# Astronomy related angle question (more of a Trig Q)

• conquertheworld5
In summary, the conversation discusses the process of measuring the depth of a crater on the moon for an astronomy lab. The speaker mentions that while measuring the diameter of the crater is easy, finding the wall height requires measuring the shadow length and using the trigonometric tangent formula. They also question whether the angle of altitude (theta) needs to be converted to radians and consider factors such as the distance to the terminator and the radius of the moon. Ultimately, the speaker decides to submit their lab report as it is, but still seeks clarification on their method.
conquertheworld5
For an astronomy lab I am looking at pictures of the moon, measuring pixel distances and converting to km. Easy enough for the diameter of a crater, but the depth gets more complicated. To find the wall height of the crater, you measure the shadow length and the angle of altitude (theta in diagram). I was told that theta is equal to the distance to the terminator(D in diagram) divided by the radius of the moon, which is also easy to calculate. But to use the trig tangent(theta)=height/shadow, doesn't theta have to be in radians? the dist. to terminator over the radius is a dimensionless number (km/km after conversions)... should I multiply by a factor of 2pi to get theta, or is it okay for theta to be dimensionless?

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• terminator.jpg
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• altitude.jpg
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well... looks like I'm handing in my lab report as is whether it's right or wrong... just printed it.

Still would like to get an answer though!

First of all, great job on your astronomy lab! It's always exciting to apply trigonometry to real-world scenarios.

To answer your question, yes, theta should be in radians when using the tangent function to calculate the height of the crater wall. This is because the tangent function takes in the angle in radians as its argument. So, in order to get the correct answer, you will need to convert your angle in degrees to radians before using it in the tangent function.

To do this, you can use the conversion factor of pi/180, where pi is equal to approximately 3.14. So, if you have an angle of 30 degrees, you would multiply it by pi/180 to get the equivalent angle in radians, which would be approximately 0.52 radians.

In terms of the dimensionless nature of theta, it is important to remember that angles are always dimensionless, regardless of the unit used to measure them. So, it is perfectly fine for theta to be dimensionless in your calculation.

In summary, to use the tangent function to calculate the height of the crater wall, you will need to convert your angle in degrees to radians, but theta itself can remain dimensionless. Keep up the good work in your astronomy lab!

## 1. What is the difference between astronomy and astrology?

Astronomy is the scientific study of celestial objects and phenomena in the universe, while astrology is a belief system that claims to interpret how these celestial objects and their movements can influence human lives.

## 2. How is trigonometry used in astronomy?

Trigonometry is used in astronomy to calculate distances between celestial objects, determine the size and shape of objects in space, and predict the movements and positions of these objects in the sky.

## 3. What is the celestial coordinate system and how is it used in astronomy?

The celestial coordinate system is a spherical coordinate system that uses two coordinates, right ascension and declination, to locate objects in the sky. This system is used in astronomy to precisely locate and track the position of celestial objects.

## 4. How do astronomers measure the distance to stars and galaxies?

Astronomers use various methods such as parallax, spectroscopy, and standard candles to measure the distance to stars and galaxies. Each method has its own advantages and limitations, and they are used depending on the distance and type of object being measured.

## 5. How does the rotation and orbit of Earth affect our view of the night sky?

The rotation of Earth causes the stars and celestial objects to appear to move across the sky throughout the night. The orbit of Earth around the sun also affects our view of the night sky as it changes our perspective of the stars and the position of objects in the sky. This is why we see different constellations and stars at different times of the year.

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