UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Question
Chapter 10, Problem 33QAP
(a)
To determine
The reason why star 2 has a smaller orbit than star 1.
(b)
To determine
The sketch of binary star system for case when star 1 has a very low mass.
(c)
To determine
The sketch of binary star system for case when mass of star 1 and star 2 is equal.
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The Algol binary system consists of a 3.7 Msun star and a 0.8 Msun star with an orbital period of 2.87 days. Using Newton’s version of Kepler’s Third Law, calculate the distance, a, between the two stars. Compare that to the size of Betelgeuse (you’ll need to look that up).
Newton’s Version of Kepler’s Law: (M1 + M2) P2 = (4p2 /G) a3
Rearrange the equation to solve for a. Pi, p, is equal to 3.14. IMPORTANT NOTE: Google the value of G (the Universal Gravitational Constant) or look it up in your text. NOTICE THE UNITS. You must convert every distance and time in your equation to the same units, otherwise, you’ll get an incorrect answer. That means you must convert distances to meters, solar masses to kilograms, and time to seconds. When you compare your value to the size of Betelgeuse, it will also help that they are in the same units.
White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a
4
sphere is Tr.)
3
km
Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size?
I Table A-10 I Properties of the Planets
ORBITAL PROPERTIES
Semimajor Axis (a)
Orbital Period (P)
Average Orbital
Velocity (km/s)
Orbital
Inclination
Planet
(AU)
(106 km)
(v)
(days)
Eccentricity
to Ecliptic
Mercury
0.387
57.9
0.241
88.0
47.9
0.206
7.0°
Venus
0.723
108
0.615
224.7
35.0
0.007
3.4°
Earth
1.00
150
1.00
365.3
29.8
0.017
Mars
1.52
228
1.88
687.0
24.1
0.093
1.8°
Jupiter
5.20
779
11.9
4332
13.1
0.049
1.30
Saturn
9.58
1433
29.5
10,759
9.7
0.056
2.5°
30,799
60,190
Uranus
19.23
2877
84.3
6.8
0.044
0.8°
Neptune
* By definition.
30.10
4503
164.8
5.4
0.011
1.8°
PHYSICAL PROPERTIES (Earth = e)…
(Astronomy)
Binary Pulsar.
Part A: Use the orbital period 27 min for the binary pulsar (two neutron stars orbit each other) to find the orbital separation of the pair in AU and solar radii. Assume a neutron star's mass is 3 solar masses. (Hints: Use the version of Kepler's third law for binary stars.)
Part B: Is this system orbiting closer or further than Mercury is to the Sun?
Chapter 10 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 10.1 - Prob. 10.1CYUCh. 10.2 - Prob. 10.2CYUCh. 10.3 - Prob. 10.3CYUCh. 10.4 - Prob. 10.4CYUCh. 10 - Prob. 1QAPCh. 10 - Prob. 2QAPCh. 10 - Prob. 3QAPCh. 10 - Prob. 4QAPCh. 10 - Prob. 5QAPCh. 10 - Prob. 6QAP
Ch. 10 - Prob. 7QAPCh. 10 - Prob. 8QAPCh. 10 - Prob. 9QAPCh. 10 - Prob. 10QAPCh. 10 - Prob. 11QAPCh. 10 - Prob. 12QAPCh. 10 - Prob. 13QAPCh. 10 - Prob. 14QAPCh. 10 - Prob. 15QAPCh. 10 - Prob. 16QAPCh. 10 - Prob. 17QAPCh. 10 - Prob. 18QAPCh. 10 - Prob. 19QAPCh. 10 - Prob. 20QAPCh. 10 - Prob. 21QAPCh. 10 - Prob. 22QAPCh. 10 - Prob. 23QAPCh. 10 - Prob. 24QAPCh. 10 - Prob. 25QAPCh. 10 - Prob. 26QAPCh. 10 - Prob. 27QAPCh. 10 - Prob. 28QAPCh. 10 - Prob. 29QAPCh. 10 - Prob. 31QAPCh. 10 - Prob. 32QAPCh. 10 - Prob. 33QAPCh. 10 - Prob. 34QAPCh. 10 - Prob. 35QAPCh. 10 - Prob. 36QAPCh. 10 - Prob. 37QAPCh. 10 - Prob. 38QAPCh. 10 - Prob. 39QAPCh. 10 - Prob. 40QAPCh. 10 - Prob. 41QAPCh. 10 - Prob. 42QAPCh. 10 - Prob. 43QAPCh. 10 - Prob. 44QAPCh. 10 - Prob. 45QAP
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