On a

On a someday, the Sun, Venus, and the Earth are in eclipse, i. E. Venus is between the Sun and the Earth. Venus orbits the Sun in 225 days. In how many years will all three bodies be in alignment again?

Correct answer:

x =  1.6071

Step-by-step explanation:

T1=225 d T2=365 d  225=3252 365=573 LCM(225,365)=325273=16425  T=LCM(T1,T2)=LCM(225,365)=16425  x0=T/T2=16425/365=45  ω1=360/T1=360/225=58=153=1.6 °/d ω2=360/T2=360/365=73720.9863 °/d  x ω1 = x ω2 + k 360  x1 (ω1ω2)=1 360 x1 (1.60.98630136986301)=1 360  0.613699x1=360  x1=0.61369863360=586.60714286  x1=2816425586.607143  x2 (ω1ω2)=2 360 x2 (1.60.98630136986301)=2 360  0.613699x2=720  x2=0.61369863720=1173.21428571  x2=14164251173.214286  x3 (ω1ω2)=3 360 x3 (1.60.98630136986301)=3 360  0.613699x3=1080  x3=0.613698631080=1759.82142857  x3=28492751759.821429  x=x1/T2=586.6071/365=1.6071



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