Stars and Galaxies (MindTap Course List)
10th Edition
ISBN: 9781337399944
Author: Michael A. Seeds
Publisher: Cengage Learning
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Chapter 4, Problem 9P
To determine
The ratio of minimum mad maximum distance from Earth. Whether the ratio is compatible with the Ptolemaic 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?
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.
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…
Chapter 4 Solutions
Stars and Galaxies (MindTap Course List)
Ch. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Which two-dimensional (2D) and three-dimensional...Ch. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQ
Ch. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 - Prob. 14RQCh. 4 - Assume the night is clear and the Moons phase is...Ch. 4 - Prob. 16RQCh. 4 - Prob. 17RQCh. 4 - Prob. 18RQCh. 4 - Prob. 19RQCh. 4 - Prob. 20RQCh. 4 - Prob. 21RQCh. 4 - Prob. 22RQCh. 4 - How did the Alfonsine Tables, the Prutenic Tables,...Ch. 4 - Prob. 24RQCh. 4 - Prob. 25RQCh. 4 - Prob. 26RQCh. 4 - Prob. 27RQCh. 4 - Draw and label a diagram of the western horizon...Ch. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - One planet is three times farther from the Sun...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 1LLCh. 4 - Prob. 2LLCh. 4 - What three astronomical objects are represented...Ch. 4 - Prob. 4LL
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- Using 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_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_forwardAs 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_forward
- If 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_forwardWrite the scientific notation (10n) 0012 = 560000 = Write out the number 3 x 104 = 8 x 10-2 = How many centimeters are in 2 kilometers? Write your answer in scientific notation. How long would it take in minutes to travel 5km if you are traveling at a speed of 30 m/s? A ship left shore 3 days ago and has been moving at a constant speed. The cruise ship is now 1440 miles away. What is the average speed in mph? 5a. A tuning fork has a period of 4s. What is the frequency? 5b. If the tuning fork above is struck in air, what is the wavelength? 5c. If the tuning fork above is struck in water, what is the wavelength? The wave below is traveling at 5 m/s. 6a. What are the wave y(x) and oscillator y(t) sinusoid equations for this wave? What is a sound wave? Identify where the compressions and the rarefactions are in both graphs.…arrow_forwarda method for determining the sizes of the orbits of pl from the sun than Earth. His method involved noting of days between the times that a planet was in the pc A and B in the diagram. Using this time and the num each planet's year, he calculated c and d. a. For Mars, c= 55.2 and d= 103.8. How far is Mars in astronomical units (AU)? One astronomical un the average distance from Earth to the center of th 93 million miles. b. For Jupiter, c 21.9 and d= 100.8. How far is Jup %3D sun in astronomical units? lo olpno er ort to rt .onte eteem-21 o to bre e ne ern 100 o ho aotem t elbl erl pnibioda lert pribiortarrow_forward
- Oxygen 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_forwardSuppose 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_forwardThe angle between two lines drawn from a point on Earth to two opposite sides of the Moon make an angle of 0.5 degrees. If you do the same thing for the two opposite ends of Andromeda (as shown above), you find an angle of 5 degrees. Let's assume Andromeda and the Moon are equally far away from our location on Earth (of course that's wrong, but how are we supposed to know?) - then how much larger would the diameter of Andromeda be (as indicated by the arrows at the top), compared to the diameter of the Moon? Pick the answer that's closest to what you get under this hypothetical assumption: A. Equal Diameter B. Twice C. Five times D. Ten timesarrow_forward
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