Assignment #6
Chapter 6 Questions:
6.26 Let the planet at distance r be labeled #1 and that at 2r be labeled #2.
Periods (using Kepler’s third law) (T1/T2)2 = (r1/r2)3
T
1/T2 = (r1/r2)3/2 = (1/8)1/2
Speeds (use Newton’s 2nd law) GMm/r2 = v2/r
v = (GMm/r)1/2
v1/v2 = √2
Accelerations (use Newton’s 2nd law with centripetal acceleration) GMm/r2 = ma
a= GM/r
2
a1/a2 = 4
6.31 Each orbital plane must contain the center of the earth at on focus of the orbital ellipse. The centers of
the Artic and Antarctic circles and the circles of the Tropics of Cancer and Capricorn are not the center of the
earth.
Chapter 7 Questions:
7.14
a) The frequency is independent of the amplitude, A, so the frequency is unaffected
b) The maximum speed is Aω, so increasing A by a factor of 3 triples the maximum speed.
c) The magnitude of the maximum acceleration is ω2A, so increasing A by a factor of 3 triples the magnitude
of the maximum acceleration
7.21
a) Nothing happens
b) Nothing happens
c) The effective value of the acceleration magnitude g (in Equation 7.22) increases, so the period decreases.
d) The effective value of the acceleration magnitude g (in Equation 7.22) decreases, so the period increases.
Chapter 6 Problems:
