The Solar System
10th Edition
ISBN: 9781337672252
Author: The Solar System
Publisher: Cengage
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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.
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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…
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Chapter 4 Solutions
The Solar System
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 - Prob. 8RQCh. 4 - In Ptolemys model, how do the epicycles of Mercury...Ch. 4 - Describe in detail the motions of the planets...
Ch. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 -
When Tycho observed the new star of 1572, he...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 Kepler’s first law of planetary motion...Ch. 4 - Prob. 19RQCh. 4 - Prob. 20RQCh. 4 - Prob. 21RQCh. 4 - Prob. 22RQCh. 4 - Prob. 23RQCh. 4 - Prob. 24RQCh. 4 - Prob. 25RQCh. 4 - Prob. 26RQCh. 4 - Prob. 27RQCh. 4 - Prob. 1PCh. 4 -
If you lived on Mars, which planets would exhibit...Ch. 4 - Prob. 3PCh. 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 - Prob. 6PCh. 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 - Prob. 11PCh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 1LLCh. 4 - Prob. 2LLCh. 4 - What three astronomical objects are represented...Ch. 4 - Use the figure below to explain how the Ptolemaic...
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- Why might Tycho Brahe have hesitated to hire Kepler? Why do you suppose he appointed Kepler his scientific heir? What is limited about Keplers third law P2 = a3, where P is the time in units of years a planet takes to orbit the Sun and a is the planets average distance from the Sun in units of AU? (Hint: Look at the units.) What does this tell you about Kepler and his laws?arrow_forwardHow Do We Know? How can a scientific model be useful if it is not a true description of nature?arrow_forwardSuppose you are on a strange planet and observe, at night, that the stars do not rise and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000 miles, and at your new location on the planet, you find that all stars rise straight up in the east and set straight down in the west, perpendicular to the horizon. How could you determine the circumference of the planet without any further observations? What is the circumference, in miles, of the planet?arrow_forward
- Use Kepler's 3rd Law and the small angle approximation. a) An object is located in the solar system at a distance from the Sun equal to 41 AU's . What is the objects orbital period? b) An object seen in a telescope has an angular diameter equivalent to 41 (in units of arc seconds). What is its linear diameter if the object is 250 million km from you? Draw a labeled diagram of this situation.arrow_forwardThinking about the Scale of the Solar System As we discussed, the radius of the Earth is approximately 6370 km. The Sun, on the other hand, is approximately 700,000 km in radius and located, on average, one astronomical unit (1 au=1.5x108 km) from the Earth. Imagine that you stand near Mansueto Library, at the corner of 57th and Ellis. You hold a standard desk globe, which has a diameter of 12 inches, and you want to build a model of the Sun, Earth, and their separation that keeps all sizes and lengths in proportion to one another. a) How big would the Sun be in this scale model? Give your answer in feet and meters. b) The nearest star to the Solar System outside of the Sun is Proxima Centauri, which is approximately 4.2 light years away (a light year is the distance light travels in one year, or approximately 9.5x1012 km). Given the scale model outlined above, how far would a model Proxima Centauri be placed from you? Give your answer in miles and km.arrow_forwardUsing Kepler’s Third Law (r3 = MT2 where M is the mass of the central star) find the orbital radius in astronomical units of this planet. M = 1.5 times the mass of the sun. Remember to convert days to years using 365.25 as the length of a year in days. Key Points to know: - The semimajor axis of the planet in AU is r = 0.0379 AU - The circumference of the orbit is l = 3.562 x 10^10 m - The orbital velocity in m/s is v = 1.874 x 10^5 m/s Questions that need to be answered: - With that orbital velocity, the radius of the orbit in meters, find the centripetal acceleration of our exoplanet: - Knowing the acceleration that our planet experiences, calculate the force that the host star exerts on the planet: - Knowing the force on the planet, the orbital radius, and the mass of the parent star, use the equation for gravitational force to find the mass of our planet (m2). (To get m1 in kg multiply the mass of the star in solar masses by 1.98 x 1030).arrow_forward
- As we discuss in class, the radius of the Earth is approximately 6370 km. Theradius of the Sun, on the other hand, is approximately 700,000 km. The Sun is located,on average, one astronomical unit (1 au) from the Earth. Imagine that you stand near Mansueto Library, at the corner of 57th and Ellis.Mansueto’s dome is 35 feet (10.7 meters) high. Let’s imagine we put a model of theSun inside the dome, such that it just fits — that is, the model Sun’s diameter is 35 feet The nearest star to the Solar System outside of the Sun is Proxima Centauri,which is approximately 4.2 light years away. Given the scale model outlined above,how far would a model Proxima Centauri be placed from you? Give your answer inmiles and kmarrow_forwardOn February 28, 2010, Earth was equidistant from the spacecraft Dawn and the Sun, forming an isosceles triangle. The distance from Earth to Dawn and Earth to the Sun was 0.99 AU (astronomical units). The distance from Dawn to the Sun was 1.84 AU. a) Draw a diagram to show Dawn, Earth, and the Sun. b) Determine the angle between the sight lines from Earth to Dawn and the Sun.arrow_forwardIf city is located in 2.8° north latitude and 46.0° east longitude. From there, you want to fly to a city in 7° north latitude and 52° east longitude. How much is the arc length of the big circle at 11000 m when the earth's radius is 6370 km? The arc length is 14223 km. Give your answer rounded to one kilmetre. Your last answer was interpreted as follows: 14223 XAnswer is incorrect. Keep centre of Earth as origin and define vectors to cities. Try again.arrow_forward
- Suppose you were given a 3 in diameter ball to represent the Earth and a 1 in diameter ball to represent the Moon. (The actual ratio of Earth diameter to Moon diameter is 3.7 to 1.) The actual average Earth–Moon distance is about 384,000 kilometers, and Earth’s diameter is about 12,800 kilometers. How many “Earth diameters” is the distance from Earth to the Moon? Based on your answer to Question 2, what is the correct scaled distance of the Moon, using the 3-inch ball as Earth? The Sun’s actual diameter is about 1,400,000 kilometers. How many “Earth diameters” is this? Given your 3-inch Earth, how large (i.e what diameter) of a ball would you need to represent the Sun? Give your answer in feet. The average Earth–Sun distance is about 149,600,000 km. To represent this distance to scale, how far away would you have to place your 3-inch Earth from your Sun? Give your answer in feet. Could we use this scale to visualize the solar system instead of just the Earth and Moon? Why or Why…arrow_forwardOxygen Atoms in People. Figure 5.7 shows that oxygen makes up about 65% of the mass of a human being. A single oxygen atom has a mass of 2.66 × 10−26 kg. (a) Use this fact to estimate the number of oxygen atoms in your body. (Hint: If you know your weight in pounds, you can convert to kilograms by dividing by 2.2.) (b) Compare your answer to the number of stars in the observable universe (which is roughly 1022).arrow_forwardExplain the geocentric view of the universe.arrow_forward
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