21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 12QP
To determine
The reason for the data that the average speed of a new planet in orbit is faster when it far from the star and slower when it is near the star.
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1. Most galaxies, including our own Milky Way, have supermassive black holes at their centers. Recently, astronomers were able to track one star, named S2, as it orbited the black hole at the center of our galaxy. The star's actual orbit is elliptical, but we'll model it as a circular orbit. S2 has a period of 15 years and an orbit radius of 1000 au, where 1 au = 1 astronomical unit is the distance of the earth from the sun.
a. What is the speed of S2? Give your answer as a fraction of c, where c is the speed of light, c=3.0×10^8m/s.
b. What is the mass of the black hole? Give your answer as a multiple of Ms, where Ms is the solar mass, Ms=2.0×1030kg
2. A projectile is shot straight up from the earth's surface at a speed of 1.10×104 km/hr. How high does it go?
Which of the following statements cannot be supported by Kepler's laws of planetary motion?
a The distance of a planet around the sun changes throughout its orbit.
b The speed a planet is moving around the sun changes throughout the year.
c The orbital period of Mercury can be calculated using the orbital period of Jupiter and the average distances of both planets.
d The age of the four largest planets can be determined using the age of the four smallest planets and the average distances of each planet.
2. From Kepler's Third Law, the period (P) squared divided by the cube of semi-major axis (d) is
the same for all planets and is expressed as P2 / d = k, where k is a constant. One can
conclude that
A. In the same amount of time, every planet orbits the sun.
B. At the same distance from the sun, every planet orbits the sun.
C. It takes more time to orbit the sun if the planets are farthest from the sun.
D. It takes less time to orbit the sun if the planets are farthest from the sun.
Chapter 3 Solutions
21st Century Astronomy
Ch. 3.1 - Prob. 3.1ACYUCh. 3.1 - Prob. 3.1BCYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3 - Prob. 1QPCh. 3 - Prob. 2QPCh. 3 - Prob. 3QPCh. 3 - Prob. 4QPCh. 3 - Prob. 5QP
Ch. 3 - Prob. 6QPCh. 3 - Prob. 7QPCh. 3 - Prob. 8QPCh. 3 - Prob. 9QPCh. 3 - Prob. 10QPCh. 3 - Prob. 11QPCh. 3 - Prob. 12QPCh. 3 - Prob. 13QPCh. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Prob. 16QPCh. 3 - Prob. 17QPCh. 3 - Prob. 18QPCh. 3 - Prob. 19QPCh. 3 - Prob. 20QPCh. 3 - Prob. 21QPCh. 3 - Prob. 22QPCh. 3 - Prob. 23QPCh. 3 - Prob. 24QPCh. 3 - Prob. 25QPCh. 3 - Prob. 26QPCh. 3 - Prob. 27QPCh. 3 - Prob. 28QPCh. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Prob. 32QPCh. 3 - Prob. 33QPCh. 3 - Prob. 34QPCh. 3 - Prob. 35QPCh. 3 - Prob. 36QPCh. 3 - Prob. 37QPCh. 3 - Prob. 38QPCh. 3 - Prob. 39QPCh. 3 - Prob. 40QPCh. 3 - Prob. 41QPCh. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Prob. 44QPCh. 3 - Prob. 45QP
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