The radius of moon is 27% of the earth radius and its mass is 1.2 % of the earth mass find the acc due to gravity on surface of moon?
a=forcegravity/r^2
amoon=9.8*.012/.27^2=1.6 m/s^2
쇼핑하우 도움말 | Daum 고객센터
To find the acceleration due to gravity on the surface of the moon, we'll need to use the formula for gravitational acceleration:
\[ g = \frac{{G \cdot M}}{{R^2}} \]
Where:
g is the acceleration due to gravity,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the moon, and
R is the radius of the moon.
Given that the radius of the moon (Rm) is 27% of the Earth's radius (Re) and the mass of the moon (Mm) is 1.2% of the Earth's mass (Me), we can substitute these values into the formula:
\[ g = \frac{{G \cdot Mm}}{{Rm^2}} \]
However, we first need to convert the values into the standard units. The average radius of the Earth is approximately 6371 km, so the radius of the moon (Rm) becomes:
\[ Rm = 27\% \times 6371 \, \text{km} \]
Similarly, the mass of the Earth is approximately 5.972 × 10^24 kg, so the mass of the moon (Mm) becomes:
\[ Mm = 1.2\% \times 5.972 \times 10^{24} \, \text{kg} \]
Now we can calculate the acceleration due to gravity on the moon's surface using the given values and the formula:
\[ g = \frac{{6.67430 \times 10^{-11} \times Mm}}{{(Rm \times 1000)^2}} \]
(Note: We converted the radius to meters by multiplying by 1000 since the gravitational constant is given in SI units.)
By plugging in the calculations, we can determine the value of g.