The mass of the earth is 5,96 multipy by 10 to the power of 2) kg and that of the moon 7,35 multiply by 10 to the power of 22kg.If the distance between their centres is 3,84 multiply by 10 to the power of 8m,calculate the mass of each ball.
To calculate the mass of each celestial body, we can use Newton's Law of Universal Gravitation formula:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between their centers.
We have the following information:
m1 (mass of the Earth) = 5.96 x 10^24 kg,
m2 (mass of the Moon) = 7.35 x 10^22 kg, and
r (distance between their centers) = 3.84 x 10^8 m.
We can rearrange the formula to solve for the mass of each celestial body:
m1 = (F * r^2) / (G * m2)
m2 = (F * r^2) / (G * m1)
Now, we need the gravitational force between the Earth and the Moon, which can be calculated using the given masses and the distance:
F = G * (m1 * m2) / r^2
Calculating F:
F = (6.67430 x 10^-11 N m^2/kg^2) * ((5.96 x 10^24 kg) * (7.35 x 10^22 kg)) / (3.84 x 10^8 m)^2
F ≈ 1.981 x 10^20 N
Using this value for F, we can now calculate the mass of each celestial body.
Calculating m1 (mass of Earth):
m1 = (1.981 x 10^20 N * (3.84 x 10^8 m)^2) / (6.67430 x 10^-11 N m^2/kg^2 * 7.35 x 10^22 kg)
m1 ≈ 5.972 x 10^24 kg
Calculating m2 (mass of Moon):
m2 = (1.981 x 10^20 N * (3.84 x 10^8 m)^2) / (6.67430 x 10^-11 N m^2/kg^2 * 5.96 x 10^24 kg)
m2 ≈ 7.348 x 10^22 kg
Therefore, the mass of the Earth is approximately 5.972 x 10^24 kg, and the mass of the Moon is approximately 7.348 x 10^22 kg.