What would the Universe be like if gravity was slightly stronger?

Not a lot would be different, actually.

Let's take the orbits of the planets around the Sun. In the Newtonian world, gravity is represented by Newton's law of universal gravitation: $$F=G\frac{m_1m_2}{r^2}$$ where $F$ is force, $G$ is the universal gravitational constant, $m_1$ and $m_2$ are the masses of the objects, and $r$ is the distance between them.

Now, gravity is the centripetal force responsible for the motion of the planets. In other words, $$F_g=F_c$$ and so, because $F_c=\frac{mv^2}{r}$ (where $v$ is the tangential velocity), $$G\frac{m_1m_2}{r^2}=\frac{mv^2}{r}$$ Given that $m=m_2$ (where $m_2$ is the smaller mass - the planet), $$G\frac{m_1}{r}=v^2$$ Solving for $r$, $$r=G\frac{m_1}{v^2} \tag{1}$$ Now let's call $G$ at its current value $G_o$, and call its future value (of $1.01G_o$) $G_f$. We now know that $$(G_f)\frac{m_1}{r}=v^2$$ $$(1.01G_o)\frac{m_1}{r}=v^2$$ and, solving for $r$, $$r=(1.01G_o)\frac{m_1}{v^2} \tag{2}$$ So the radius of the planet's orbit is just a bit smaller - in fact, if we write $(1)$ as $$\frac{r_o}{G_o}=\frac{m_1}{v^2} \tag{1.1}$$ and write $(2)$ as $$\frac{r_f}{1.01G_o}=\frac{m_1}{v^2} \tag{2.1}$$ and do a bit of algebra, we find that $$r_f=1.01r_o$$ assuming that $v$ is the same for both $G$s. For Earth, $r=150 \text { million km}$, so we would be about $1.5 \text { million km}$ further away from the Sun. Would that make a huge difference? Maybe a little. As I wrote here, we could have minor seasons if Earth was 1.05 AU away from the Sun in its new "winter" and 0.95 AU from the Sun in its new "summer" (this all neglects axial tilt, as per the question). So there would be some change if we were further away from the Sun, but not a lot.

We can do this kind of approximation on larger scales, too - that is, like stellar orbits around the Galactic center.

Would this have impacted how the universe formed? I'm not sure. 0.1% isn't a very big change. If things were changed substantially, we'd be in trouble. This is the case with some of the other forces, such as the strong nuclear force. As Wikipedia says,

If, for example, the strong nuclear force were 2% stronger than it is (i.e., if the coupling constant representing its strength were 2% larger), while the other constants were left unchanged, diprotons would be stable and hydrogen would fuse into them instead of deuterium and helium. This would drastically alter the physics of stars, and presumably preclude the existence of life similar to what we observe on Earth. The existence of the di-proton would short-circuit the slow fusion of hydrogen into deuterium. Hydrogen would fuse so easily that it is likely that all of the Universe's hydrogen would be consumed in the first few minutes after the Big Bang.

So it's a good thing that all the constants are the way they are. But I'm not sure just how a small change like the one mentioned could affect a universe from the very beginning.

posted over 9 years ago

HDE 226868‭

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