Kepler\'s third law can be simplified to T/ 1 or T if the orbit period T is expr
ID: 1584142 • Letter: K
Question
Kepler's third law can be simplified to T/ 1 or T if the orbit period T is expressed in earth years and r in Astronomical Units (A.U.), the sun I A.U.-1.5x10" m) sun-earth distance. 7. Calculate how long it takes Mars in earth years for one trip around the sun by using an average Sun-Mars distance of 1.5 A.U. ) 0.735 earth years ) 1.84 earth years ) 3.37 earth years ) 164 earth years Show calculation: 8. Caleulate how long it takes Neptune in earth years for one trip around the sun by using an average Sun-Neptune distance of 30 A.U ) 0.735 earth years ) 1.84 earth years ) 3.37 earth years ) 164 earth years Show calkulation: 9-10. Find the gravitational force (the weight) of a 75 kg person standing on the surface of the earth. a) By using the gravitation acceleration g-9.8 m/s ) 9.8 m/s ) 9.8 N O 735 N O 737 N Show ealculation: b) By using Newton's law of gravitation. ) 9.8 m/s ) 9.8 N ) 735N ) 737 N (See sample exercise "try this box 5.2) m-598k10 Show calculation Bonus questions more difficult) 11." "Weighing the Earth" By measuring the gravitation acceleration on the earth surface (g-9.8 m/s),e.g. with the pendulum experiment, we can determine the mass of the earth (m,-5.97x10M kg) by using the following equation (see book 4th Ed., p.92) or m-gr/G where the earth radius r, -6.38 x 10° m and the universal gravitation constant G 6.67 x 10l m'/kgs'. Show calculation: Calculate the mass of the earth me! 12.** “Weighing the sun" Newton's formulation of Kepler's third law can be rearranged to determine the mass of the sun from the orbit of a planet r-1.5x10" m (sun-earth distance G-6.67x 10" m/kg s Calculate the mass of the sun from the orbit of the earth around the sun with Show calculation: (use separate sheet if necessary) T- I year (orbital period of Earth) Hint: convert T to seconds!Explanation / Answer
7.
Te = time taken by earth =1 yr
Tm = time taken by mars = ?
re = average earth-sun distance = 1 Au
rm = average mars-sun distance = 1.5 Au
using kepler's third law
(Te/Tm)2 = (re/rm)3
(1/Tm)2 = (1/1.5)3
Tm = 1.84 earth-yrs
8.
Te = time taken by earth =1 yr
Tn = time taken by neptune = ?
re = average earth-sun distance = 1 Au
rn = average mars-sun distance = 30 Au
using kepler's third law
(Te/Tn)2 = (re/rn)3
(1/Tn)2 = (1/30)3
Tn = 164 earth-yrs
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