the earth 's moon has a gravitational field strength of about 1.6 n/kg near its surface. the moon has a mass of 7.35x10^22 kg. what is the radius of the moon?
To answer this, you need to know
M, the mass of the earth
R, the radius of the earth
on moon, g = Gm/r^2 = 1.6
on earth, g = GM/R^2 = 9.81
(m/r^2) / (M/R^2) = 1.6/9.81
m/M * R^2/r^2 = 1.6/9.81
mr^2/MR^2 = 1.6/9.81
r^2 = M/m R^2 * 1.6/9.81
To find the radius of the moon, we can use the formula for gravitational field strength:
g = G * (M / r^2)
Where:
g is the gravitational field strength near the moon's surface (1.6 N/kg),
G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2),
M is the mass of the moon (7.35 x 10^22 kg),
and r is the radius of the moon (which we need to find).
Rearranging the formula, we have:
r^2 = G * M / g
Now, let's substitute the given values into the formula:
r^2 = (6.67 x 10^-11 Nm^2/kg^2) * (7.35 x 10^22 kg) / (1.6 N/kg)
Calculating this expression gives us:
r^2 ≈ 3.06234375 x 10^31 m^2
To find the radius (r), we take the square root of both sides:
r ≈ √(3.06234375 x 10^31 m^2)
r ≈ 5.536 x 10^15 m
Therefore, the radius of the moon is approximately 5.536 x 10^15 meters.