Question

Discuss the important features of the law of gravitation.

Answer 1

1. As the distance between two masses increases, the strength of the force tends to decrease because of inverse dependence on r². Physically it implies that the planet Uranus experiences less |F| gravitational force from the Sun than the Earth since Uranus is at a larger distance from the Sun compared to the Earth.

2. The gravitational forces between two particles always constitute an action-reaction pair. It implies that the gravitational force exerted by the Sim on the Earth is always towards the Sun. The reaction force is exerted by the Earth on the Sun. The direction of this reaction force is towards Earth.

Variation of gravitational force with distance

3. The torque experienced by the Earth due to the gravitational force of the Sun is given by

${\displaystyle \overrightarrow{\tau }=\overrightarrow{\text{r}}\times \overrightarrow{\text{F}}=\overrightarrow{\text{r}}\times (-\frac{{\text{GM}}_{\text{S}}{\text{M}}_{\text{E}}}{{\text{r}}^2}\hat{\text{r}})=0}$

Since ${\displaystyle \overrightarrow{\text{r}}=\text{r},\hat{\text{r}},(\hat{\text{r}}\times \hat{\text{r}})=0}$

So ${\displaystyle \overrightarrow{\tau }=\frac{\text{d}\overrightarrow{\text{L}}}{\text{dt}}=0}$

It implies that angular momentum ${\displaystyle \overrightarrow{\text{L}}}$ is a constant vector.

      Hollow sphere of mass

4. The expression ${\displaystyle \overrightarrow{\text{F}}=-\frac{{\text{GM}}_1{\text{M}}_2}{{\text{r}}^2}\hat{\text{r}}}$ has one inherent assumption that both M₁, and M₂ are treated as point masses. When it is said that Earth orbits around the Sun due to Sun’s gravitational force, we assumed Earth and Sun to be point masses.

5. Point masses hold even for a small distance.

6. There is also another interesting result. Consider a hollow sphere of mass M. If we place another object of mass ‘m’ inside this hollow sphere the force experienced by this mass ‘m’ will be zero.