Astronomy 102, Fall 2004
Homework Assignment #9
This homework set is due into my office by 5:00AM on Friday, December 10. Late homework will not be accepted.
Staple. If you have more than one page, staple them together; do not just fold the corner. If you have multiple pages and do not staple, I will deduct one point from your score..
This homework assignment is optional. If you do it, it will replace the grade on your lowest previous homework assignment.
Please write out the problem statement at the top of your solution. (This is for two reasons; it is so I can know which problems you answered, and that you answered the right problem from the bit. It also will make your graded homework more useful as a study aid later.)
You may consult with other students (as well as with the TAs and professor) on this homework set. However, your final answer should be your own. Do not write down an answer you don't understand, and do not "dictate" an answer to somebody else.
Using F=G M m/R2 for the the force of gravity, and knowing that 1N=0.225lbs and 1N=1 kg m/s2, calcaulte the following:
(a) The tidal difference in gravity between the foot and head of a 2m (6'6") tall person who masses 70kg (corresponding to an Earth weight of 150 lbs), in pounds, at the surface of the Earth. (I gave you the answer in class; show me that you know how to do this mathematically.) Use 6,378,140. m for the average radius of the Earth.
(b) The tidal difference in gravity bweteen the foot and head of a 2m tall person who masses 70kg, just outside the event horizon of a black hole of mass 2.00 times the mass of the Sun, in pounds.
(c) The tidal difference in gravity between the foot and head of a 2m tall person who masses 70kg, just outside the event horizon of a black hole of mass 2×106 times the mass of the Sun, in pounds.
(d) (One point extra credit for Physics majors and those who've taken Math 170/175): use the binomial theorem to show that tidal forces are proportional to 1/R3.
When a white dwarf reaches the Chandrasaekar mass (1.4 solar masses), electron degeneracy pressure can no longer support it. Similarly, when the degenerate core of a very massive star reaches the Chandrasaekar mass, electron degeneracy pressure can no longer support it. In the latter case, the core collapses down to a neutron star. In the former case, however, no neutron star is left behind. Explain why there is this difference.
Recall from homework assignment #7 that when you bring some mass m close to another mass M, it loses gravitational energy equal to G M m /R. (Notice: not divided by R squared, just R.)
When you dump some mass into a black hole of mass 2×106 times the mass of the Sun, what fraction of its rest mass energy is released from gravitational energy? Comment on the relative efficiency of black hole gravity versus nuclear fusion for producing energy.