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Last edited by ddac; 07-20-09 at 06:40 PM.
In this diagram, the arc length from the pole to the horizon at 5 feet is 18 degrees (90 - 72). The length of an 18 degree arc on a circle of diamater 100 is 15.5 feet, so the two people are 31 feet apart.
how did you end up with those numbers?
Food for thought: if you aren't dead by 2050, you and your entire family will be within a few years from starvation. Now that is a cruel gift to leave for your offspring. ;)
http://sanfrancisco.ibtimes.com/arti...ger-photos.htm
light can bend you know
I pretty much came up with the same equation as ehidle
Food for thought: if you aren't dead by 2050, you and your entire family will be within a few years from starvation. Now that is a cruel gift to leave for your offspring. ;)
http://sanfrancisco.ibtimes.com/arti...ger-photos.htm
Going back to ddac's image, would the lines of the triangle representing the people be pointing outward a little bit? Otherwise they would be leaning forward in relation to the Earth's surface, eh?
That's where the difference in ehidle's and ddac's nubmers stems from. ehidle assumes that the people will be perpendicular to the planet's surface. ddac assumed (like I did) that with such a small planetary diameter, you can calculate for additional distance by allowing the subjects to lean forward and increase their sightline distance.
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- Mandi M.
Also, a planet (more of an asteroid, really) one hundred feet in diameter is going to be too small to have any meaningful gravitational pull, so not only does it not have the pull to keep these two people planted on terra firma, but it doesn't have a usable atmosphere!
The fact that these two people are alive indicates that they have some kind of spacesuit on, but that oxygen supply is limited. They should really quit dicking around and work together to figure out how to get home.
Whoops! I had a factor of 2 in there.. tee hee...
...
Now I get 42.93 feet
As soon as the 2 start to move back from being eyeball to eyeball they will lose eye contact. Unless you allow them to look at the other person on a plane other than perfectly level relative to their own body position. (IOW, they can only look straight ahead, not "down" as they back away.)
As for the normal arc length calc's you will need to compensate in some fashion for the change in vertical positioning as the two persons move along the circumference of the planet. As each goes further towards the equator, they will move from a vertical position to a more horizontal position. This will decrease the "line of sight height" from 5' to something "shorter."
Someone plot another circle outside of the original at 5'. A line between 2 points on the outside circle would intersect the original circle where the "head position" of the 2 spacemen would be. A line from each of those points through the center would show the "foot position." The distance between the two "foot position" points would be the arc length distance between them.
Oh crap, ehilde did the diagram already. The answer is 31 feet.
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***
2006 60cm Orbea Orca with 2009 Rival
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1987 Haro Extreme (undermount rear brake) mtn bike with Shimano LX and Rock Shox fork
2009 Kona Hei-Hei 2-9
I get 43.5 feet.
(ehidle, your original diagram is wrong, the greater circle should have a diameter of 110, not 105. I didn't check your math from there).
So. Imagine a right triangle with one vertex at the center of the planet. The Y height is 50 (the radius of the planet, which defines the horizon). The hypotenuse R is 55 (the radius of the outer circle). The angle gamma is therefore approximately 65 degrees. (SOHCAHTOA, sin(gamma) = 50/55 = 0.9).
The angle theta defining the arc between the two people will be 180 - 2*gamma. Theta, therefore, is 50 degrees.
50 degrees is 0.87 radians. The length of an arc is given by theta (in radians) * radius (which is the planet radius, 50). 50 * 0.87 = 43.5.
Last edited by tjwarren; 06-04-09 at 03:30 PM.
^^ Yeah I know... I'm not with it today... been a bad week
Here's the real physics question. On a planet this small gravity is very week. Assuming a density similar to that of earth, They can only walk backwards at a rate where gravity is sufficient to provide the centripetal acceleration to keep them on the ground. Thus, the question is not how far apart they are, but what is the theoretical minimum amount of time required to arrive at this location.
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