by bruce » Thu Aug 21, 2003 10:46 pm
Ice Cream Jonsey wrote:
Just looked something up -- Phobos is only 6,000 kilometers away from the surface of Mars. It's incredibly tiny, however. How much of the sky does it take up when it's overhead? It'd still have to be more than the Moon does for Earth, right? I need to find these things out.
Well, depends on what you mean by "how much of the sky". Let's assume you mean "area". Let's be generous to Phobos: it's 27 x 21 x 17 km, roughly, so let's call that 560 thingies (I'm multiplying the two largest dimensions, roughly. The pis and such are constants and so they'll divide out anyway, and what I'm interested in is a dimensionless constant: the size of Phobos relative to the size of the sky.) Now, it's 6000 km out, so let's call 1000 km our unit of distance, and say that, therefore, the inner surface of the sphere is 36 thingies (again, the pis and constants will all eventually cancel; what we care about is that the area of a spherical shell is proportional to the square of its radius). So the chunk of sky that Phobos takes up is 560/36, or roughly 16 mogelschnitzers.
Now on to Luna. It's about 1750 km radius, so let's call that 3500 km diameter. It's pretty close to round, so that's 12 and a quarter million thingies. But it's also much farther away: 380,000 km, more or less, so 380 units. Square that and you get 144,400. The chunk of sky that the moon takes up is therefore 12 and a quarter million divided by 144,400, which is roughly 85 mogelschnitzers.
So, sorry, ICJ, but the moon looks bigger from Earth than Phobos does from Mars.
Bruce
[quote="Ice Cream Jonsey"]
Just looked something up -- Phobos is only 6,000 kilometers away from the surface of Mars. It's incredibly tiny, however. How much of the sky does it take up when it's overhead? It'd still have to be more than the Moon does for Earth, right? I need to find these things out.[/quote]
Well, depends on what you mean by "how much of the sky". Let's assume you mean "area". Let's be generous to Phobos: it's 27 x 21 x 17 km, roughly, so let's call that 560 thingies (I'm multiplying the two largest dimensions, roughly. The pis and such are constants and so they'll divide out anyway, and what I'm interested in is a dimensionless constant: the size of Phobos relative to the size of the sky.) Now, it's 6000 km out, so let's call 1000 km our unit of distance, and say that, therefore, the inner surface of the sphere is 36 thingies (again, the pis and constants will all eventually cancel; what we care about is that the area of a spherical shell is proportional to the square of its radius). So the chunk of sky that Phobos takes up is 560/36, or roughly 16 mogelschnitzers.
Now on to Luna. It's about 1750 km radius, so let's call that 3500 km diameter. It's pretty close to round, so that's 12 and a quarter million thingies. But it's also much farther away: 380,000 km, more or less, so 380 units. Square that and you get 144,400. The chunk of sky that the moon takes up is therefore 12 and a quarter million divided by 144,400, which is roughly 85 mogelschnitzers.
So, sorry, ICJ, but the moon looks bigger from Earth than Phobos does from Mars.
Bruce