- The largest airliner, the Airbus 380, is about 50 dtons.
I get the fuselage to be about 200 Dt?
Height: 8.41 m
Width: 7.14 m
Length: ~60 m?
Volume roughly ≈ π × 8.41/2 × 7.14/2 × 60 ≈ 2 800 m³ ≈ 200 Dt.
Oops! And . . .
Old School said:
Steve, Something's definitely off. 747 is bigger than the space shuttle it carried, and the 380 is definitely bigger than the boeing.
. . . Another oops!
It looks like I had a critical failure on my mental arithmetic roll. I probably used fuselage radius (or half-axis, in cases where fuselages are ellipses instead of circles) instead of diameter. I recall that I intended to just multiply height by width by length, instead of half-height by half-width by pi by length, to allow some extra for the wing volume. But maybe I did half-height by half-width by length. That seems consistent with my numbers compared to both of yours.
As far as gravitation force at altitude, if I remember correctly, (and that's pretty iffy), it is a factor of inverse square of the radius (i.e. the distant from the gravitational center of the planet). . . .
If you want to do these calculations, just remember that the distance you are calculating from is the center of mass, not the surface. Or better yet, look it up, because I might be talking out of my rear end.
The gravity formula is mass1 × mass2 × gravitational constant / distance^2.
But that only works for point masses, or at great enough distances that point mass is anacceptable approximation. Otherwise you have to integrate by mass/volume.
For example, imagine a spherical cloud of interstellar gas, 1 parsec in diameter, 100 solar masses. (Never mind whether that's a realistic size.) If you treat the cloud as a point mass, it's OK if you are calculating its gravitational pull on a star 20 parsecs away. But what if you're 1 AU from its center? Treating it as a point mass gives it 100 times the gravitational pull of the Sun at 1 AU. At 0.1 AU, it's 10k times the pull of the Sun at 1 AU. That doesn't make sense.
The problem is that the cloud is an extended object, and the mass in the direction of the center of mass is very nearly balanced by the mass in the opposite direction and any other direction.
So consider Jupiter at edge-of-space altitude. A volume of Jupiter gas at cloud-top altitude at the nearest point within Jupiter is quite a few times closer than an equal volume of Jupiter-gas at cloud-top altitude at the farthest point.So the nearest part of Jupiter exerts more gravitational force than the farthest point, and every part in between is different.
Making matters more complicated, Jupiter's density is not constant. At cloud-top altitude, it's low-density gas, but its overall density is more than that of water, because the core is so dense.
I don't know the density curve of Jupiter, but Earth has an average density of about five times water. The oceans are slightly more dense than pure water (because of the salts), surface rocks are typically 2.5 to 3 times water, and the mostly-iron core is about 12 times water. (Normally iron is about 7.9 times water, but Earth core iron is under extreme pressure.) Whatever is at the center of Jupiter is under much greater pressure, so iron there might be even more dense than 12 times water.