Talk:Zebia
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- Tmeister
- Gsandi
- Praesidium(Servator_Mundi)
- Cedh Audmanh
- Corumayas
Discussion on the size of Zebia:
[quote="Tmeister"] Obviously the planet cannot be exactly the same size as Earth (~ 3960 miles or 6372 km as the radius), but in light of the discussion about the size of the planet, it needn't be significantly larger. So how about around 4100 miles (6600 km)? The increase in gravity is very low - if the density is comparable to Earth's, an object weighing 50 pounds on Earth would weigh 51.8 pounds on the new planet. On the other hand, this gains an extra 4,513,600 sq miles of surface area (11,690,170 sq. km, about 68% of Russia, admittedly not very much).[/quote]
I don't know how you got this answer, I arrive at a different one.
If r is the mean radius of thre Earth, and x is the difference between Zebia's and the Earth's radius, then the new surface area is 4п(r+x)^2 = 4п(r^2 + 2rx + x^2). Since we want the increase in surface area only, we subtract the Earth's actual surface area, and the resulting difference can be calculated (at r=6372 and x=228):
4п(2rx+x^2) = 4п(2,906,000 + 52,000) [rounding off the thousands]
= 4п(2,958,000)
= 37,152,000 sq.km.
This is more than 1.5 times the area of the ex-USSR.
Nevertheless, I would be in favour of making the planet even larger - or, alternatively, quite a bit smaller - then the Earth. Adding 228 km to the actual radius of the Earth adds only about 3% - this, to me, is too much of a coincidence. Let's make it a good 15% more (or less). I suggest, more - making a radius of, say, 7350 km. This should certainly give us a large enough surface area to play on. (If heavier gravity becomes a problem, we can always decrease the average density of the planet - as a general principle in conworlding, always vary the parameters you know the least about!)
So, what's the increased surface area now, with an x value of (at r=6372 and x=978)?
4п(2rx+x^2) = 4п(12,464,000 + 956,000) [rounding off the thousands]
= 4п(13,420,000) = 168,555,000 sq.km.
This is slightly more than the actual total land area of the Earth (roughly 150,000,000 sq.km.), so that by applying our 15% or so increase in the radius, we can double the land area and still have about 20,000,000 sq.km left over as more oceans.
Let's wait and see what others think.
Gsandi 02:07, 26 February 2007 (PST)
I'd be in favor of the smaller increase in radius, as too much and too many things become alien, making it harder to work with. Then you have the fact that increased mass wouldn't just mean that things were heavier, but they fall faster too (with an increase of 15% in radius fravitational acceleration would nearly double, if my equation is even close to being correct [g*m1^2*m2^2/r^2](?) increasing the radius by 15% should result in a volume increase of ~32%, assuming the same (or similar) density that would mean that gravity would be ~74% greater). Praesidium
Not quite, as I already showed once in a thread on the zompist board. Assuming that average density remains the same, the mass of the planet goes up with the cube of the radius, but at the same time the surface is further away from the centre of the planet, and gravity decreases with the square of the distance. Therefore the actual acceleration on an object due to gravity is subject to the relationship r^3/r^2, i.e. it is exactly proportional to the distance from the centre. Thus, a 15% increase in radius results in a 15% increase in the acceleration due to gravity.
I am not sure how to interpret your equation g*m1^2*m2^2/r^2. If m1 and m2 refer to the masses of the objects, it is simply incorrect: gravitational force F=Gm1m2/r^2, i.e. it is proportional to the masses of the objects in question, not to the squares of their masses. G (and not g) is the gravitational constant, of course.
It is also very important to make a clear difference between force and acceleration. The force between two objects due to gravity is indeed proportional to the product of their masses, but acceleration being the product of mass and acceleration, you have the equation: gm1 = Gm1m2/r^2, where the two m1's cancel, so that the acceleration g of an object in a gravitational field is going to be g = Gm2/r^2, i.e. it is independent of its own mass (as Galileo already proved experimentally at the Tower of Pisa).
Weight and gravitational force on an object are basically the same thing, you don't have to specify that "things were heavier, but they fall faster too".
Pragmatically speaking, I don't think that a 15% increase in surface gravity would make much of a difference to animals evolving on the planet - their muscles and other physiological parameters will have evolved in order to deal with the prevalent gravity. Conceivably they would be a bit smaller and squatter than we are (on the average), but conceivably they would have evolved a somewhat more efficient way to use sugar (or other) - based energy use.
Gsandi 03:03, 28 February 2007 (PST)
