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69 sats \ 0 replies \ @south_korea_ln 14 Jan \ parent \ on: Why scientists say we need to send clocks to the moon — soon science
\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 Earth
  • M_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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