove...Ch. 4 - Prob. 26RQCh. 4 - How Do We Know? Describe the differences between a...Ch. 4 - Draw and label a diagram of the western horizon...Ch. 4 - If you lived on Mars, which planets would exhibit...Ch. 4 - How long does it take for one retrograde cycle of...Ch. 4 - If a planet has an average distance from the Sun...Ch. 4 - If a space probe is sent into an orbit around the...Ch. 4 - Uranus orbits the Sun with a period of 84.0 years....Ch. 4 - An object takes 29.5 years to orbit the Sun. What...Ch. 4 - One planet is three times farther from the Sun...Ch. 4 - Galileos telescope showed him that Venus has a...Ch. 4 - Which is the phase of Venus when it is closest?...Ch. 4 - Galileos telescopes were not of high quality by...Ch. 4 - Arrange the following in order of increasing...Ch. 4 - Arrange the following in order of increasing...Ch. 4 - Prob. 1LTLCh. 4 - Study Figures 4-11 and 4-16 and describe the...Ch. 4 - What three astronomical objects are represented...Ch. 4 - Use the figure below to explain how the Ptolemaic...
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