So I'm trying to calculate the latitude of where I am via a few factors. My lesson says I need to know the following:
The date of my measurements: 4/3/17
the time: 12:30
my height: 5' 10"
my shadows length: 4' 6"
It then says first, compute the angle of the sun when the photo was taken, a, given by
a = arctan (known height / length of shadow.
I got 1.2 but am not sure if its correct. The arctan of 1.2 is 50.19442891? is there anything else needed to figure this out?
Since the distances involved are minuscule compared to the size of the earth, all you really need to know is your height and shadow length.
And you are correct that arctan(1.2) = 50.19°
You have listed the time as 12:30, so the sun should have been almost directly overhead (90°). The angle of 51° indicates that you were at a rather northern latitude. If it matters, you can research how the angle of the sun at noon relates to your latitude.
Well my assignment is asking that I use the equation and info provided to estimate the latitude of Tempe, AZ. which according to google earth is about 33 degrees. so I'm not sure what I am doing wrong. should've posted that originally, sorry.
I expect this article will help:
https://astronavigationdemystified.com/latitude-from-the-midday-sun/
Since your time of day is 12:30 rather than 12:00, you will need to factor that in.
Thanks a lot that did help. on another related note, the second part of the question asks what would the length of my shadow be if I did this on June 21st (summer solstice). Wouldn't my shadow be non-existent because the sun isn't behind me, but directly above me?
To calculate the latitude of where you are using the factors provided, you would need to use a different approach. The angle you calculated (1.2 radians) using the arctan function actually represents the angle between the height of the object (your height) and the length of the shadow. This angle is not directly related to the latitude calculation.
To calculate the latitude using the given factors, you can use the following steps:
1. Determine the declination angle: The declination angle represents the angle between the sun at noon and the celestial equator on a particular day. To calculate the declination angle for a given date, you can refer to tables or use online calculators.
For the date 4/3/17, the declination angle is approximately -3.93 degrees.
2. Calculate the zenith angle: The zenith angle is the angle measured from the vertical direction to the location of the sun at a given time. It can be calculated using the declination angle and the latitude.
Latitude = Zenith angle - Declination angle
To determine the zenith angle, you can use the formula:
Zenith angle = arctan(sin(Declination angle) / (cos(Latitude) * tan(h)))
Here, h denotes the time in hours past noon, where 12:00 is considered noon. In this case, if the time is 12:30, h is 0.5.
Substituting the known values and solving for the latitude, we get:
Latitude = arctan(sin(-3.93) / (cos(Latitude) * tan(0.5)))
To solve for the latitude, we need to use an iterative approach because the latitude appears on both sides of the equation. You can use numerical methods or approximation techniques to find an estimate of the latitude.
Without further information, it's not possible to determine the exact latitude with just the provided factors. Additional information, such as the length of the shadow at local noon, would be required to calculate the latitude accurately.