# Gravity of an ancient Mars

If Mars is thought to have once been like Earth several billion years ago, with an atmosphere, magnetic field, oceans, etc., then what would the planets true surface gravitational acceleration "m/s²" have been before the planet 'died'?

• the same, the mass didn't change significantly since then – ratchet freak Dec 15 '14 at 14:59

As was said in the comments, Mars' mass hasn't changed. The loss of the atmosphere had to do with the loss of the planet's magnetic field.

Gravity is not dependent on the composition of the body. In fact, Jupiter exerts exactly the same gravitational influence that a solid body of the same mass would. So does the Sun, or a black hole.

The gravitational accelleration between two bodies for point masses can be simplified as $$g = -\frac{GM}{r^{2}} \hat{r}$$ where $G$ is the graviational constant, $M$ is the mass of the larger body, $r$ is the distance between the two masses and $\hat{r}$ is a unit vector directed from the large mass to the smaller mass. For our purposes, we can set $\hat{r} = 1$ and ignore the minus sign, which reduces the formula to the perhaps better known $$g = \frac{GM}{r^{2}}$$

There is nothing in here that changes based on the type of matter making up $M$. Hence, for any given mass $M$ and a body with graviational constant $G$, the type of matter in $M$ makes no difference. We can therefore conclude that the gravitational accelleration on a Mars made up of any other material composition compared to our real, current-day Mars, but with the same total mass, would exert the same graviational influence on any surrounding bodies.

In the specific case of Mars, that is approximately $3.71\text{ m/s}^{2}$.

Mars has never been "like earth". It was however "more like earth".

It had an atmosphere, it had liquid water on the surface, it had seasons and a climate. So far we do not know if it had life or not, it had conditions that may have allowed life but we have so far found no evidence of anything living there.

However it has lower gravity than earth and no magnetic field to protect it from the solar wind. (It did have a magnetic field at some point but that has gone now and was probably always weaker than Earth's, it's also possible according to some theories that it only covered the southern half of the planet!). This means that the atmosphere was gradually lost into space, as the atmospheric pressure dropped the water either froze or evaporated and was also lost until in the end you have the Mars we see today.

• Should note that Mars likely had a magnetic field at one point in it's history, but that wouldn't have any effect on Gravity. – Twelfth Dec 15 '14 at 16:49
• @Twelfth Good point, added. – Tim B Dec 15 '14 at 16:55