Use Newton's law to estimate the distance of Jupiter to the sun by assuming that the orbits of the earth and Jupiter are circles A long time ago before scientists could measure the speed of lightaccurately, O. Römer, a Danish astronomer studied the times of eclipses ofthe planet Jupiter. He was able to determined the velocity of light fromobserved periods of a satellite around the planet Jupiter. Fig. 1-1 shows theorbit of the earth E around the sun S and one of the satellites M around theplanet Jupiter. (He observed the time spent between two successiveemergences of the satellite M from behind Jupiter.)EMFig. 1-1. The orbits of the earth E around the sun S and a satellite Maround Jupiter J. The average distance of the earth E to the Sun is Rg =149. 6 X10° km. The maximum distance is REa = 1. 015RĘ. The period ofrevolution of the earth is 365 days and of Jupiter is 11. 9 years.A long series of observations of the eclipses permitted an accurateevaluation of the period. The observed period T depends on the relativeposition of the earth with respect to the frame of reference SJ as one of theaxis of coordinates. The average time of revolution is To42 h 28 m 16s%3Dand maximum observed period is (T +15) s.

Given: To calculate the distance of the Jupiter to the sun using the Newton's law as,

Answered: Jupiter to the sun by assu

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