The Cosmic Perspective
The Cosmic Perspective
7th Edition
ISBN: 9780321839558
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: Addison-Wesley
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Chapter 1, Problem 49EAP

Earth Rotation Speed. Mathematical Insight 1.3 shows how to find Earth’s equatorial rotation speed. To find the rotation speed at any other latitude, you need the following fact: The radial distance from Earth’s axis at any latitude is equal to the equatorial radius times the cosine of the latitude. Use this fact to find the rotation speed at the following latitudes. (Hint: When using the cosine (cos) function, be sure your calculator is set to recognize angles in degree mode, not in radian or gradient mode.)

a. 30°N b. 60°N c. your latitude

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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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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?

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The Cosmic Perspective

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