Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 2LTL
Look at Figure 1-6. How can you tell that Mercury does not follow a circular orbit?
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When the Earth passes directly between the Sun and Mars, the Earth and Mars are closest to each other. If Mars is 1.52 AU from the Sun and there are 1.5 x 108 km in 1 AU, how many times will the width of
the U.S. (2,530 miles) fit end-to-end between Mars and Earth?
Planets and Sun not drawn to
scale.
Mars
Earth
Sun
Part 1 of 4
Mars is 1.52 AU from the Sun. How many times further away from the Sun is Mars than the Earth? (The distances in AU are relative to the distance between the Sun and the Earth, so however many AU a
planet is away from the Sun is how many times farther it is from Sun than Earth.)
1.52✔
1.52 times further away
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?
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:
Chapter 1 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 1 - Prob. 1RQCh. 1 - What is the largest dimension of which you have...Ch. 1 - What is the difference between the Solar System,...Ch. 1 - What is the difference between the Moon and a...Ch. 1 - Why do astronomers now label Pluto a dwarf planet?Ch. 1 - Why are light-years more convenient than miles,...Ch. 1 - Why is it difficult to detect planets orbiting...Ch. 1 - Prob. 8RQCh. 1 - What is the difference between the Milky Way and...Ch. 1 - What are the Milky Way Galaxys spiral arms?
Ch. 1 - Prob. 11RQCh. 1 - Where are you in the Universe? If you had to give...Ch. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - How do we know? How does the scientific method...Ch. 1 - The equatorial diameter of Earth is 7928 miles. If...Ch. 1 - The equatorial diameter of the Moon is 3476...Ch. 1 - One astronomical unit (AU) is about 1.5 108 km....Ch. 1 - A typical galaxy is shown on the first page of the...Ch. 1 - The time of the Cambrian explosion is listed on...Ch. 1 - Venus orbits 0.72 AU from the Sun. What is that...Ch. 1 - Light from the Sun takes 8 minutes to reach Earth....Ch. 1 - The Sun is almost 400 times farther from Earth...Ch. 1 - If the speed of light is 3.0 105 km/s, how many...Ch. 1 - Prob. 10PCh. 1 - How long does it take light to cross the diameter...Ch. 1 - The nearest galaxy to our home galaxy is about 2.5...Ch. 1 - How many galaxies like our own would it take if...Ch. 1 - Arrange the following in order of increasing size:...Ch. 1 - Prob. 2SOPCh. 1 - The Sun is roughly 100 times the diameter of...Ch. 1 - Prob. 4SOPCh. 1 - Look at the center of Figure 14. Approximately...Ch. 1 - Look at Figure 1-6. How can you tell that Mercury...Ch. 1 - Prob. 3LTLCh. 1 - Look at Figure 1-9. Would you say that the...Ch. 1 - Of the objects listed here, which would be...Ch. 1 - Prob. 6LTL
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- How many precession periods are in one cycle of Earths axis inclination variation? In one cycle of Earths orbit eccentricity variation? In the time span shown in Figure 2-11b, how many periods or fractions of periods did the Earths axis precess, nod, and Earths orbit change shape? Of the three periods, which is likely to have the most effect on the changes shown in Figure 211?arrow_forwardEx/13: The mean radius of earth is 6400 km. The acceleration due to gravity at its surface is 9.8 m/s². Estimate the mass of earth. "" 11 › (G = 6.67 × 10-¹¹ Nm²/kg²)arrow_forwardGalileos 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?arrow_forward
- 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_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_forwardSaturn 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.arrow_forward
- Would you expect the distance between Earth and Mars to vary? Briefly explain your answer.arrow_forwardMars is 1.5 times as far away from the Sun as Earth. Earth’s axis is tilted at 23.5o compared to the ecliptic. The axis of Mars is tilted at 25o compared to the ecliptic. The atmosphere on Earth is 100 times as thick as the atmosphere on Mars. Which of the following statements is true? 1.)Mars is so cold that the water there is ice, while Earth does not have any ice 2.)When it is summer in Earth’s northern hemisphere, it is winter on Mars’ southern hemisphere 3.) Earth has seasons, Mars does not 4.) All of the water on Mars is frozen, while Earth has water in solid, liquid and gas formarrow_forwardquestion 1 & 2 please , using 2 AU and the formulaarrow_forward
- a) What is the semimajor axis of the spacecraft’s elliptical orbit around the Sun (in AU)? Hint: The semimajor axis of Earth’s orbit is 1 AU and the semimajor axis of Mars’ orbitis 1.52 AU. Consider the diagram above and assume for simplicity that the orbits of Earth and Mars are circular. b) What would be the period of the spacecraft’s orbit around the Sun (in Earth years)? c) Assuming that the spacecraft’s launch is timed properly to arrive at Mars, what is the time required (in days) for the spacecraft to reach Mars from Earth?arrow_forwardAssume that the planet's orbit is circular of radius R = 130 × 106 km and planet's period is T = 30 × 10° s. What is the magnitude of the vector J = r x r' (in units of square kilometers per second)? (Use decimal notation. Give your answer to three decimal places.) ||J|| = x10° km²/s Find the rate at which the planet's radial vector sweeps out area in units of square kilometers per second. (Use decimal notation. Give your answer to three decimal places.) dA x10° km²/s dtarrow_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
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