The radius of the moon is one fourth and its mass is one eighty first that of the earth. If the acceleration due to gravity on the earth's surface is 9.8meter per square. What is its value on the moon's surface?
1800m/s
The radius of the moon is one-fourth, and its mass is one eighty-first that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8 m/s2, what is its value on the moon’s surface
To find the value of the acceleration due to gravity on the moon's surface, we can use the relationship between the mass, radius, and acceleration due to gravity.
1. First, let's denote the acceleration due to gravity on the moon's surface as "g_moon" and the acceleration due to gravity on the Earth's surface as "g_earth".
2. We'll use the formula for the acceleration due to gravity:
g = (G * M) / r^2,
where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the celestial body, and r is the radius of the celestial body.
3. Given that the radius of the moon (r_moon) is one fourth and its mass (M_moon) is one eighty-first that of the Earth (r_earth and M_earth), we can write:
r_moon = 1/4 * r_earth,
M_moon = 1/81 * M_earth.
4. We know that the acceleration due to gravity on the Earth is 9.8 m/s^2. So we have:
g_earth = 9.8 m/s^2.
5. Now, substitute the values into the formula for the moon's surface:
g_moon = (G * M_moon) / r_moon^2.
6. Substitute the expressions for r_moon and M_moon:
g_moon = (G * (1/81 * M_earth)) / ((1/4 * r_earth)^2).
7. Simplify the equation:
g_moon = (G * (1/81 * M_earth)) / (1/16 * r_earth^2).
g_moon = 16/81 * G * M_earth / r_earth^2.
8. Finally, substitute the value of g_earth = 9.8 m/s^2 and combine with the known value of G (gravitational constant) = 6.67 * 10^-11 Nm^2/kg^2:
g_moon = (16/81) * (9.8 m/s^2),
g_moon = (16/81) * 9.8 m/s^2.
9. Calculate the value of g_moon:
g_moon = 1.933 m/s^2 (rounded to three decimal places).
Therefore, the acceleration due to gravity on the moon's surface is approximately 1.933 m/s^2.
To find the acceleration due to gravity on the moon's surface, we need to use the formula:
acceleration due to gravity = gravitational constant * mass of the celestial body / (radius of the celestial body)^2
Given that the radius of the moon is one fourth and its mass is one eighty-first that of the earth, we can substitute these values into the formula.
Let's assume the acceleration due to gravity on the moon's surface is represented by 'g_moon'.
The radius of the moon is 1/4 times the radius of the earth, so the radius of the moon is (1/4) * R (where R is the radius of the earth).
The mass of the moon is 1/81 times the mass of the earth, so the mass of the moon is (1/81) * M (where M is the mass of the earth).
Now, plug these values into the formula:
g_moon = gravitational constant * (1/81 * M) / ((1/4 * R)^2)
The gravitational constant is approximately 6.67430 x 10^-11 m^3/(kg·s^2).
Substituting the values:
g_moon = (6.67430 x 10^-11) * (1/81 * M) / ((1/4 * R)^2)
Since the value of the gravitational constant and the mass and radius of the earth are not provided, we cannot calculate the exact value of the acceleration due to gravity on the moon's surface. However, we can explain how to calculate it once you have those values.