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?
The radius of moon is 27% of the Earth's radius and it's mass is 1.2% of the earth mass find the acceleration due to gravity on the surface of the moon .How much will a 424N body weigh there?
To find the acceleration due to gravity on the surface of the moon, we can use the following formula:
\[ g_m = \frac{{G \cdot M_m}}{{r_m^2}} \]
where:
\( g_m \) = acceleration due to gravity on the surface of the moon
\( G \) = gravitational constant (\( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \))
\( M_m \) = mass of the moon
\( r_m \) = radius of the moon
Given that the radius of the moon is 27% of the Earth's radius and its mass is 1.2% of the Earth's mass, we can write:
\( r_m = 0.27 \times r_e \)
\( M_m = 0.012 \times M_e \)
where:
\( r_e \) = radius of the Earth
\( M_e \) = mass of the Earth
Now, let's substitute these values into the formula to calculate the acceleration due to gravity on the surface of the moon.
First, note that the radius and mass of the Earth are not explicitly given in the question. Therefore, we need to look up these values:
\( r_e = 6,371 \, \text{km} \) (approximately)
\( M_e = 5.972 \times 10^{24} \, \text{kg} \) (approximately)
Substituting these values into the formula:
\[ g_m = \frac{{(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}) \cdot (0.012 \times 5.972 \times 10^{24} \, \text{kg})}}{{(0.27 \times 6,371 \, \text{km})^2}} \]
Calculating this expression will give us the value for the acceleration due to gravity on the surface of the moon.
To find the acceleration due to gravity on the surface of the moon, we can use the formula:
acceleration due to gravity (g) = (Gravitational Constant * mass of the celestial body) / (radius of the celestial body)^2
1. Convert the given percentage values to decimals:
- The moon's radius is 27% of the Earth's radius, so it would be 0.27 (27/100).
- The moon's mass is 1.2% of the Earth's mass, so it would be 0.012 (1.2/100).
2. Determine the values for the Earth:
- The radius of the Earth can be found in scientific literature or taken as an average value of approximately 6,371 kilometers (6,371,000 meters).
- The mass of the Earth is approximately 5.972 × 10^24 kilograms.
3. Calculate the radius of the moon:
- Multiply the Earth's radius by the decimal value for the moon's radius: 6,371,000 * 0.27 = 1,722,570 meters.
4. Calculate the mass of the moon:
- Multiply the Earth's mass by the decimal value for the moon's mass: 5.972 × 10^24 * 0.012 = 7.165 × 10^22 kilograms.
5. Plug in the values into the formula:
acceleration due to gravity (g) = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 7.165 × 10^22 kg) / (1,722,570 meters)^2
6. Calculate the acceleration due to gravity on the surface of the moon:
- Simplify the equation and solve for g.
By following these steps, you should be able to find the acceleration due to gravity on the surface of the moon.
gravitational force between two masses is directly proportional to the product of the masses, and inversely proportional the the square of the distance between them
g-moon = g-earth *.012 / .27^2