MadSci Network: Earth Sciences |
Dear Leslie, thank you very much for your question, which i must admit needs a lot of discussion. I will give you first some basic information regarding earth and its relation to the sun. 1)Earth's distance from the sun is approximately: 152100000km at Aphelion and 147090000km at Perihelion. As you can see these numbers are quite large, which means that a difference of 4365meters is neglectible. 2)Earth is rotating around its axis. This is why we have day and night. Now this is very crucial to your question regarding the longitude coordinates (East-West). 3)Earth is rotating around the sun but its axis is tilted by 23.5degrees and this is why we have the various seasons. Now lets examine the coordinates you provided. These coordinates are called geographic or geodetic coordinates and of course are part of a coordinate reference system which is defined by the Greenwich meridian and the equatorial plane. If we look this reference system from space we'll see that it is fixed only for us on earth. This is due to the fact that the earth is rotating around its axis. So when for e.g. you say 97 degrees West X degrees North this would not be a fixed spot for someone who is looking down on earth from a spaceship, since he would watch it move below him. So if two points had the same latitude but different longitude we would have to specify also the time at which we would want to calculate their distance from the sun. So in order to answer your question i will have to make certain assumptions: 1)The earth is not rotating 2)I will ignore the longitude (as explained in the previous paragraph) and assume that both points are in the same longitude 3)I will consider earth to be a sphere with a mean radius R=6371Km 4)I will assume that the earth's position towards the sun is the one during December 5)The earth and the sun lay on the same plane defined by an horizontal line passing from the earth's and the sun's center as shown in the figure. This means that we will now give an very approximate value for the distance between point A (42.87N and 4365meters height) and point B (34.52N and 0 meters height). I will explain the calculation for point A and point B can be calculated in the same way. -According to the figure (a simple figure just for understanding what i am going to do) we know the geographic latitude and we have to calculate first the geocentric latitude which is defined by (AES). Since we assumed that the earth is a circle and not an ellipsoid of revolution (as geodesists do for more precise calculations) then the geographic latitude is equal to the geocentric latitude. -Now we will add the tilt of the earth's axis. This is done by adding 23.5 degrees to 42.87N which will give us: 42.87 + 23.5 = 66.37 degrees and this is point A in the figure If there weren't any tilt then point A' would be the one that we would use -We calculate the distance of point A from the earth's center which is height + mean Radius of the Earth: 6371000meters + 4365meters = 6375365meters or 6375.365km -Now our problem is to find the distance (AS) which is what we are looking for. The (ASE) form a triangle where we know the distances (A'E),(ES) and the angle (AES). The solution is given by the following expression: (AS) = square root of( AE^2 + ES^2 - 2*A'E*ES*cos(AES) ) which gives: (A'S)= 6375.365^2 + 152100000^2 - 2 * 6375.365 * 152100000 * cos(66.37) => (AS) = 152097444km For (B'S) following the above procedure we'll have: (BS) = 6371^2 + 152100000^2 - 2 * 6371 * 152100000 * cos(58,02) => (BS) = 152096625km By comparing both results we see that point B is closer to the sun then point A. We must not forget that we reached to this result after making certain assumptions, which of course leads us to make calculations under an ideal enviroment. I will gladly answer any further questions or comments, thanks again for thinking as a mad scientist:) Vassilios N. Grigoriadis MSc Surveyor Engineer Thessaloniki, Makedonia Greece (Hellas) {Admin note: Although Vassilios made a number of assumptions and simplifications in his calculation, the bottom line is quite clear: If we are thinking about how close to the sun we are, latitude is much more important than altitude as a determining factor. }
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