# Equivalent gravitational forces in other galaxies

• B
Could it be imagined that due to a particular stars' distribution in a galaxy the gravitational force felt would be like $$f(\vec{e}_r)/r^{\alpha}$$ where $$\alpha\neq 2$$ but near 2 and f a non spherically symmetric function (like a comet around a flat galaxy) ?

## Answers and Replies

mfb
Mentor
What do you mean by "like a comet around a flat galaxy"?

The force has to be conservative, ##\displaystyle \int_0^\infty \frac{f(\vec e_r)}{r^\alpha} dr## has to be the same for all directions. If you have a weaker gravitational attraction in some direction at some point you need a stronger one in this direction at a different point.

ohwilleke
Gold Member
Could it be imagined that due to a particular stars' distribution in a galaxy the gravitational force felt would be like $$f(\vec{e}_r)/r^{\alpha}$$ where $$\alpha\neq 2$$ but near 2 and f a non spherically symmetric function (like a comet around a flat galaxy) ?

So basically, could the strength of the gravitational pull of an asymmetric galaxy e different in different directions at distances that are near to the galaxy relative to infinity?

If I understand you correctly, yes. It could. But, the formula you use is a point particle formula like the one in your post, and you'd need instead a formula that captures the sum of gravitational pulls from a whole host of different point-like masses. ∑ (f(i)/ri2 for i=1 . . . . billions of stars, which would create an effective force with r != 2 for an arbitrary point in space used to represent the galaxy as a whole.

stefan r
Could it be imagined that due to a particular stars' distribution in a galaxy the gravitational force felt would be like $$f(\vec{e}_r)/r^{\alpha}$$ where $$\alpha\neq 2$$ but near 2 and f a non spherically symmetric function (like a comet around a flat galaxy) ?