How Do You Calculate Angular Dimensions in Astronomy Photography?

In summary: Moving on to the second question, we need to determine the maximum angular distance a star can be from the south celestial pole and still be visible from the observatory. To do this, we first need to calculate the angular distance from the pole to the observatory. This can be done using the longitude and latitude of the observatory, as well as the declination of the south celestial pole (90 degrees). We can use the following equation:angular distance = 90 degrees - latitude + declinationTherefore, the angular distance from the south celestial pole to the observatory would be:angular distance = 90 degrees - 19
  • #1
JoshMP
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Homework Statement



From my astronomy textbook: "The photograph that opens this chapter was taken next to the Gemini North Observatory atop Mauna Kea in in Hawaii. The telescope is at longitude 155 28' 09" west and latitude 19 49' 26" north. a) By making measurements on the photograph, find the approximate angular width and angular height of the photo. b) How far (in degres, arcminutes, and arc-seconds) from the south celestial pole can a star be and still be circumpolar as seen from the Gemini North Observatory?

Homework Equations



The Small Angle Formula D=ad/206,265 where D= linear size of an object, a=angular size of the object in arcsec, and d= distance to the object

The Attempt at a Solution



I really don't even understand what the two questions are asking for. Can someone get me started and possibly talk me through this one? Thanks.
 
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  • #2


Dear student,

I would be happy to help you with this problem. First, let's break down the questions and their specific goals:

a) By making measurements on the photograph, we are trying to find the approximate angular width and angular height of the photo. This means we need to use the small angle formula to calculate the linear size of the photo (D) using the angular size (a) and the distance (d). We can use the given longitude and latitude of the observatory to determine the distance to the photo.

b) The second question is asking how far a star can be from the south celestial pole and still be circumpolar as seen from the observatory. This means we need to calculate the angular distance from the south celestial pole to the observatory, and then use the small angle formula to determine the maximum angular distance a star can be from the pole and still be visible from the observatory.

Now, let's get started with the first question. We can use the given longitude and latitude of the observatory to determine the distance to the photo. The distance (d) is the hypotenuse of a right triangle, where the longitude and latitude are the two sides. We can use the Pythagorean theorem to calculate the distance:

d = √(155^2 + 19^2) = √(24,025 + 361) = √24,386 = 156.1 km

Next, we need to determine the angular size of the photo (a). To do this, we can use a ruler to measure the width and height of the photo in centimeters. Then, we can convert those measurements to arcseconds by multiplying by 206,265 (since 1 arcsecond = 206,265 cm). Let's say the width of the photo is 10 cm and the height is 8 cm. Then, the angular width would be:

a = 10 cm x 206,265 = 2,062,650 arcseconds

And the angular height would be:

a = 8 cm x 206,265 = 1,650,120 arcseconds

Now, we can use the small angle formula to calculate the linear size of the photo:

D = 2,062,650 arcseconds x 156.1 km / 206,265 = 1.56 km

Therefore, the approximate angular width and height of the photo are 2,062,650 arc
 
  • #3


I would first clarify the questions being asked. It seems that the first question is asking for the angular width and height of the photograph, which can be calculated using the small angle formula. This formula relates the linear size of an object (in this case, the photograph) to its angular size and distance. The distance to the photograph can be assumed to be the distance from the Gemini North Observatory to the location where the photograph was taken.

To find the angular width and height, you would need to measure the linear size of the photograph in the units given (such as centimeters or inches) and convert it to arcseconds. Then, using the small angle formula, you can calculate the angular width and height of the photograph.

For the second question, it seems to be asking how far a star can be from the south celestial pole and still be seen as circumpolar from the perspective of the Gemini North Observatory. This would require knowledge of the altitude and declination of the star, as well as the latitude of the observatory. The altitude and declination can be used to calculate the angular distance from the south celestial pole, and this value can be compared to the latitude of the observatory to determine if the star would be circumpolar or not.

I hope this helps get you started on solving these questions. It would also be helpful to refer to your astronomy textbook or other resources for more information on the small angle formula and celestial coordinates.
 

Related to How Do You Calculate Angular Dimensions in Astronomy Photography?

1. What is the difference between angular width and height?

The angular width and height refer to the measurement of an object's apparent size in degrees as seen from a specific point of view. The angular width is the measurement of the object's apparent size from left to right, while the angular height is the measurement of the object's apparent size from top to bottom.

2. How is angular width and height calculated?

Angular width and height are calculated by dividing the actual width and height of an object by its distance from the observer. This results in a measurement in degrees, which represents the object's apparent size from the observer's point of view.

3. What is the significance of angular width and height in astronomy?

In astronomy, angular width and height are important measurements used to determine the apparent size and position of celestial objects. These measurements are crucial in understanding the distance and scale of objects in the universe.

4. How does angular width and height affect our perception of objects?

Angular width and height play a significant role in our perception of objects. The larger the angular width and height, the larger the object appears to be. Conversely, a smaller angular width and height result in a smaller perceived size of the object.

5. Can angular width and height change?

Yes, angular width and height can change depending on the distance between the observer and the object. As the distance increases, the angular width and height decrease, making the object appear smaller. Similarly, as the distance decreases, the angular width and height increase, making the object appear larger.

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