Basic Question about angle of inclination of a circle

In summary, the conversation discusses measuring supernovae and the assumption of a circular ring that appears at an angle from Earth. The author of the content assumes that the ring is inclined at a specific angle to the observer, but the question asks for a method to determine the angle of inclination based on the size of the ring in arcseconds. The solution involves using simple geometry and measuring the longest and shortest diameters of the ring to calculate the angle of inclination.
  • #1
kungfuscious
15
0
I've seen some measurements of supernovae, and they often mention a ring that's expanding. I can follow that. What is often stated is that they assume the ring is a circle, but of course it's seen at an angle from Earth.

One such example was a ring that looks like it's a certain size in the sky (x arcseconds, by y arcseconds). Assuming it was a circular ring, the auther just jumps to a conclusion, something like: "using geometry, we can see that the ring is inclined at an angle of e.g. i=29 degrees to face-on"

This should be simple geometry, and yet I'm stumped as to how to get the angle of inclination of the ring, assuming it's circular and looking at it's size in the sky in arcseconds.

Does anyone have any ideas?
 
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  • #2
Welcome to PF!

kungfuscious said:
… One such example was a ring that looks like it's a certain size in the sky (x arcseconds, by y arcseconds). Assuming it was a circular ring, the auther just jumps to a conclusion, something like: "using geometry, we can see that the ring is inclined at an angle of e.g. i=29 degrees to face-on"

This should be simple geometry, and yet I'm stumped as to how to get the angle of inclination of the ring, assuming it's circular and looking at it's size in the sky in arcseconds.

Hi kungfuscious ! Welcome to PF! :smile:

Yes, it's simple geometry …

a circle seen at a angle is an ellipse …

take a vertical circle of angular diameter x, and turn it round the vertical diameter, through an angle θ …

the vertical diameter will have the same angular size, x, but the horizontal diameter will be reduced to angular size y = x cosθ …

so just measure the longest and shortest diameters, x and y, and the angle is cos-1 y/x :smile:
 

1. What is the angle of inclination of a circle?

The angle of inclination of a circle is the angle formed between the tangent line to the circle at a given point and the x-axis of the coordinate system.

2. How is the angle of inclination of a circle measured?

The angle of inclination of a circle is typically measured in degrees, with 360 degrees representing a full circle. It can also be measured in radians, with 2π radians representing a full circle.

3. What is the significance of the angle of inclination in a circle?

The angle of inclination in a circle is important because it helps determine the direction and slope of the circle at a given point. It is also used in various mathematical calculations and equations involving circles.

4. How does the angle of inclination affect the shape of a circle?

The angle of inclination does not affect the overall shape of a circle, as it remains a perfect round shape. However, it does affect the orientation and position of the circle in relation to the coordinate system.

5. Can the angle of inclination of a circle be negative?

Yes, the angle of inclination of a circle can be negative. This typically occurs when the circle is oriented in a clockwise direction, resulting in a negative angle measurement. However, the absolute value of the angle of inclination remains the same regardless of its sign.

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