same direction and in the same plane. Pat orbits in 3 hours and Mike in 7.5 hours. At 12 noon Toronto time, Mike sees Pat directly below. What will be the next time that Mike's capsule is directly above Pat's capsule?
2006-09-01 16:56:27 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
whatever
2006-09-01 16:57:20 · answer #1 · answered by Mike R 5 · 0⤊ 1⤋
Because of the different orbital periods, there must needs be different orbital altitudes and the two orbits will precess around the earth at different rates. This factor depends on the inclination of the orbit -- and it's how the low altitude weather satellites (those that are at about 1000 miles altitude with a period of two hours) keep their orbital plane aligned with the sun so they take pictures of each area at nearly the same sun angles each day.
Now for the hard part... I don't remember the equations for this precession, but the bottom line is that they likely won't be directly over each other for a very long time. What it means is the orbital planes wobble around the earth due to the attraction of the earth's equatorial bulge. (The equatorial diameter of the earth is about 1/297 larger than the polar diameter, and there are other bulges that have much smaller effects as well.
2006-09-01 17:05:00 · answer #2 · answered by birchardvilleobservatory 7 · 0⤊ 0⤋
The Least Common Multiple solution (15 hours) works to find when they are both above the same spot, but does not answer the question as is.
The next time is when they pass each other, Pat has traveled one orbit further than Mike. That is,
t / 3 = 1 + t / 7.5
5 t = 15 + 2 t
3 t = 15
t = 5 hours
2006-09-01 17:12:00 · answer #3 · answered by dutch_prof 4 · 1⤊ 0⤋
The least common multiple of 3 and 7.5 is 15, so the next coincidence will be at 3 AM Toronto time the next day. If they are in the earth's shadow, they will need to show lights to see each other.
2006-09-01 17:01:03 · answer #4 · answered by Anonymous · 1⤊ 0⤋
3 am?
2006-09-01 16:58:17 · answer #5 · answered by Anonymous · 0⤊ 0⤋
12 Noon Toronto Time...
They were in the same capsule.
2006-09-01 16:58:33 · answer #6 · answered by Anonymous · 0⤊ 1⤋
I just got a headache trying to figure this one out. Much props to anyone who can figure out this brain twister.
2006-09-01 16:58:14 · answer #7 · answered by Apple Pie 2 · 0⤊ 1⤋