Comic Discussion > ALICE GROVE
Alice Grove MCDLT - February 2017
A small perverse otter:
--- Quote from: jheartney on 20 Feb 2017, 09:06 ---
--- Quote from: A small perverse otter on 20 Feb 2017, 08:28 ---In principle, there's a way to estimate the orbital radius of the tree by looking at the curvature of Earth's image as seen from the spaceship (assuming that the flyer is in roughly the same orbit as the tree), since the radius of the resulting circle can be estimated from its curvature. Given the apparent radius, we can then compute the distance between Earth's center and the spaceship by a straightforward application of plane analytic geometry.
That would permit anyone to determine whether the tree is in geosynchronous orbit.
--- End quote ---
That would depend on the focal length of the "camera" used in the making of the image. A telephoto lens would foreshorten distances, making the planet seem nearer, with a larger apparent radius. A wide-angle lens would have the opposite effect.
Granted, these are drawings rather than photos. But the principle is the same: apparent radius is a subjective quality based on foreshortening, as chosen by the artist.
--- End quote ---
Actually, no.
Any three point on a circle define that circle completely. Because the earth is a sphere, the image of the earth through any (reasonable) camera is also a circle. In addition, each viewpoint line is perpendicular to the line which runs from the point at which that line touches the sphere to the radius. (Using the fact that the Earth is a sphere.) Now we have a tetrahedron about which we know a great deal (some faces are isosceles triangles, others are right triangles, and we have a bunch edges.) I'm going to assert without proof that we have enough data to reconstruct the solid completely, from which we can actually compute the distance to the Earth's center.
(ETA: also, we know the exact length of the edges which run from each point were the line from the eye to the point at which the ray grazes the sphere, since we know the radius of the Earth.)
But, as you say, this is a pure and absurd exercise, since Jeph drew it and there's no relationship between the drawing and reality.
A small perverse otter:
--- Quote from: A small perverse otter on 20 Feb 2017, 09:43 ---
--- Quote from: jheartney on 20 Feb 2017, 09:06 ---
--- Quote from: A small perverse otter on 20 Feb 2017, 08:28 ---In principle, there's a way to estimate the orbital radius of the tree by looking at the curvature of Earth's image as seen from the spaceship (assuming that the flyer is in roughly the same orbit as the tree), since the radius of the resulting circle can be estimated from its curvature. Given the apparent radius, we can then compute the distance between Earth's center and the spaceship by a straightforward application of plane analytic geometry.
That would permit anyone to determine whether the tree is in geosynchronous orbit.
--- End quote ---
That would depend on the focal length of the "camera" used in the making of the image. A telephoto lens would foreshorten distances, making the planet seem nearer, with a larger apparent radius. A wide-angle lens would have the opposite effect.
Granted, these are drawings rather than photos. But the principle is the same: apparent radius is a subjective quality based on foreshortening, as chosen by the artist.
--- End quote ---
Actually, no.
Any three point on a circle define that circle completely. Because the earth is a sphere, the image of the earth through any (reasonable) camera is also a circle. In addition, each viewpoint line is perpendicular to the line which runs from the point at which that line touches the sphere to the radius. (Using the fact that the Earth is a sphere.) Now we have a tetrahedron about which we know a great deal (some faces are isosceles triangles, others are right triangles, and we have a bunch edges.) I'm going to assert without proof that we have enough data to reconstruct the solid completely, from which we can actually compute the distance to the Earth's center.
(ETA: also, we know the exact length of the edges which run from each point were the line from the eye to the point at which the ray grazes the sphere, since we know the radius of the Earth.)
But, as you say, this is a pure and absurd exercise, since Jeph drew it and there's no relationship between the drawing and reality.
--- End quote ---
Oops. No, you'r right. Sorry.
jheartney:
--- Quote from: A small perverse otter on 20 Feb 2017, 09:43 ---
(ETA: also, we know the exact length of the edges which run from each point were the line from the eye to the point at which the ray grazes the sphere, since we know the radius of the Earth.)
--- End quote ---
No, we don't know that length. That length is what you are trying to determine.
Consider this diagram:
If you were hanging in space, looking at the Earth, you would be able to measure Angle C. With that measurement, plus knowledge of the Earth's radius, you could then determine the length of sides A and B using trigonometry.
But we're not hanging in space. All we have is a flat image. Depending on the focal length of the camera used to capture the image, both Observer 1 and Observer 2 could capture an identically sized image of the Earth (Observer 2 would just have to zoom in a bit). Given that is the case, there's no way to tell what Angle C is, using only the photo. Without that known measurement, there's no way to solve for A or B.
brasca:
--- Quote from: Welu on 20 Feb 2017, 09:38 ---Das a very big tree.
I'm worried for Gavia. That looks like fear on her face to me.
--- End quote ---
I think she's afraid of what Pate will do next. She's seen what Church can do and knows that Pate won't take no for an answer. I also think that she's in denial about the benevolence of the Praeses and fears the revelation that she and her brother were just pawns in a grand scheme that could've got them killed.
Sorflakne:
So basically...there's a giant tree in space whose base looks like a giant butt?
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