In this problem, we will directly calculate the surface gravity and your weight on another planet. In metric, your weight is measured in "Newtons", and Newton = 1 kg m/s². Newton's constant G = 6.67 x 10-11 m³/(kg s²). Earth has a mass = 5.97 x 1024 kg and a radius of 6378 km. You should be able to verify that g = 9.8 m/s² on Earth using the formula for surface grav f your mass is 64 kg, you should also be able to verify you should weigh 626 Newtons. If you can do that you should be OK for what's next. The mass of Venus is 4.87E+24 kg, and it's radius is 6.05E+3 km. What is the surface gravity of this planet? (Watch your units!). m/s² f your mass is 64 kg, what would you weigh on Venus? Newtons.

(a) The formula to calculate the surface gravity of the planet is 

${\mathrm{g}}_{\mathrm{v}}=\frac{{\mathrm{GM}}_{\mathrm{v}}}{{\mathrm{r}}_{\mathrm{v}}}$

where ${\mathrm{g}}_{\mathrm{v}}$ is the surface gravity of Venus, G is the gravitational constant, ${\mathrm{M}}_{\mathrm{v}}$ is the mass of Venus planet and ${\mathrm{r}}_{\mathrm{v}}$ is the radius of planet 

Substitute all the values in above equation 

$$\begin{gathered} {\mathrm{g}}_{\mathrm{v}}=\frac{6.67\times {10}^{-11} {\mathrm{m}}^3/\mathrm{kg}.{\mathrm{s}}^2\times 4.87\times {10}^{24} \mathrm{kg}}{{\left(6.05\times {10}^3 \mathrm{km}\right)}^2} \\ {\mathrm{g}}_{\mathrm{v}}=\frac{6.67\times {10}^{-11} {\mathrm{m}}^3/\mathrm{kg}.{\mathrm{s}}^2\times 4.87\times {10}^{24} \mathrm{kg}}{{\left(6.05\times {10}^3\times {10}^3 \mathrm{m}\right)}^2} \\ {\mathrm{g}}_{\mathrm{v}}=8.87 \mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

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