Question

Saturn’s moon Titan has a mass of $1.35*1023kg$and a radius of$2580km.$ What is the free-fall acceleration on Titan?

Short answer

The free-fall acceleration on Titan is $1.35m/s^2.$

Step-by-step solution

Given information.

Mass of Titan = $1.35*1023kg,$radius of Titan = $2580km.$

Calculation.

The formula for free-fall acceleration is given by : $g=GMR2.$

Here $G,M\text{and}R$are universal gravitational constant, mass of titan and radius of titan respectively.

Calculation:

Now substitute this values to the equation to calculate g :

localid="1648481878598" $$\begin{gathered} g=(6.67\times {10}^{-11}\mathrm{N}·\mathrm{m}2/\mathrm{kg}2)(1.33\times {10}^{23}\mathrm{kg})(2580\times {10}^3\mathrm{m})2 \\ =1.35\mathrm{m}/{\mathrm{s}}^2. \end{gathered}$$

Final answer.

The free-fall acceleration on Titan is$1.35m/s^2.$