Curiosity: Gravity on Mars

[Allan]

This is a hypothetical question:

Its my understanding that gravity on Mars is approximately 2/5 that of Earth (40%). So a person weighing 200lbs would effectively weigh 80lbs on Mars.

If it were possible to play a baseball game on the Mars a ball would travel 60% farther than it would on Earth.

If that ball game were played beneath the Martian surface would the gravitational effects on the thrown ball be greater or less than on the surface?

Would the closer you get to the red planets heavy metal core increase or decrease the gravitational effect on the ball (or a person) the deeper you go (200ft, 300ft, 500ft, a mile)?

 

[fsci123]

This is a hypothetical question:

Its my understanding that gravity on Mars is approximately 2/5 that of Earth (40%). So a person weighing 200lbs would effectively weigh 80lbs on Mars.

If it were possible to play a baseball game on the Mars a ball would travel 60% farther than it would on Earth.

If that ball game were played beneath the Martian surface would the gravitational effects on the thrown ball be greater or less than on the surface?

Would the closer you get to the red planets heavy metal core increase or decrease the gravitational effect on the ball (or a person) the deeper you go (200ft, 300ft, 500ft, a mile)?

It will surely decrease as most of the mass would be above you...
If you were to find a bubble in the center of the core you will experience micrgo-g.

 

[Allan]

So to have a regular ball game on Mars the ball would have to be 60% heavier to increase Mars' gravitational effect, right?

 

[fsci123]

So to have a regular ball game on Mars the ball would have to be 60% heavier to increase Mars' gravitational effect, right?

No because weight dont matter a plane and a pen in the same trajectory would travel the same speed in no atmosphere but mars atmosphere is insignificant.

 

[Izack]

To some extent, yes it would. Gravitational force is inversely proportional to the square of the distance between two objects' centres of mass, so naturally it increases with shorter distance (according to Newton's law of universal gravitation.)

However, as you descend farther under the surface, more of the planet's mass is above or around you, and so isn't attracting you towards the planet's core. If you create a hypothetical chamber at the very core, you would be equally attracted in all directions...essentially in microgravity. Of course, you would also have the entire mass of the planet attracting itself and trying to crush you from all sides with incomprehensible force...

At any rate, good luck attempting to make habitable chambers so deep in Mars. There is a reason why we haven't been able to do so on Earth...

EDIT: Ninja'd.

It will surely decrease as most of the mass would be above you...

Not exactly. A planet's mass is not uniformly distributed. The density of the planet increases with depth, so to a certain depth acceleration would increase, if I understand correctly. However, even if we assume universal gravitation to work at depth, the force of gravity would not increase significantly even if we traveled deep into the lithosphere. Earth's gravitational acceleration is not much diminished even at orbital altitude of hundreds of kilometres; the same applies both up and down.

 

[Allan]

This question was less about my book as it was toward a silly drunken bar argument. I guesstimated, incorrectly, that the core of the planet would have greater effect the deeper you go. He argued that a baseball hit by a bat would easily travel more than the 320 feet in center field...maybe even 500 or 600 feet. I guess I owe the next round. thanks guys

 

[Jarvitä]

Theoretically, planets are gravitational Faraday cages, so the gravity anywhere below the surface should be the same as on the surface. In practice, however, this is not the case, and is in reality far more complex due to non-uniform mass distribution.

 

[jedidia]

No because weight dont matter a plane and a pen in the same trajectory would travel the same speed in no atmosphere but mars atmosphere is insignificant.

Well, yes... but making the ball heavier would counter some of the effect because you'd have to hit it much harder to achieve the same trajectory. So if you hit the heavier ball with the same amount of force, you will have a shorter trajectory.
It still wouldn't be the same as on earth, though...

 

[Rtyh-12]

Theoretically, planets are gravitational Faraday cages, so the gravity anywhere below the surface should be the same as on the surface.

I think that's not true. If you had a planet with a mass completely evenly distributed (this isn't really possible, but anyway) then the gravity at the exact center would still be zero (or very small, if you're slightly off )

 

[hribek]

The mass doesn't have to be evenly distributed for your "exact center" example. it's enough if it's even in any given depth, which is could be quite likely for large bodies.

If you think about it thoroughly (on paper), you'll find that when you're at ANY point inside a spherical hollow inside a sphere and this layer has an even mass distribution, it will have zero gravitational effect. This takes some integration to prove it, but good secondary school teachers should help you with that.

So yeah, within reasonable approximations the gravity for the hypothetical baseball game would be lower, if the core isn't dense enough to counteract this. Though the hundred feet or a mile you proposed will make very little difference, you can do some additional homework - estimate how much more dense would the material below you have to be to counteract the effect of all the lighter material above you (while retaining the same mean density of Mars).

Also, for your baseball game example, the atmo drag effects on the baseball ball are not negligible in this case. Martian atmosphere (at surface) is a lot thinner, so the ball would go even farther.

 

[martins]

Theoretically, planets are gravitational Faraday cages, so the gravity anywhere below the surface should be the same as on the surface. In practice, however, this is not the case, and is in reality far more complex due to non-uniform mass distribution.

That this statement can't be quite right should already be suspected from the fact that it would create a singularity at the centre.

You may be confusing it with another situation: The gravitational potential is zero everywhere inside a hollow spherical shell (a simple school physics exercise in integration). This means that the deeper you go, the less of the Earth's mass contributes to your weight (even if the mass density increases towards the centre).

Edit: Ninja'd by previous posters.

 

[HarvesteR]

Uh, interesting... my first impulse was to say it would increase... but I'm always thinking of these things in point mass terms...

So, if you were to try this in a physics simulation, gravity would, in fact, increase, since AFAIK, most sims do their gravitational math using a single point at the center that carries all the mass... (unless you wanna calculate the gravitational pull of mote-sized particles for a planet-sized volume of them... Good luck getting IBM to lend you their RoadRunner rig )

Cheers

 

[agentgonzo]

I think that's not true. If you had a planet with a mass completely evenly distributed (this isn't really possible, but anyway) then the gravity at the exact center would still be zero (or very small, if you're slightly off )

If you treat the body as being of uniform density, then gravity decreases linearly from its maximum at the surface to zero at the exact centre of the planet. This can be done (as I remember from A-Level physics) by integrating over the area of the body and noting various symmetries between what is below and above you. I can't remember the exact maths, but remember the linear falloff result.

 

[hribek]

If you treat the body as being of uniform density, then gravity decreases linearly from its maximum at the surface to zero at the exact centre of the planet. This can be done (as I remember from A-Level physics) by integrating over the area of the body and noting various symmetries between what is below and above you. I can't remember the exact maths, but remember the linear falloff result.

The mass below (that matters) is then proportional to the applicable volume, so cube of the radius of the body you'r standing on. This spherical mass below you can be replaced by a single point of equal mass. The gravitational effect it will have on you is proportional to square of your distance from it. so it's F=k*(r^3)/(r^2) which is indeed linear F=k*r where k is a constant and r is body radius (you're on the surface - any spherical shell above has no effect).

On the other hand, you could perhaps drill a hole into the Martian surface to experience atmospheric pressure similar to Earth sea level (1E+05 Pa) at some depth. Humans can cope with down to half of that if they have higher concentrations of oxygen to breathe.

 

[RisingFury]

It will surely decrease as most of the mass would be above you...
If you were to find a bubble in the center of the core you will experience micrgo-g.

Don't be so quick to jump to conclusions! Non-uniform density of the planet matters. I know that under the surface of Earth for the first few km the gravity actually increases. The reason is that the light stuff - water and rock are above you and you're closer to the metal core. The change isn't much, but it is noticeable.


If you had a uniform density planet, then gravitational acceleration would drop linearly with depth.