What is the centre of mass if the mass of the earth is 81 times that of the moon and the distance between them is 384 Mm=60 rj ?
To find the center of mass between two objects, we need to consider their masses and distances from each other. In this case, we have the mass of the Earth and the mass of the Moon, as well as the distance between them.
Let's denote the mass of the Earth as M1 and the mass of the Moon as M2. Given that the mass of the Earth is 81 times that of the Moon (M1 = 81 * M2), and the distance between them is 384 Mm (60 times the radius of the Moon), we can use the concept of center of mass to determine its position.
The center of mass (COM) is the point at which the two masses balance each other out. Mathematically, it can be calculated using the formula:
COM = (m1 * r1 + m2 * r2) / (m1 + m2)
where m1 and m2 are the masses of the objects, and r1 and r2 are their respective distances from the center of mass.
In this case, the distance from the center of mass to the Earth (r1) is equal to 60 times the distance from the center of mass to the Moon (r2). So, we can write r1 = 60 * r2.
Let's substitute the given values into the formula:
COM = (M1 * r1 + M2 * r2) / (M1 + M2)
Since M1 = 81 * M2, we can replace M1 in the formula:
COM = (81 * M2 * r1 + M2 * r2) / (81 * M2 + M2)
Simplifying this expression further:
COM = (81 * r1 + r2) / (81 + 1) * M2
Since the ratio of M1 to M2 is 81:1, the result will depend solely on the mass of the Moon (M2), as the mass of the Earth (M1) is 81 times greater.
Therefore, to calculate the center of mass, we need to know the mass of the Moon (M2). Without that information, we cannot determine the center of mass accurately.