The radius of the earth is 6.4 * 10^6 m. What is the acceleration of a meteor when it is 8.4*10^6M FROM THE CENTER OF THE EARTH?
To find the acceleration of a meteor when it is a certain distance from the center of the Earth, we need to use the formula for the gravitational acceleration. The formula is:
a = (G * M) / r^2
Where:
a = acceleration
G = gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2)
M = mass of the Earth
r = distance from the center of the Earth to the meteor
Given:
Radius of the Earth, R = 6.4 * 10^6 m
Distance from the center of the Earth to the meteor, r = 8.4 * 10^6 m
First, let's find the mass of the Earth. We can use the formula:
M = (4/3) * π * R^3 * ρ
Where:
M = mass of the Earth
R = radius of the Earth
ρ = average density of the Earth (approximately 5515 kg/m^3)
Substituting the values:
M = (4/3) * π * (6.4 * 10^6)^3 * 5515
Now, we can calculate the acceleration using the formula:
a = (G * M) / r^2
Substituting the values and solving for a:
a = (6.67430 × 10^-11 * M) / (r^2)
Finally, plug in the values to calculate the acceleration.