# What is the magnitude of the gravitational force on Mars, with a mass of 6.34 \times 10^ 23 and a radius of 3.43 \times 10^6m?

Feb 25, 2018

3.597 N/kg

#### Explanation:

According to Newton's law of universal gravitation, the force of gravity is equal to the gravitational constant (G) multiplied by both masses, all over the square of the distance between them:

${F}_{g r a v i t y} = \frac{G {M}_{1} {m}_{2}}{r} ^ 2$

Since we want to work out the force per kilogram on mars, we can divide the above equation by ${m}_{2}$ (which we could say is 1kg) to give:

${F}_{g r a v i t y} / {m}_{2}$ $= \frac{G M}{r} ^ 2$

Plugging in Mars' mass and its radius, as well as the gravitational constant ($6.674 \times {10}^{-} 11$),

$\frac{F}{m} = \frac{G \cdot 6.34 \times {10}^{23}}{3.43 \times {10}^{6}} ^ 2 = 3.597 N k {g}^{-} 1$