There have been suggestions that the value of the gravitational constant $$G$$ becomes smaller when considered over very large time period (in billions of years) in the future. If that happens, for our earth,
Supposing Newton's law of gravitation for gravitation forces $$\mathbf{F}_1$$ and $$\mathbf{F}_2$$ between two masses $$m_1$$ and $$m_2$$ at positions $$\mathbf{r}_1$$ and $$\mathbf{r}_2$$ read
$$\mathbf{F}_1=-\mathbf{F}_2=-\frac{\mathbf{r}_{12}}{r_{12}^3} \mathrm{GM}^2 0\left(\frac{m_1 m_2}{M_0^2}\right)^n$$
where $$M_0$$ is a constant of dimension of mass, $$\mathbf{r}_{12}=\mathbf{r}_1-\mathbf{r}_2$$ and $$n$$ is a number. In such a case,
Which of the following are true?
The centre of mass of an extended body on the surface of the earth and its centre of gravity
Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.
Air molecules in the atmosphere are attracted vertically downward by gravitational force of the earth just like an apple falling from a tree. Air molecules move randomly due to their thermal velocity and hence the resultant motion of air molecules is not exactly in the vertical downward direction.
But in case of apple, only vertical motion dominates because of being heavier than air molecules. But due to gravity, the density of atmosphere increases near to the earth's surface.