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
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).
Latest Answers