Calculate the mass of the moon if the free fall acceleration near its surface is known as 1.62 meter per second square and radius of the moon is 1738km.
F = m g = G m M/R^2
so
g = G M/R^2
here G = 6.677 * 10^-11
R = 1.738*10^6
g is given = 1.62
solve for M
To calculate the mass of the moon, we can use the formula for gravitational acceleration:
g = G * (M / r^2)
where:
- g is the free fall acceleration near the surface of the moon (1.62 m/s^2),
- G is the gravitational constant (approximately 6.674 x 10^-11 m^3/kg/s^2),
- M is the mass of the moon (what we want to find),
- r is the radius of the moon (1738 km, which needs to be converted to meters).
To solve for M, we need to rearrange the equation:
M = (g * r^2) / G
Now, let's plug in the values and calculate:
- g = 1.62 m/s^2
- r = 1738 km = 1738000 m
- G = 6.674 x 10^-11 m^3/kg/s^2
M = (1.62 * 1738000^2) / (6.674 x 10^-11)
To simplify the calculation, we can break it down into steps:
Step 1: Calculate r^2
r^2 = 1738000^2 = 3.018404 x 10^12
Step 2: Multiply r^2 by g
(1.62 * 3.018404 x 10^12) = 4.8882225 x 10^12
Step 3: Divide the result by G
(4.8882225 x 10^12) / (6.674 x 10^-11) = 7.316618 x 10^22
Therefore, the mass of the moon is approximately 7.316618 x 10^22 kilograms.