Suppose that a planet was reported to be orbiting the sun-like starIota Horologi

Question

Suppose that a planet was reported to be orbiting the sun-like starIota Horologii with a period of 345days. Find the radius of the planet's orbit, assuming that IotaHorologii has twice the mass as theSun. (This planet is presumably similar to Jupiter, but it may havelarge, rocky moons that enjoy a pleasant climate.) (Use 2.00 x 10^30 kg for themass of the Sun.) I just can't get it right. I change the days to seconds andmultiplied the suns mass by two for the mass of iota horologii.Then i used the equation I thought was right? Can someonehelp!?

Explanation / Answer

You probably used [P/(2) ]2 = a3 /(G(M+m)) M= 2 x 2.0 × 1030kg= 4 x × 1030 kg m= 1.9 × 1027kg (mass of the Jupiter?) G= 6.67 x 10 -11 m3/(kg s2) P= 345 x 24 x 3600 = 29808000s a = [ [P/(2) ]2(G(M+m))]1/3 a=(Rmax + Rmin)/ 2 a=R is ecentricity -> 0 we have R= [ [P/(2) ]2(G(M+m))]1/3 R= [ [29808000 / (2) ]2(6.67 x 10 -11 (4.0 + x 1030   +1.9 ×1027 )]1/3 R= 1.82 x 1011m

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