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 object, we can use the formula for gravitational force:
F = G * ((m1 * m2) / r^2)
Where:
F = Gravitational force between the two objects
G = Gravitational constant (6.67430 × 10^-11 N*(m/kg)^2)
m1 = Mass of the first object
m2 = Mass of the second object
r = Distance between their centers
In this case, we want to calculate the mass of each ball, so we'll assign the variables as follows:
m1 = Mass of the Earth (unknown)
m2 = Mass of the Moon (unknown)
r = Distance between their centers (3.84 * 10^8 m)
The gravitational force between the two bodies can also be expressed as:
F = G * ((m1 * m2) / r^2)
We can rearrange this equation to solve for m1 (Mass of the Earth):
m1 = (F * r^2) / (G * m2)
Now, we know the gravitational force exerted by the Earth on the Moon can be calculated using:
F = G * ((m1 * m2) / r^2)
We substitute the given values into the equation:
F = G * ((m1 * m2) / r^2)
F = 6.67430 × 10^-11 N*(m/kg)^2 * ((5.96 × 10^24 kg * 7.35 × 10^22 kg) / (3.84 × 10^8 m)^2)
Simplifying this equation will give us the value of F.
Similarly, the gravitational force exerted by the Moon on the Earth can be calculated using the same equation. By substituting the values, we can solve for the mass of the Earth (m1) in the equation.
Finally, by calculating the gravitational force using both the formula for the gravitational force exerted by the Earth on the Moon and the formula for the gravitational force exerted by the Moon on the Earth, we can find the values of m1 (mass of the Earth) and m2 (mass of the Moon).