I just had a quiz where I learned that Earth has the largest density of all the planets in the solar system.
My thought was that density would directly correlate to the gravity of the planet, and the planet with lower jumping heights had higher gravitational pull because of a higher density. While not having any clear mental table of the gravity or jumping height for the different planets, I thought that you’d jump the shortest distance on Jupiter, and deduced that Jupiter therefore would have the heighest gravitational pull and the largest density. This was wrong. Probably on multiple levels. I tried searching google for ”planets gravity jumping density reddit” but didn’t find anything suitable for my attention span to understand the data and the concepts.
Therefore I’m turning to you. What are the flaws in my childish thinking? What are the relationships for mass/gravity/density/jumping distance, and do you know of any good table where these are shown for the different planets?
In: Physics
Its not based on density, it is based on total mass. Volume * density is mass so if a planet has higher density it increases gravity, but higher volume can also increase it.
No. The sun is a lot less dense than the Earth but it has a gravitational pull that is thousands, probably millions of times stronger than the Earth.
That is because of mass, not density.
As another said the mass matters but density is also important since it influences the distance from. The surface to the center of the planet.
If earth was twice denser gravity would be stronger at the surface and it would also be harder to jump.
Well, it doesn’t work like that.
If you have two planets of the same size, the surface gravity is higher on the more dense one, you can’t jump as high. But, for a planet of uniform the gravity is a function of total mass and distance from the center. The formula is:
F = G • M1 • M2 / r^2
G is a constant; M1 is your weight (also a constant); M2 is the mass of the planet; and r is the radius of the planet.
But M2 can be calculated from density. It’s just density times volume.
M2 = p • C • r^3
p is density; C is a constant (four thirds times pi); and r is radius.
So, the mass changes as r^3 and the force is reduced by r^2 , and these numbers are not the same. Doubling the radius of a planet of constant density makes it 8 times as massive and decreases the gravitational force due to distance to the center by 4. On this double size planet of equal density to your initial planet you can just half as far (because the gravity is twice as strong).
Every particle that has mass is able to exert a weak attractive force on another particle that has mass. It is the Gravitational constant and is a very small number. So if you have lots of particles in one place. You multiply the Gravitational constant value with the number of particles you have or the mass (Mass = how much particles a thing has) to work out the total force felt. The other thing to consider is how far away you are from the object’s centre of mass. At the defined surface of each planet you should experience a certain amount of force for every kg of mass you have sitting on the surface. This is often called the Gravitational field strength (GFS)of a planet. On Earth for every kg you experience a force of 9.81Newtons. So the GFS of Earth is 9.81N/kg. On Jupiter it is 24.7N/kg but Jupiter is around 300 times more massive. Has 300 times more particles. So why is the GFS not 300 times stronger. It is because the defined surface of Jupiter is so far from the centre of the planet. The 1/r^2 rule means the force felt is weaker due to the diameter of Jupiter. So Jupiter is less dense and which means it’s particles take up more space. I believe I am correct in saying that if Jupiter had all its particles crammed into the same volume as Earth it would have a higher GFS at the surface. A quick Google for GFS of each planet should give you an idea of the force you would feel due to Gravity on each planet in our Solar
System.
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