Which body has a larger escape velocity, Mars or Saturn?
MMars = 0.1 MEarth
MSaturn = 95 MEarth
RMars = 0.5 REarth
RSaturn = 9.4 REarth
To determine which body has a larger escape velocity between Mars and Saturn, we can use the formula for escape velocity:
Ve = sqrt(2GM/R)
Where:
Ve is the escape velocity,
G is the gravitational constant,
M is the mass of the celestial body, and
R is the radius of the celestial body.
Since we are given the mass and radius of Mars and Saturn, we can calculate their respective escape velocities.
Escape velocity for Mars (VeMars):
VeMars = sqrt(2 * G * MMars / RMars)
Escape velocity for Saturn (VeSaturn):
VeSaturn = sqrt(2 * G * MSaturn / RSaturn)
Substituting the given values:
VeMars = sqrt(2 * G * 0.1 MEarth / 0.5 REarth)
VeSaturn = sqrt(2 * G * 95 MEarth / 9.4 REarth)
To compare the values, we can simplify the solution by dividing the equation for VeSaturn by VeMars:
(VeSaturn / VeMars) = sqrt((2 * G * 95 MEarth / 9.4 REarth) / (2 * G * 0.1 MEarth / 0.5 REarth))
(VeSaturn / VeMars) = sqrt((95 / 9.4) * (0.5 / 0.1))
Computing the numerical value:
(VeSaturn / VeMars) ≈ sqrt(10.1064) ≈ 3.18
Therefore, the ratio of the escape velocities is approximately VeSaturn:VeMars = 3.18.
From this calculation, we can conclude that Saturn has a larger escape velocity compared to Mars.