Question

The time period of Jupiter is $11.6years.$. How far is Jupiter from the Sun? The distance of the earth from the sun is $1.5x{10}^{11}m$.

Answer 1

Step 1: GIven parameters

The time period of Jupiter $T_j=11.6years.$

The time period of earth $T_e=1year$

The distance of the earth from the sun $r_e=1.5x{10}^{11}m.$

Step 2: What to find

Distance of Jupiter from the Sun $r_j=?$

Step 3: Calculating the distance of Jupiter

According to Kepler's equation

$T^2\propto R^3$

Therefore, by using above equation

$\frac{{T_j}^2}{{T_e}^2}=\frac{{r_j}^3}{{r_e}^3}$

${r_j}^3=\frac{{T_j}^2}{{T_e}^2}\times {r_e}^3$

$r_j={\left(\frac{T_j}{T_e}\right)}^{\frac{2}{3}}\times r_e$

$r_j={\left(\frac{11.6}{1}\right)}^{\frac{2}{3}}\times 1.5x{10}^{11}$

$r_j=7.68\times {10}^{11}m$

The distance of Jupiter from the Sun is $7.68x{10}^{11}m$