Calculation on Romer's theory of the speed of light

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SUMMARY

This discussion focuses on the calculation of the average distance between the Earth and the Sun based on Romer's observations of Io's eclipses. Using the speed of light, 2.998 × 108 m/s, and the time interval of 20.5 minutes (1230 seconds), the calculated distance is approximately 368,754,000 km. The standard velocity equation, v = x/t, was applied to derive this distance, confirming the relationship between time, velocity, and distance in the context of celestial observations.

PREREQUISITES
  • Understanding of basic physics concepts, particularly velocity and time.
  • Familiarity with the speed of light as a constant (2.998 × 108 m/s).
  • Knowledge of unit conversions between meters and kilometers.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Explore the implications of Romer's findings on the historical understanding of light speed.
  • Study the principles of celestial mechanics and their relation to observational astronomy.
  • Learn about the methods used to measure astronomical distances, such as parallax and standard candles.
  • Investigate the effects of relative motion on the perception of time intervals in physics.
USEFUL FOR

Astronomy students, physics enthusiasts, and anyone interested in the historical context of light speed measurements and celestial mechanics.

Gothy
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Homework Statement


As a result of his observations, Romer concluded
that the time interval between eclipses
of Io by Jupiter increased by 20.5 min during
a 5.78 month period as the Earth moved
from a point in its orbit where its motion
is toward Jupiter to a diametrically opposite
point where it moves away from Jupiter. The
presently accepted value of the speed of light
in vacuum is 2.998 × 108 m/s.
Find an average value for the distance between
the Earth and the Sun.
Answer in units of km

c=2.998 × 108 m/s
t= 20.5 min (1230s)
x= ?

Homework Equations


my guess would be the standard velocity equation, v= x/t (x=vt)
but it appears i am wrong, is there another formula that includes velocity and time?


The Attempt at a Solution


v=x/t
x=vt
x= (2.998 × 108 m/s)*(20.5*60)
x= (2.998 × 108 m/s)*1230
x= 3.68751 x 1011 meters
x= 368754000 km
 
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Hi Gothy! :smile:

Hint: if a lighthouse flashes once a second, what is the difference between the time between the flashes as observed by someone moving towards it at speed v, and by someone else moving away at speed v? :wink:
 

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