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35 sats \ 2 replies \ @south_korea_ln 14 Jan \ on: Why scientists say we need to send clocks to the moon — soon science
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Even on Earth, GPS navigation systems need to account for these relativistic effects when communicating with the satellites.
\frac{\Delta t_M}{\Delta t_E} = \sqrt{\frac{1 - \frac{2GM_M}{r_M c^2}}{1 - \frac{2GM_E}{r_E c^2}}}
where
M_E, r_E
: mass and radius of EarthM_M, r_M
: mass and radius of the Moon- G: gravitational constant
c
: speed of light\Delta t
: proper time interval far from the massive body\Delta t'
: time interval closer to the massive body
from math import sqrt
G = 6.674e-11
c = 3e8
M_E = 5.972e24
r_E = 6_371e3
M_M = 7.342e22
r_M = 1_737e3
factor_E = sqrt(1 - (2 * G * M_E) / (r_E * c**2))
factor_M = sqrt(1 - (2 * G * M_M) / (r_M * c**2))
time_dilation_ratio = factor_M / factor_E
day_in_seconds = 24 * 60 * 60
time_difference = (1 - time_dilation_ratio) * day_in_seconds
print(time_dilation_ratio, time_difference)
This gives 57 microseconds.
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True. Tiny differences will cause major problems in navigation and communication. Maybe they could set up atomic clocks on the Moon or sync them with Earth somehow to keep everything accurate?
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