Question

What is acceleration due to gravity on Jupiter?

Answer 1

Step 1: Assuming the quantities

The value of the gravitational constant $\mathrm{G}=6.6743\times {10}^{-11}{\mathrm{m}}^3.{\mathrm{kg}}^{-1}.{\mathrm{s}}^{-2}$

Jupiter is the largest planet having a mass of $\mathrm{M}=1.89\times {10}^{27}\mathrm{kg}$

The radius of the Jupiter planet, $\mathrm{R}=69911\times {10}^3\mathrm{m}$

Step 2: Calculating the acceleration due to gravity on Jupiter

The equation of the acceleration due to gravity is given as:$\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$,
Where, $\mathrm{G}$ is the gravitational constant, $\mathrm{M}$ is the mass of Jupiter, $\mathrm{R}$ is the radius of the Jupiter

The acceleration due to gravity on Jupiter is
$$\begin{gathered} \mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2} \\ \mathrm{g}=\frac{6.6743\times {10}^{-11}{\mathrm{m}}^3.{\mathrm{kg}}^{-1}.{\mathrm{s}}^{-2}\times 1.89\times {10}^{27}\mathrm{kg}}{{\left(69911\times {10}^3\right)}^2\mathrm{m}} \\ \mathrm{g}=25.8\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Thus, the acceleration due to gravity on Jupiter is approximately $25.8\mathrm{m}/{\mathrm{s}}^2$