Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 1, Problem 2LTL
To determine
How can you tell that mercury does not follow a circular orbit?
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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:
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?
Two exoplanets, UCF1.01 and UCF1.02 are found revolving around the same star. The period of planet UCF1.01 is 4.8 days, and that of planet UCF1.02 is 5.2 days. If the average distance of planet A to the sun is 2,885.4 km, what is the average distance of planet B to the sun km? Please keep four digits after decimal points.
Chapter 1 Solutions
Horizons: Exploring the Universe (MindTap Course List)
Ch. 1 - What is the largest dimension of which you have...Ch. 1 - What is the difference between our Solar System,...Ch. 1 - Why are light-years more convenient than miles,...Ch. 1 - Why is it difficult to detect planets orbiting...Ch. 1 - Prob. 5RQCh. 1 - What is the difference between the Milky Way and...Ch. 1 - What are the largest known structures in the...Ch. 1 - Prob. 8RQCh. 1 - How Do We Know? How does the scientific method...Ch. 1 - You and three of your friends have won an...
Ch. 1 - Think back to the last time you got a new phone...Ch. 1 - The diameter of Earth across the equator is 7928...Ch. 1 - The diameter of the Moon across its equator is...Ch. 1 - One astronomical unit is about 1.50108 km. Explain...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 3.00105 km/s. how many...Ch. 1 - How long does it take light to cross the diameter...Ch. 1 - The nearest large galaxy to our n is about 2.5...Ch. 1 - How many galaxies like our own would it take Laid...Ch. 1 - In Figure 1-4, the division between daylight and...Ch. 1 - Prob. 2LTLCh. 1 - Prob. 3LTLCh. 1 - Prob. 4LTL
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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_forwardEAn astronaut arrives on the planet Oceania and climbs to the top of a cliff overlooking the sea. The astronaut's eye is 100 m above the sea level and he observes that the horizon in all directions appears to be at angle of 5 mrad below the local horizontal. What is the radius of the planet Oceania at sea level? How far away is the horizon from the astronaut? 6000 km and 50 km 3600 km and 20 km 2000 km and 40 km 8000 km and 40 kmarrow_forwardThe angle on the sky between Venus and the Sun is measured to be 46.3° when Venus is at greatest eastern elongation. What is the distance of Venus from the Sun, measured in AU? Choose the answer below that most closely matches your answer. Select one: а. 1.763 AU O b. 0.587 AU Ос. 0.652 AU O d. 0.846 AU Ое. 0.723 AUarrow_forward
- The distance between Jupiter and the sun is usually measured in astronomical units.one astronomical unit is defined as:...arrow_forwardAs an aspiring science fiction author, you are writing about a space-faring race and their home planet, Krypton, which has one moon. This moon takes 1,702,948 seconds to complete an orbit around Krypton. If the distance from the center of the moon to the surface of Krypton is 462.5 x 106 m and the planet has a radius of 37.2 x 106 m, calculate the moon's centripetal acceleration. Your Answer: Answerarrow_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_forward
- Comet Halley has a semi-major axis of 17.7 AU. (The AU, or Astronomical Unit, is the distance from the Sun to the Earth. 1 AU = 1.50x1011 m.) The eccentricity of Comet Halley is 0.967. a. How far is Comet Halley from the sun at Aphelion, the farthest position from the sun? (Give your answer in AU.)? b. What is comet Halley's orbital time? (Give your answer in years.) Note: Using Kepler's third law in the form: P2 = a3 is convenient. This equation works for any object orbiting the sun when the orbital period is in years and the semi major axis is in AU. The reason this works is because this equation is normalized to earth. The AU and year are both 1 for Earth. c. In what year will Comet Halley start to move back toward 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_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_forward
- A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of 12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU ..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.] Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]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_forwardWould you expect the distance between Earth and Mars to vary? Briefly explain your answer.arrow_forward
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Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY