- #1
SimpliciusH
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Hi, I've been tinkering with this problem occasional over the past few days, but still little progress and I don't have much time left.
I basically can't get over my first (&second) attempt at solving it since it seemed so damned reasonable. I've tried to modify for the measurment being taken in my geographical location, but that dosen't work and just assuming that it was taken at a location just right is too much even for my sloppy non-scientific thinking. I also tought about optical effects that may come into play due to the light traveling basically the maximum distance it can through the atmosphere, but I quickly dismissed it since it can't possibly be the same order of magnitude.
My brain is locked and out of ideas :( please help
1.
Rough translation of the text:
Measure the radius of the Earth with nothing but a stopwatch.
While lying down and watching the sun set start your timer as the Sun touches the horizont, then stand up (your eyes are 1.7 m from the ground while standing) and wait for the Sun to touch the horizont again. 11.1 seconds have passed.
Is it possible to estimate (calculate) the radius of the Earth? [I would say yes, but the best estimate I got was way off so I might be mistaken :( ]
The method works best near the equator.
t= 11.1 s
h= 1.7 m
R = ? (R... the radius of the Earth)
I tried approaching this in two way's which are prety related (I'll skip most of the reasoning since I think people will see how I did it).
a) cos alpha = R / (R + h)
alpha = (11.1s * 360 degrees) / (24 * 3600 s)
R= h * cos alpha / (1- cos alpha) =~ 5300 km :( [my result is just 80% is the real R]b) I got to this by thinking about the distance to the horizont.
(2*R*h)^(1/2)/ 2* pi * R = t/24 * 3600s
R = h * (24*3600s)^2 / 2 * (t*pi)^2 =~ 5200 km [as you see slightly worse than before]I hope you guys can understand me despite my horrible English. :) Also terribly sorry for the bad math notation, I don't have much experience typing this sort of thing.
I basically can't get over my first (&second) attempt at solving it since it seemed so damned reasonable. I've tried to modify for the measurment being taken in my geographical location, but that dosen't work and just assuming that it was taken at a location just right is too much even for my sloppy non-scientific thinking. I also tought about optical effects that may come into play due to the light traveling basically the maximum distance it can through the atmosphere, but I quickly dismissed it since it can't possibly be the same order of magnitude.
My brain is locked and out of ideas :( please help
1.
Rough translation of the text:
Measure the radius of the Earth with nothing but a stopwatch.
While lying down and watching the sun set start your timer as the Sun touches the horizont, then stand up (your eyes are 1.7 m from the ground while standing) and wait for the Sun to touch the horizont again. 11.1 seconds have passed.
Is it possible to estimate (calculate) the radius of the Earth? [I would say yes, but the best estimate I got was way off so I might be mistaken :( ]
The method works best near the equator.
t= 11.1 s
h= 1.7 m
R = ? (R... the radius of the Earth)
Homework Equations
&The Attempt at a Solution
:I tried approaching this in two way's which are prety related (I'll skip most of the reasoning since I think people will see how I did it).
a) cos alpha = R / (R + h)
alpha = (11.1s * 360 degrees) / (24 * 3600 s)
R= h * cos alpha / (1- cos alpha) =~ 5300 km :( [my result is just 80% is the real R]b) I got to this by thinking about the distance to the horizont.
(2*R*h)^(1/2)/ 2* pi * R = t/24 * 3600s
R = h * (24*3600s)^2 / 2 * (t*pi)^2 =~ 5200 km [as you see slightly worse than before]I hope you guys can understand me despite my horrible English. :) Also terribly sorry for the bad math notation, I don't have much experience typing this sort of thing.