Distance of a point on the earth from the sun

[Adyssa]

A question was posed that I decided to have a crack at, and I want to check my understanding. This isn't homework by the way, just trivia. Also the thread title is not really correct but I didn't want to complicate things! Here's the question:

What is the relative difference in the distance from the sun of two points on the earth. Specifically Montreal, Canada and Melbourne, Australia.

I started by finding out their respective latitudes. With these in hand, I drew a circle and some interior right triangles and set about finding the horizontal distance component from the equator to the point on the circle. I'm pretty sure I have these correct, here is my data so far:

Radius of Earth: 6378.1km

Montreal:
-Latitude: 45.5081° N
-Horizontal distance from equator: 1908.3km

Melbourne:
-Latitude: 37.7833° S
-Horizontal distance from equator: 1337.3km

Now, I need to account for the axial tilt of the earth, which is 23°. Given that it's the middle of summer/winter, the difference in distance from the sun will be at a maximum. What I did was to get the horizontal distance component for a point (the equator) at 23° latitude, which is 507km, and +/- from my above results, and I get a relative difference in distance of 1585km between the two cities.

Anyone care to comment or correct my reasoning? :)

Also, what is a good resource for astronomical measurements? I'd like to turn this into a program but I need to know about the elliptical orbit of the earth.

 

[Simon Bridge]

Some considerations:

On a scale that the curvature of the Earth is important (as here) the curvature of the Sun is also important.
So - distance from "where" on the Sun?

The distance will depend on the time of day.
The distance will depend (as you've noticed) on the time of year.

Do you also want to account for the Earth's axial wobble? What about altitude? You know the Earth is not exactly a sphere - so would you want to consider the "oblacity" as well?

What usually governs the form of these sorts of calculations is what you want to use the end result for.

 

[Adyssa]

Thanks Simon, you've brought up some things I had not considered. It's just an exercise for curiosities sake at the moment, but it would be nice to arrive at an accurate answer. The question was posed to get some perspective on how the distance from the sun affects the temperature experienced on the ground in different locations. To this end, I think all of the things you have mentioned are important, particularly altitude, and, as you say, "oblacity" - I've never heard the word but I guess you are referring to the fact that the Earth is a squashed sphere which I believe is due to centrifugal force from rotation. Distance from "where" on the sun is an interesting one. Perhaps I will think about that a little more.

 

[Simon Bridge]

For ideas about modelling the Earth's surface:
http://kartoweb.itc.nl/geometrics/reference%20surfaces/body.htm

There is such a thing as being too "accurate" ... at some point the extra decimal places will be meaningless.

 

[CellCoree]

I am glad to see that you are using your curiosity and problem-solving skills to explore this question. Your approach seems reasonable and your calculations appear to be correct. However, there are a few factors that you may want to consider in order to get a more accurate answer.

Firstly, the distance between two points on the Earth's surface is not a straight line, but rather follows the curvature of the Earth's surface. This means that the distance between Montreal and Melbourne would be slightly longer than the straight line distance you have calculated.

Secondly, the Earth's orbit around the sun is not a perfect circle, but rather an ellipse. This means that the distance between the Earth and the Sun varies slightly throughout the year. In fact, the difference in distance between the Earth's closest and farthest point from the sun is about 5 million kilometers. This may not seem like a significant difference when compared to the Earth's average distance from the sun (about 150 million kilometers), but it could still affect your calculations.

To get a more accurate answer, you could use online tools or software that take into account these factors and provide precise measurements. Some good resources for astronomical measurements include NASA's Solar System Dynamics website and the WolframAlpha website.

In conclusion, your approach to the question is commendable, but to get a more accurate answer, you may want to consider the curvature of the Earth's surface and the elliptical orbit of the Earth around the sun. I hope this helps and good luck with your program!