Astrophysics: finding the azimuth the moment sun rises

[JordanGo]

Homework Statement

Suppose you seen the Sun rise on the day of the summer solstice from latitude 43.5. What is its azimuth at the moment when it rises? (Note that to specify an
azimuth, you can describe it as being so many degrees in a particular direction starting from
a reference point on the horizon, e.g. 20 degrees south of the western point.)

Homework Equations

The Attempt at a Solution

I'm having a problem finding the altitude...any hints?

 

[mark726]

I would first like to clarify that the term "altitude" typically refers to the height above sea level. In this context, I believe you are referring to the altitude of the Sun, which is the angle between the horizon and the center of the Sun at a given moment.

To find the altitude of the Sun at a specific time and location, you can use a tool such as a sextant or an online calculator that takes into account the date, time, and location. However, since this is a homework question, I assume you are expected to use your knowledge of astronomy and geometry to solve it.

First, we need to understand the concept of the summer solstice. This is the time when the Sun reaches its highest point in the sky, which is directly overhead at the Tropic of Cancer (23.5 degrees north). From this information, we can infer that at the moment of sunrise on the day of the summer solstice, the Sun's altitude at latitude 43.5 degrees will be 43.5 - 23.5 = 20 degrees.

Next, we need to determine the azimuth of the Sun at the moment of sunrise. The azimuth is the angle between the direction of the Sun and a reference point on the horizon. In this case, we can take the western point as our reference, and the direction of the Sun at sunrise will be towards the east.

To find the azimuth, we can use the following formula:
Azimuth = arctan(sin(20 degrees)/cos(20 degrees))
Azimuth = arctan(0.342/0.939)
Azimuth = 19.7 degrees east of the western point

Therefore, the azimuth of the Sun at the moment of sunrise on the day of the summer solstice from latitude 43.5 degrees will be 19.7 degrees east of the western point. I hope this helps with your homework question.