Astronomy Today (9th Edition)
9th Edition
ISBN: 9780134450278
Author: Eric Chaisson, Steve McMillan
Publisher: PEARSON
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Chapter 2, Problem 10MC
To determine
The correct option, from the following options, for the effect on the more massive star out of the two stars of unequal masses, orbits of which are shown in Figure
(a) moves more slowly than
(b) moves more rapidly than
(c) has half the gravity of
(d) has twice the eccentricity of the less massive star
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Consider a star of mass M₁ that hosts a planet of mass M₂ on a circular orbit with semi-
major axis a. The mass of the planet is related to the orbital velocity of the star by the
expression
G
M₂1 Μια
Using Kepler's 3rd law show that this expression can be written as
V₁ =
2πG
(27²) ¹/3
9
M²P
where P is the orbital period of the planet around the star.
V₁ = M₂
Use a distance of R = 1.48x10^11 meters for the distance between the earth and the sun.
Use a mass of 1.99x10^30 kg to be 1 solar mass.
For each of the different sun masses (as values of solar mass, aka 0.5 solar masses = 1x10^30 kg), as outlined in the lecture, calculate the period of the earth's orbit in days using Kepler's law for circular orbits (I double-checked it with these values and it works) and also calculate the corresponding orbital velocity of the earth.
Questions:
1.) Using these values, and 6x10^24 kg for the mass of the earth, what is the strength of the gravitational force between the earth and the sun?
2.) If the earth were twice as far from the sun, what would be its period of orbit?
3.) Mars orbits the sun at a distance of 2.18x10^11 meters. How long is a Martian year, using Kepler's law for circular orbits?
An object of mass mm is launched from a planet of mass M and radius R.
Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M=5.38×1023kg and R=83.2×103km.
V= ( 2 G M/R )0.5=
Chapter 2 Solutions
Astronomy Today (9th Edition)
Ch. 2 - Prob. 1DCh. 2 - Prob. 2DCh. 2 - Prob. 3DCh. 2 - Prob. 4DCh. 2 - Prob. 5DCh. 2 - Prob. 6DCh. 2 - Prob. 7DCh. 2 - Prob. 8DCh. 2 - Prob. 9DCh. 2 - Prob. 10D
Ch. 2 - Prob. 11DCh. 2 - Prob. 12DCh. 2 - Prob. 13DCh. 2 - Prob. 14DCh. 2 - Prob. 15DCh. 2 - Prob. 1MCCh. 2 - Prob. 2MCCh. 2 - Prob. 3MCCh. 2 - Prob. 4MCCh. 2 - Prob. 5MCCh. 2 - Prob. 6MCCh. 2 - Prob. 7MCCh. 2 - Prob. 8MCCh. 2 - Prob. 9MCCh. 2 - Prob. 10MCCh. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - Prob. 8P
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