Calculate the orbital semi-major axis of the Sun\'s orbit about the barycenter o

Question

Calculate the orbital semi-major axis of the Sun's orbit about the barycenter of the solar system,in AU, in response to Jupiters orbital motion. Since Jupiter constitutes ~70% of the non-solar mass of our solar system, you can ignore solar system bodies less massive than Jupiter in your computation. Need to use Kepler laws somehow but I have to be doing something wrong. Calculate the orbital semi-major axis of the Sun's orbit about the barycenter of the solar system,in AU, in response to Jupiters orbital motion. Since Jupiter constitutes ~70% of the non-solar mass of our solar system, you can ignore solar system bodies less massive than Jupiter in your computation. Need to use Kepler laws somehow but I have to be doing something wrong. Calculate the orbital semi-major axis of the Sun's orbit about the barycenter of the solar system,in AU, in response to Jupiters orbital motion. Since Jupiter constitutes ~70% of the non-solar mass of our solar system, you can ignore solar system bodies less massive than Jupiter in your computation. Need to use Kepler laws somehow but I have to be doing something wrong. Calculate the orbital semi-major axis of the Sun's orbit about the barycenter of the solar system,in AU, in response to Jupiters orbital motion. Since Jupiter constitutes ~70% of the non-solar mass of our solar system, you can ignore solar system bodies less massive than Jupiter in your computation. Need to use Kepler laws somehow but I have to be doing something wrong.

Explanation / Answer

The barycentre of the Sun–Jupiter system
is such that
mass of Jupiter, MJ,=1.90 × 1027 kg,
mass of the Sun Mo = 1.99 × 1030 kg,
Jupiter’s orbital semi-major axis, aJ =7.784 × 1011 m.

Mj*aj=aoMo

ao=Mj/Mo*aj
=(1.90*1027/1.99*1030)*7.784*1011m
=7.432*108 m
The semi-major axis of the Sun’s orbit
is 7.43 × 108 m.

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