Assume the moon is a perfect sphere and a straight tunnel has been drilled through the center. How long would it take a 1kg ball dropped from one end of the tunnel to reach the center? Ignore all resistances.
If a second 1kg ball is dropped 10 seconds after the first one, when and where in the tunnel would they first meet?
Idealized Moon Stats:
- Diameter: 3480 kilometers
- Mass: 7.38x10^22 kilograms (uniform density)
(In reply to
re: part 1: another method; another answer (wrong assumption) by np_rt)
Yes, you're correct; I had given the wrong proportionality for the acceleration due to gravity. The corrected line is
acc = acc0 * r
The resulting corrected table is
100 162.407 8126.67
200 323.297 32430.79
300 481.167 72685.34
400 634.543 128514.35
500 781.992 199396.34
600 922.137 284669.20
700 1053.668 383536.44
800 1175.357 495074.56
900 1286.067 618241.69
1000 1384.764 751887.35
1100 1470.526 894763.16
1200 1542.552 1045534.55
1300 1600.169 1202793.15
1400 1642.840 1365070.04
1500 1670.164 1530849.39
1600 1681.888 1698582.65
1624.63 1682.365 1740006.97
27.07708333333333
Giving 1624.63 seconds or 27.077 minutes as the answer to part 1. This confirms my first answer, using the argument from a circular orbit of the moon. I had been wondering why the two answers did not match.
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Posted by Charlie
on 2004-11-23 00:06:41 |
re(2): part 1: another method; another answer (wrong assumption)
