The radius of the moon is one eighty-first that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8m/s^2 , What is its value on the moon's surface.
(9.8m/s^2)/6 = 1.63 m/s^2.
I guess you are to assume the density rho is the same
g = G M/R^2
if M = rho V = rho (4/3) pi R^3
then
g = G rho (4/3) pi R^3/R^2 = constant * R if the density is constant
that would say g earth is 81 times that of the moon
HOWEVER as Henry pointed out it is SIX times
in other words the earth is far less dense than the moon.
NOW WITHOUT YOUR TYPING ERROR!!!!!!
Mass of moon = Mass of earth / 81
Radius of moon = Radius of earth / 4
gearth = G M/R^2
gmoon = G M/81 / R^3/16
gearth/gmoon = 81/16 = 5.06 or close to what Henry told you (6)
To find the acceleration due to gravity on the moon's surface, we need to use the formula for gravitational acceleration:
acceleration due to gravity = (gravitational constant * mass of the celestial object) / (radius^2)
Here, the gravitational constant is a universal constant that is approximately equal to 6.67430 × 10^(-11) N(m^2/kg^2).
Given that the radius of the moon is one eighty-first (1/81) that of the Earth, we can say:
radius of the moon (r_moon) = (1/81) * radius of the Earth (r_earth)
The question provides the acceleration due to gravity on the surface of the Earth, which is 9.8 m/s^2.
Here are the steps to calculate the acceleration due to gravity on the moon's surface:
Step 1: Obtain the radius of the Earth (r_earth). The average radius of the Earth is approximately 6,371 km, which is equal to 6,371,000 meters.
Step 2: Calculate the radius of the moon (r_moon) by substituting the given information:
r_moon = (1/81) * r_earth = (1/81) * 6,371,000 meters
Step 3: Plug the values of the gravitational constant (G), mass of the celestial object (m_celestial), and the radius of the moon (r_moon) into the formula:
acceleration due to gravity on the moon's surface = (G * m_celestial) / (r_moon^2)
Step 4: The mass of the celestial object, in this case, is the mass of the moon, which is approximately 7.348 × 10^22 kilograms.
Step 5: Calculate the acceleration due to gravity on the moon's surface using the formula. Substitute the values of G, m_celestial, and r_moon in meters into the formula:
acceleration due to gravity on the moon's surface = (6.67430 × 10^(-11) N(m^2/kg^2)* 7.348 × 10^22 kg) / ((1/81) * 6,371,000 meters)^2
By solving this equation, we can find the acceleration due to gravity on the moon's surface.