# Relationship between Planets size, mass, age and gravity?

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It's a thought I had earlier today and I've done no research on it at all, so if it's wrong, be sure to tell me.

But I was reviewing the String Theory and the way many physicists view the way our solar system as sitting on a large bedsheet, the planets are weights in the bedsheet causing pull on other objects.

Well I had a thought and recalled some information. There seems to be no real corellation between planet size and gravitational pull. Saturn has the same mass as 95.162 Earths but has a gravitational pull of 8.96 m/s^2 or .914 g's.

The thought was that the all these factors came into play to determine the amount of gravity. Size, mass, and age all play a part in how far down the plants pull the bedsheet.

Then the idea that if the earths size and mass stay the same, the only thing that changes is age. And although I'm relating the solar system to a bedsheet, would time play a role in increasing our planets gravity? Would the be a day that our gravity could be twice what it is today? Or am I getting worried for no reason.

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I think there may be some issue with gravity "on the surface" of planets, due to the fact that bigger planets have a good amount of their mass a good distance away from you.

I don't have the numbers off the top of my head, but I remember looking at the mass of Mars vs Earth, then the gravity, and noticing the discrepency was caused by the size issue.

If you were the distance from the Earth to the Sun away from the Earth, vs being that distance away from Saturn, then Saturn would have 95.162 times the attractive force of the Earth, since the radius of even Saturn would have no real impact that far out.

If planets gained or lost gravitational force over time, we'd have to assume stars would too, and an increase in gravitational force would cause us to fall into the sun, whereas a decrease would sling us out into space.

I am pretty sure when we look back at stars billions of light years away (and thus are looking at the light from gravitational systems that happened a billion years ago) we see them moving with the same identical gravitational constants we see today on Earth.

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$g = -\frac{GM}{x^2}$ for mass m and distance x.

Saturn may have a greater mass, but some of it's mass is far away due to the planet being a large sphere.

Age does not affect gravity afaik unless m or x increases or decreases with time.

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Interesting, I love these nifty equations.

Thankyou for the information.

But, could you go one further and give me an example? I seem to comprehend better if an actual example is involved. Also, what is the large G in the equation represent?

Any and all help will be appreciated.

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The 'G' is the universal gravitational constant and is equal to

$6.673 x 10^{-11}$N-m²/kg²

Examples:

mass of Earth : $5.97 x 10^{24}$kg

radius of Earth : $6.378 x 10^{6}$ m

acceleration of gravity at the Surface of the Earth:

$\frac{(6.673 x 10^{-11})(5.97 x 10^{24})}{(6.378 x 10^{6})^2} = 9.792 m/sec^2$

mass of Moon : $7.35 x 10^{22}$kg

radius of Moon : $1.738 x 10^{6}$ m

acceleration of gravity at the Surface of the Moon:

$\frac{(6.673 x 10^{-11})(7.35 x 10^{22})}{(1.738 x 10^{6})^2} = 1.623 m/sec^2$

mass of Uranus : $8.68 x 10^{25}$kg

radius of Uranus : $2.556 x 10^{7}$ m

Acceleration of gravity at the Surface of Uranus:

$\frac{(6.673 x 10^{-11})(8.68 x 10^{25})}{(2.556 x 10^{7})^2} = 8.887 m/sec^2$

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The big G is just the gravitational constant. Looking at Earth and Saturn, we see that Saturn, as you say, is 95 times as massive as Earth. However, gravitational pull varies inversely as the square of the distance from the center of gravity. So if you move twice as far from the center of gravity, gravitational attraction is only one quarter as great. If you move three times as far away, the gravity is only one ninth of what it was. Since Saturn has roughly ten times the diameter of Earth, someone on its surface would be ten times as far away from its center of gravity as someone on Earth is from the Earth's center. Thus, its gravity is decreased by one hundred times, which is about as many times as Saturn is more massive than Earth. Thus, the gravity on the surface of each is very similar.

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Wow, I love you guys, thankyou so much for the help.

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Well, hate to say this, but your answer only raises more questions.

What about abnormally shaped objects? i.e. humans?

For instance, what is the gravitational pull of a 79 kg human with a height of 1.5574 meters. How would you find the gravitational pull of said individual?

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Would probably be easier to model it as a sphere. Humans have barely any gravitational pull so you wouldn't really need it for any useful purpose anyway.

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Or model it as a group of spheres and work out the gravity of each. Or you could work out the mass density as a function of position and use guasses law for gravity...

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Well' date=' hate to say this, but your answer only raises more questions.

What about abnormally shaped objects? i.e. humans?

For instance, what is the gravitational pull of a 79 kg human with a height of 1.5574 meters. How would you find the gravitational pull of said individual?[/quote']

From a very large distance away you can model objects as points; so you can ignore their radii and shapes and just do the calculation based on mass.

If you really wanted to get the gravitational pull from an abnormally shaped object from a short distance away you could just think of it as a series of smaller spheres strung together.

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