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Super drat or just a matter of physics?
On a planet the size of earth a drat moves 100m
south, 100m east, 100m north, and ends up where he
(or she) started. Thinking out of the box, how did this in
fact happen, and what is the subtended angle
More details:
The drat is very confused. This keeps happening no matter
where he is on the planet. Spherical polar coordinate systems
do not exist relative to the drat.
Radius of earth 6378 km
The north pole does not exist.
The triangle like path is composed of
three arcs. There is no planetary dipole
magnetic field. This question is related
to a contact's now deleted question.
Actually, Anthony Hopkins had a similar problem;
he ended up where he started.
az_, thank you for answering. The drat must have a way of
ascertaining cardinal directions along THE PATH let's call
it's vertices, ABC; it moves thus: A= B=C= A. If one mentally
rotates a "NORTH-SOUTH" spherical polar coordinate system
tangent to a static sphere, it is clear that and infinite number of
poles are allowed, hence the concepts of poles are null and
void relative to the drat. So, I respectfully disagree regarding
the realism of my question.
Side note, Anthony Hopkins also had a problem with a rather
large Bear.
Correction above: A= B= C= A
YA is not accepting the greater than symbol.
The drat moves from A to B to C to A to B......
subtended angle: In this case the angle between radius
vectors RA and RB for example. Radius vector RA = 6378 km.
The math is simple. No complex field theory is involved. Once the
subtended angle is calculated, a thing will become clearly evident.
Read the question header again. Yes, it is indeed a matter of physics,
well known EM physics. You must give the drat a way to navigate his simple
invisible coordinate system otherwise he gets hopelessly lost. SO, let
there be shelter at A, water at B, and food at C for the tiny drat. Let him
complete each metric in 1 day in order to stay alive on this featureless planet
unless we, in our privileged frame of reference, think otherwise.
2 Answers
- 9 years agoFavorite Answer
There are an infinite number of locations where this can happen. These solutions can be classified into two groups of possibilities:
1. Start at north pole, go 100m south, 100m east, 100m north and end up at the starting location.
2.i. Start near the south pole, 100m north of where the circumference of the earth is 100m. Go 100m south, 100m east (one circumference of the earth at this location), 100m north to end up at the starting location.
ii. Start near the south pole, 100m north of where the circumference of the earth is 50m. Go 100m south, 100m east (two circumferences of the earth), 100m north to end up at the starting location.
iii. Start near the south pole, 100m north of where the circumference of the earth is 33.3m. Go 100m south, 100m east (three circumferences of the earth), 100m north to end up at the starting location.
...
n. (where n is iv. thru ∞). Start near the south pole, 100m north of where the circumference of the earth is (100/n)m. Go 100m south, 100m east (n circumferences of the earth), 100m north to end up at the starting location.
I'm not sure what you mean by subtended angle. Please clarify.
EDIT:
I'm not sure I agree with your definition of subtended angle because it seems arbitrary that the point C does not figure into the definition of subtended angle. More generally, your definition has no meaning in a solution that contains more than two points (which actually includes both solution 1 and 2 above).
I think a better definition for subtended angle (if this is required), is the solid angle. In solution 1, for example, compute the area of triangle ABC and divide by the surface area of the sphere. In solution 2, it would be the area on the surface of the sphere near the south pole bounded by the circle, divided by the surface area of the sphere.
- az_lenderLv 79 years ago
My reaction to the first paragraph is,
of course this would happen if one started out at the north pole.
In a later paragraph, you say "the north pole does not exist,"
and you say this sequence of events keeps recurring no matter where on the planet the starting point is located.
But if "the north pole does not exist,"
what then is the DEFINITION of "north" ?
I don't think any of north, east, or south can be defined if the planet does not have a rotation axis. And if it has a rotation axis, then it has a north pole (the pole about which rotation appears to be counter-clockwise).
This is certainly not the desired answer, but I'm claiming that the question is unrealistic.
