Conic projection of a sphere

In summary, the person is seeking help in understanding the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light. They provide an example of a light source at a certain height and a sphere located at a vertical distance and horizontally deviated from the perpendicular axis. They mention that when the horizontal deviation is zero, the projection is a circle but they want to know the relationship when the deviation is not zero. They also mention the possibility of using conic projections or perspective in drawings to find this relationship.
  • #1
Chandi
2
0
Hi everybody,

Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light.

For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of 'r') is located at y vertical distance from the source of light and horizontally deviated at x distance from the perpendicular axis of the plane and the source of light.
Obviously if the horizontal deviation is zero, then the projection is a circle. But I would like to know the relationship of the ellipse to the radius of the sphere when horizontal deviation is not zero.
 
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  • #2
Chandi said:
Hi everybody,

Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light.

For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of 'r') is located at y vertical distance from the source of light and horizontally deviated at x distance from the perpendicular axis of the plane and the source of light.
Obviously if the horizontal deviation is zero, then the projection is a circle. But I would like to know the relationship of the ellipse to the radius of the sphere when horizontal deviation is not zero.

Not sure what your question is about.

First thing comes to mind is chart conic projections (search for <cartography AND "conic projection"> or <"Lambert Conformal">.

But that doesn't explain the reference to an elipse. Possibly you are referring to perspective as used in drawings.

I'm probably not the person to answer your question, just though I'd help you ask it.

Also, you mentioned not having a background in physics, but how's your math?
 

1. What is a conic projection of a sphere?

A conic projection of a sphere is a method of representing the curved surface of the Earth on a flat map. It involves projecting the Earth's surface onto a cone, which is then unwrapped onto a flat surface.

2. How does a conic projection of a sphere differ from other map projections?

Unlike other map projections that involve projecting the Earth's surface onto a cylinder or a plane, a conic projection uses a cone as the intermediary surface. This results in a map that is more accurate in the middle latitudes, but distorted towards the poles.

3. What are the advantages of using a conic projection of a sphere?

One advantage of a conic projection is that it preserves the shapes and areas of land masses, making it useful for thematic maps such as population density or climate maps. It is also relatively easy to construct and has less distortion in the middle latitudes compared to other projections.

4. What are some limitations of a conic projection of a sphere?

One limitation of a conic projection is that it is not suitable for mapping large areas near the poles, as the distortion becomes too severe. Additionally, the projection only accurately represents the Earth's surface along the standard parallel used in the projection, and becomes increasingly distorted further away from this line.

5. How is a conic projection of a sphere used in cartography?

A conic projection is commonly used in creating maps of mid-latitude regions, such as Europe, North America, and parts of Asia. It is also used for thematic maps that require accurate representation of shapes and areas, such as political or economic maps.

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