Mars has a radius of about 0.38 Earth radius and a mass of only 0.11 Earth mass. Estimate the acceleration due to gravity on Mars.'
gravity proportional to mass, indirectly prop to square of radius.
First, the radius above is wrong. The mars radius is about .53 re, not .38
Forcegravity=GMm/r^2
gearth=GMe/re^2=9.8
gmars=GMm/rm^2
gmars=G.11Me/(.38re)^2=
gmars=.11/.38^2 *9.8 which is much more than what we find on Mars.
To estimate the acceleration due to gravity on Mars, we can use the relationship between the gravitational force between two objects, their masses, and the distance between them.
The formula for the acceleration due to gravity is given by:
g = G * (M / r^2)
where:
g = acceleration due to gravity
G = gravitational constant
M = mass of the celestial object
r = radius of the celestial object
Given that Mars has a radius of about 0.38 Earth radius and a mass of only 0.11 Earth mass, we need to convert these values to Earth units.
1 Earth radius is approximately 6,371 kilometers.
1 Earth mass is approximately 5.97 x 10^24 kilograms.
Therefore, the radius of Mars is:
r = 0.38 * 6,371 km = 2,421.98 km
And the mass of Mars is:
M = 0.11 * 5.97 x 10^24 kg = 6.57 x 10^23 kg
Now, we can substitute these values into the formula:
g = G * (M / r^2)
The value of G is approximately 6.67430 x 10^-11 N(m/kg)^2.
Plugging in the values:
g = 6.67430 x 10^-11 N(m/kg)^2 * (6.57 x 10^23 kg) / (2,421.98 km)^2
Simplifying the equation will then give us the estimated acceleration due to gravity on Mars.