Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Question
Chapter 4, Problem 28Q
To determine
The planet which exhibits the greatest dissimilarity in apparent brightness as observed from Earth and the planet which exhibits the greatest variation in angular diameter.
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Use Kuiper Belt Object Haumea's eccentricity; e = 0.189, semimajor axis, a = 43.3
AU, and Period, P = 285 yrs, values to
a) calculate its perihelion and aphelion distances with Dp = a (1 e) and D₂ = a (1 + e),
b) verify if Haumea's a and P satisfy Kepler's third law for all objects orbiting the Sun:
p2 = a³.
Show your work.
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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…
Direction: Use your knowledge about solving equations to work out to
complete the table below. Show your solution with proper units.
R° (meters)
T
R° / T° { (meters) /
Planet
Average
Times of
Radius of
Revolution
(seconds) (seconds) }
Planet's Orbit
(Planet's
year)
R
T (seconds)
(meters)
Mercury
5.7869 x 10:0
7.605 x 10
Venus
1.081 x 101
1.941 x 107
Earth
1.4996 x 10"
3.156 x 10
Mars
2.280 x 101
5.936 x 10
Jupiter
7.783 x 10"
3.743 x 10
Saturn
1.426 x 10
9.296 x 10
Chapter 4 Solutions
Universe
Ch. 4 - Prob. 1CCCh. 4 - Prob. 2CCCh. 4 - Prob. 3CCCh. 4 - Prob. 4CCCh. 4 - Prob. 5CCCh. 4 - Prob. 6CCCh. 4 - Prob. 7CCCh. 4 - Prob. 8CCCh. 4 - Prob. 9CCCh. 4 - Prob. 10CC
Ch. 4 - Prob. 11CCCh. 4 - Prob. 12CCCh. 4 - Prob. 13CCCh. 4 - Prob. 14CCCh. 4 - Prob. 15CCCh. 4 - Prob. 16CCCh. 4 - Prob. 17CCCh. 4 - Prob. 18CCCh. 4 - Prob. 19CCCh. 4 - Prob. 20CCCh. 4 - Prob. 21CCCh. 4 - Prob. 22CCCh. 4 - Prob. 23CCCh. 4 - Prob. 24CCCh. 4 - Prob. 1CLCCh. 4 - Prob. 2CLCCh. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10QCh. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 14QCh. 4 - Prob. 15QCh. 4 - Prob. 16QCh. 4 - Prob. 17QCh. 4 - Prob. 18QCh. 4 - Prob. 19QCh. 4 - Prob. 20QCh. 4 - Prob. 21QCh. 4 - Prob. 22QCh. 4 - Prob. 23QCh. 4 - Prob. 24QCh. 4 - Prob. 25QCh. 4 - Prob. 26QCh. 4 - Prob. 27QCh. 4 - Prob. 28QCh. 4 - Prob. 29QCh. 4 - Prob. 30QCh. 4 - Prob. 31QCh. 4 - Prob. 32QCh. 4 - Prob. 33QCh. 4 - Prob. 34QCh. 4 - Prob. 35QCh. 4 - Prob. 36QCh. 4 - Prob. 37QCh. 4 - Prob. 38QCh. 4 - Prob. 39QCh. 4 - Prob. 40QCh. 4 - Prob. 41QCh. 4 - Prob. 42QCh. 4 - Prob. 43QCh. 4 - Prob. 44QCh. 4 - Prob. 45QCh. 4 - Prob. 46QCh. 4 - Prob. 47QCh. 4 - Prob. 48QCh. 4 - Prob. 49QCh. 4 - Prob. 50QCh. 4 - Prob. 51QCh. 4 - Prob. 52QCh. 4 - Prob. 53QCh. 4 - Prob. 54QCh. 4 - Prob. 55QCh. 4 - Prob. 56QCh. 4 - Prob. 57QCh. 4 - Prob. 58Q
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- Venus can be as bright as apparent magnitude −4.7 when at a distance of about 1 AU. How many times fainter would Venus look from a distance of 1 pc? What would its apparent magnitude be? Assume Venus has the same illumination phase from your new vantage point. (Hints: Light follows an inverse square law as does gravity, review Section 5-1c; also, review the definition of apparent visual magnitudes, Chapter 2.) (Note: 1 pc = 2.1 × 105 AU.)arrow_forwardAgain using Appendix F, which planets might you expect to have extreme seasons? Whyarrow_forwardLet's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Earth. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth yearsarrow_forward
- The figure below is a scaled representation of a planet's orbit with a semimajor axis of 1.598 AU. (Use the exact values you enter in previous answer(s) to make later calculation(s).) (a) Find the ratio of the aphelion-to-perihelion distance. TA (b) Find the perihelion and aphelion distances in astronomical units. AU AU (c) Find the distance the Sun is from the center of the orbit. AUarrow_forwardYou are given the following data from observations of an exoplanet: 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. What is the semimajor axis of this planet in AU? - Knowing the orbital radius in both kn and AU, use the value in km to find the circumference of the orbit, then convert that to meters. (Assume the orbit is a perfect circle). - Knowing the orbital circumference and the period in days, convert the days to seconds (multiply by 86,400) and find the orbital velocity in m/s - 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…arrow_forwardUse 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_forward
- The Mars Robotic Lander for which we are making these calculations is designed to return samples of rock from Mars after a long time of collecting samples, exploring the area around the landing site, and making chemical analyses of rocks and dust in the landing area. One synodic period is required for Earth to be in the same place relative to mars as when it landed. Calculate the synodic period (in years) using the following formula: 1/Psyn = (1/PEarth) - (1/PMars) where PEarth is the sidereal period of the Earth (1 year) and PMars is the sidereal period of Mars. If 3/4 of a Martian year was spent collecting samples and exploring the terrain around the landing site, calculate how long the Mars Robotic Lander expedition took!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
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