Question

If the gravitational force exerted by the planet Saturn on a 560 kg lunar vehicle is 5.83 x 10 to the power of 3 N, the radius of Saturn is?

Answer 1

Answer on Question #43412, Physics, Mechanics — Kinematics — Dynamics

If the gravitational force exerted by the planet Saturn on a 560 kg lunar vehicle is 5.83 * 10 to the power of 3 N, the radius of Saturn is?

Solution

Gravitational force is equal to weight:

$F=\frac{GM_{saturn}m_{vehicle}}{R_{saturn}^{2}}$

Hence, radius of Saturn is

$R_{saturn}=\sqrt{\frac{GM_{saturn}m_{vehicle}}{F}}=sqrt{\frac{6.67\cdot 10^{-11}5.68\cdot 10^{26}\cdot 560}{5.83\cdot 10^{3}}}\approx 60.2\cdot 10^{6}\,m=60200km$

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