Respuesta :
m₁ = 5.97 * 10²⁴
m₂ = 7.35 * 10²²
r₁ = 0
r₂ = 3.84 * 10⁸
r = distance from earth center to center of mass
r*(m₁+m₂) = r₁m₁ + r₂m₂
r = (r₁m₁ + r₂m₂) / (m₁ + m₂) = (0 + 2.82 * 10³¹) / 6.0435 * 10²⁴ = 4,66 * 10⁶
m₂ = 7.35 * 10²²
r₁ = 0
r₂ = 3.84 * 10⁸
r = distance from earth center to center of mass
r*(m₁+m₂) = r₁m₁ + r₂m₂
r = (r₁m₁ + r₂m₂) / (m₁ + m₂) = (0 + 2.82 * 10³¹) / 6.0435 * 10²⁴ = 4,66 * 10⁶
The center of mass gives point where a force can be applied without
causing rotation.
The distance of the center of mass from the center of the Earth is
approximately 4.670 × 10⁶ meters.
Reasons:
Given parameters are;
Mass of the Earth, M₁ = 5.97 × 10²⁴ kg
Mass of the Moon, M₂ = 7.35 × 10²² kg
Distance of separation, d = 3.84 × 10⁸ m
Required:
To locate the center of mass of the Earth-Moon system
Solution:
The center of mass is given by the equation;
[tex]x_{cm} = \dfrac{M_1 \cdot x_1 + M_2 \cdot x_2}{M_1 + M_2}[/tex]
Taking measurement from the Moon, we have;
x₁ = The distance of separation of the Earth from the Moon = d
x₂ = 0
[tex]x_{cm}[/tex] = The center of mass distance from the Moon
[tex]x_{cm} = \dfrac{5.97 \times 10 ^{24} \times 3.84 \times 10^8 +7.35\times 10 ^{22} \times 0}{5.97 \times 10 ^{24} + 7.35\times 10 ^{22}} = 379329858.526[/tex]
Distance of the center of mass from the Moon is 3.79329858526 × 10⁸ m
The distance of the center of mass measured from the Earth is therefore;
3.84 × 10⁸ m - 3.79329858526 × 10⁸ m = 4670141.474 m
The center of mass of the Earth-Moon system as measured from the center
of the Earth is 4670141.474 meters ≈ 4.670 × 10⁶ meters which is
below the Earth's surface.
Learn more here:
https://brainly.com/question/14420084
