Physics 53
Summer 2010
Quiz 6
Solutions
Check the best answer.
1.
Which of the following is NOT true about Kepler’s laws?
All three of the laws are explained by Newton’s law of universal
gravitation.
√
The 1st law says that planetary orbits are ellipses with the sun at the
geometric center. [One focus of the ellipse.]
The 2nd law (the law of areas) is a consequence of conservation of
angular momentum.
One can use the 3rd law to determine the mass of a planet, to a good
approximation, if the planet has a moon of relatively small mass.
Check T or F depending on whether the statement is true or false.
2.
A person falling feet first in the vicinity of a neutron star (a small but very
massive star) would feel weightless, but would experience severe stretching due
to tidal forces.
√
T
F
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Physics 53
3.
Summer 2010
The total energy of a spaceship’s orbit around the earth is −3 × 1010 J. The orbit is
an ellipse with apogee distance r2 equal to 3 times the perigee distance r1 . {All
answers are numerical.]
a.
What is the potential energy at perigee? [Relate r1 to a and use the general
formulas for E and U.]
a.
b.
What is its kinetic energy at perigee?
c.
What is the kinetic energy at apogee?
Since 2a = 4r1 we have
U(r1 ) = −
GMm
= 3 × 1010 J. The potential energy at perigee is
4r1
GMm
= 4E = −12 × 1010 J.
r1
b.
K(r1 ) = E − U(r1 ) = 9 × 1010 J.
c.
Since U(r2 ) = −
GMm
GMm 1
=−
= 3 U(r1 ) = −4 × 1010 J, we have
r2
3r1
K(r2 ) = E − U(r2 ) = 1 × 1010 J. [Can also use v(r1 ) = 3v(r2 ) .]
2