How gravitational force works for higher mass body with distance?

Question

$$F= \frac{Gm_1m_2}{r^2}$$

This is the newton's universal gravitation law. Here, I want to ask how does a very very higher mass body affect the smaller body, whereas they are far away from each other.

Answer 1

There is no limit to the Newton's universal gravitation law. The force exerted by the bodies on each other become negligible when r approaches infinity, or one of the two or both the bodies have a negligible mass.

Answer 2

This is an answer to the content question, as the title question has already been adressed

Here, I want to ask how does a very very higher mass body affect the smaller body, whereas they are far away from each other.

The formula is a mathematical model of an enormous number of measurements. Physics mathematical models are true for a range of variables and parameters where the measurements have validated them. In the case of Newtonian physics ( mechanics and gravitational laws) this means the classical times and dimensions . Since the formula fits where the laboratory or observational measurements have been done, it is expected to be valid from zero to infinity even if not possible to measure the effect at very large distances .

This of course is not true for the microscopic world of elementary particles and atoms, and different laws than Newton's laws pertain to very large cosmic distances.

How one object affects gravitationally another object at very large distances is still a study at the frontier of physics research. At present it is expected that gravitational attraction is the exchange of gravitons, in a similar way that electric attraction is the exchange of photons, once the gravitational field is quantized and a unified theory is established. This means that objects at very large distances respond to the gravitational field of each other with the speed of light limit.

Answer 3

Notice, $$F=\frac{Gm_1m_2}{r^2}$$ $\implies F\alpha m_1$ & $F\alpha 1/r^2$

the gravitational force $F$ varies linearly with the mass say $m_1$ while it varies inversely with the square of the distance $(r^2)$ i.e. the effect of distance $r$ is more than that of mass say $m_1$

If body has very very large mass i.e. $m_1\to \infty$ & its distance from a smaller body i.e. $m_2\to 0$is also very very large i.e. $r\to \infty$ then the force $F\to 0$

hence the force of a very very large body on a smaller body is almost negligible for larger distances.