Question

universal gravitation figure 1 how does the gravitational attraction between these people compare to the gravitational attraction between the people and earth? notebook enter note here

Explanation:

Step1: Recall gravitational force formula

The gravitational force formula is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational - constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers of mass.

Step2: Analyze masses and distances

The mass of the Earth ($M_E$) is extremely large compared to the mass of a person ($m_p$). The distance between people is much smaller than the distance between a person and the center of the Earth ($r_{p - E}$), but the mass - product $m_p\times m_p$ for two people is much smaller than $m_p\times M_E$.

Step3: Compare the forces

Since $F_{p - p}=G\frac{m_p\times m_p}{r_{p - p}^2}$ and $F_{p - E}=G\frac{m_p\times M_E}{r_{p - E}^2}$, and $M_E\gg m_p$, even though $r_{p - p}\lt r_{p - E}$, the gravitational attraction between people is much smaller than the gravitational attraction between people and the Earth.

Answer:

The gravitational attraction between people is much smaller than the gravitational attraction between people and Earth.