What is the force of gravity between the earth (m=6.0x10^24 kg) and the moon (m=7.35X10.22kg) when they are 3.44x10^8 m apart?
To calculate the force of gravity between the Earth and the Moon, we can use Newton's law of universal gravitation. This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula for the force of gravity (F) between two objects is:
F = G * (m1 * m2) / r^2
Where:
F is the force of gravity
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Given:
m1 (mass of Earth) = 6.0 × 10^24 kg
m2 (mass of Moon) = 7.35 × 10^22 kg
r (distance between Earth and Moon) = 3.44 × 10^8 m
Let's substitute these values into the formula to find the force of gravity:
F = (6.67430 × 10^-11 N m^2/kg^2) * ((6.0 × 10^24 kg) * (7.35 × 10^22 kg)) / (3.44 × 10^8 m)^2
To simplify this calculation, let's do it step by step:
1. Multiply the masses of the Earth and the Moon:
m1 * m2 = (6.0 × 10^24 kg) * (7.35 × 10^22 kg) = 4.41 × 10^47 kg^2
2. Calculate the square of the distance between Earth and Moon:
r^2 = (3.44 × 10^8 m)^2 = 1.1856 × 10^17 m^2
3. Substitute the calculated values into the formula:
F = (6.67430 × 10^-11 N m^2/kg^2) * (4.41 × 10^47 kg^2) / (1.1856 × 10^17 m^2)
4. Simplify the expression:
F = (6.67430 × 4.41) × (10^-11 × 10^47) / (1.1856 × 10^17) × (N m^2/kg^2 m^2) = 29.41 × 10^36 / 1.1856 × 10^17 N
5. Perform division and convert scientific notation:
F ≈ 2.4774 × 10^19 N
Therefore, the force of gravity between the Earth and the Moon when they are 3.44 × 10^8 m apart is approximately 2.4774 × 10^19 Newtons.