Question

7 Given that the mass and radius of Jupiter are respectively
1:90×1027
kg and
7:15×104
km, calculate the escape velocity from the surface of the planet

Answer 1

Answer on Question #40802, Physics, Mechanics

Question:

7 Given that the mass and radius of Jupiter are respectively $1.90 \times 10^{27} \, \mathrm{kg}$ and $7.15 \times 10^{4} \, \mathrm{km}$, calculate the escape velocity from the surface of the planet.

Answer:

If the kinetic energy of an object launched from the Jupiter were equal in magnitude to the potential energy, then it could escape from the Jupiter:

$$\frac{m v^{2}}{2} = \frac{G M m}{r}$$

where $M$ is mass of Jupiter, $R$ is radius of Jupiter, $v$ is escape velocity.

Escape velocity equals:

$$v = \sqrt{\frac{2 G M}{r}} = 59.5 \, \frac{\mathrm{km}}{\mathrm{s}}$$

Answer: $59.5 \, \frac{\mathrm{km}}{\mathrm{s}}$