Starship Asterisk*

For my physics class I have the students work out the acceleration of gravity on our different planets. We all know that gravity increases linearly with mass and decreases with the inverse square of the distance. For planets this distance is the planet's radius. The acceleration due to gravity on earth is roughly 9.81 m/s² and is regularly called g. Surprisingly (to me at least) the "g" on Saturn--if we assume we could stand on the surface at the equator--is 10.4m/s^2 (choosing a radius from random book). This is due to the fact that even though Saturn is almost 100 times more massive than Earth the density of its gaseous composition is much less. This gives a large radius relative to mass. Even Jupiter's 24.78 m/s² at the equator seems small given the planets mass (317.8 times that of Earth!). These calculations got me wondering: What would the relationship be between size and gravity for a larger rocky planet? Assuming uniform density based on Earth's average density and assuming it physically possible to build larger rocky planets, we can figure this out. The easiest method is to ask what the gravity would be as a function of the radius. In other words if the radius of a planet of uniform density went up, what would the gravity do and how? Using our equation for gravity (eliminating the second mass term gives the acceleration instead of the force), using mass in terms of density and volume, and then using the volume of a sphere (m= d* 4/3pi*r³), we can figure that g is directly proportional to a single power of the radius (r³/r²= r). i.e. If the radius doubles then the gravity doubles. When verifying this formula against other rocky planets in our solar system (data from book) we see that it follows very closely to Mercury (radius = 0.38r_E, grav = 0.38g) and Venus (radius = 0.95r_E, grav = 0.91g), but not as much to the moon (radius = 0.27r_E, grav = 0.166g )and Mars (radius = 0.53r_E, grav = 0.377g). Remember we made an assumption on similar uniform density so it is not perfect. Because the radius is proportional to the cube root of the mass, and because mass is directly proportional to the volume, we would need an increase in eightfold of mass (and subsequently volume) in order to double the radius and double the gravity. Why worry about all this?? Well, if a hypothetical Earth-like, rocky planet of uniform density had twice Earth's radius it's gravity would be double or around 20m/s^2. Now for the real mystery. How would this affect the geology, the weather, the oceanography, and the possible evolution of life???

hstarbuck wrote:Well, if a hypothetical Earth-like, rocky planet of uniform density had twice Earth's radius it's gravity would be double or around 20m/s^2. Now for the real mystery. How would this affect the geology, the weather, the oceanography, and the possible evolution of life???

Quick answer? To many variables in your possible answer. Example: Earth, Venus, Same size, But totally different planets.
Why? Distance from sun? Think about all those other variables.

Mark

mark swain wrote:

hstarbuck wrote:Well, if a hypothetical Earth-like, rocky planet of uniform density had twice Earth's radius it's gravity would be double or around 20m/s^2. Now for the real mystery. How would this affect the geology, the weather, the oceanography, and the possible evolution of life???

Quick answer? To many variables in your possible answer. Example: Earth, Venus, Same size, But totally different planets.
Why? Distance from sun? Think about all those other variables.

Venus is hotter primarily because of its thick CO₂ atmosphere.

An earth with twice the gravity (and, more importantly, twice the escape velocity) would no doubt also have a very thick and hot atmosphere. Presumably this would contribute a major influence on "the geology, the weather, the oceanography, and the possible evolution of life."

Otherwise, physical structures of half the size, both organic and inorganic, would scale pretty well to a planet with twice the gravity.

what ive always wanted to know, is if you went to a planet which had double the gravity for a year and got used to it, does it mean when you come back to earth you can jump double the height etc? Dragonball z was good at using this idea. (for those that don't know, dbz is a japanese manga cartoon about martial arts fighters who save the world regularly, its brilliant)

wonderboy wrote:what ive always wanted to know, is if you went to a planet which had double the gravity for a year and got used to it, does it mean when you come back to earth you can jump double the height etc? Dragonball z was good at using this idea. (for those that don't know, dbz is a japanese manga cartoon about martial arts fighters who save the world regularly, its brilliant)

http://www.seinfeldscripts.com/TheStockTip.htm wrote: [Setting: Coffee Shop]

JERRY Seinfeld: I think Superman probably has a very good sense of humor.

GEORGE Costanza: I never heard him say anything really funny.

JERRY: But it's common sense. He's got super strength, super speed.. I'm sure he's got super humor.

GEORGE: You would think that, but either you're born with a sense of humor, or you're not. It's not going to change even if you go from the red sun of Krypton all the way to the yellow sun of the Earth.

JERRY: Why? Why would that one area of his mind not be affected by the yellow sun of Earth?

GEORGE: I don't know but he ain't funny.

Planet with 2g: The baseball is boring because there are never any homeruns but the downhill skiing is a blast.

But practice Baseball in 2G and then return to G and put Barry Bonds, Mark McGwire, and Sammy Sosa to shame

With twice as much gravity; would you have to use twice as much yeast to get your cake to rise? What about growth of plants? Half as tall?

orin stepanek wrote:With twice as much gravity; would you have to use twice as much yeast to get your cake to rise? What about growth of plants? Half as tall?

Dunno but it would be twice as hard to get out of bed in the morning and the bathroom scales wouldn't be kind.