The Earth has mass 5.89 $\times$ 10²⁴ kg.The moon has mass 7.36 $\times$ 10²² kg and is 3.84 $\times$ 10⁵ km from Earth.How far from the center of Earth is the center of mass of the Earth-moon system? A)4.7 $\times$ 10³ km B)7.4 $\times$ 10³ km C)1.9 $\times$ 10⁵ km D)2.1 $\times$ 10⁵ km E)3.8 $\times$ 10³ km

Question

Quizplus · Accepted Answer

The center of mass (COM) of a two-object system can be found using the formula: $d = \frac{r \times m_{moon}}{m_{earth} + m_{moon}}$, where $d$ is the distance of the COM from the center of the Earth, $r$ is the distance between the Earth and the Moon, $m_{earth}$ is the mass of the Earth, and $m_{moon}$ is the mass of the Moon. Plugging in the given values: $d = \frac{3.84 \times 10^5 km \times 7.36 \times 10^{22} kg}{5.89 \times 10^{24} kg + 7.36 \times 10^{22} kg}$ results in a distance of approximately $4.7 \times 10^3 km$ from the Earth's center.

The Earth Has Mass 5 ×\times× 1024 Kg ×\times× 1022 Kg and Is 3

The Earth Has Mass 5 $\times$ 10²⁴ Kg $\times$ 10²² Kg and Is 3