You are located at 53 degree N: What is the solar angle at noon at the Summer So

Question

You are located at 53 degree N: What is the solar angle at noon at the Summer Solstice? What is the solar angle at noon at the Winter Solstice? What is the highest possible solar angle during the year if you live at 38.5 degree S? On what day will it occur? You are on a ship in the Pacific Ocean: On June 21^st (Summer Solstice), you measure the solar angle at noon - it is 83.5 degree to your south. What is your latitude? Six months later, on December 22nd (Winter Solstice), you measure the solar angle at noon-it is 12.5 degree to your south. What is your new latitude? Assuming you traveled directly along a single meridian, how far (in Km) did you travel from June 21s^t to December 22^nd?

Explanation / Answer

Solar angle is the angle made by sun over a region. That is on summer solstice solar angle of tropic of cancer is 90 degrees.

1. If I am locatelocated at 53 degree northe the solar angle at noon of summer solstice will be {90-(53-23.5)} or (90-29.5) or 60.5 degrees.

That is for winter solstice will be {90-(53+23.5+23.5)} or 0 dedegree.

2. The highest possible solar angle will occure on winter solstice. And that is {90-(38.5-23.5)} or 75 degrees.

3. If the solar angle is 83.5 degree S on summer solstice the The ship is on {23.5+(90-83.5)} or (23.5+6.5) or 30 degree N.

If on winter solstice tge sosolar angle is 12.5 degrees the tge latitude will be (90-12.5-23.5) or 54 degrees N.

So tge ship has traveled (54-30) or 24 degrees towards N.

A complete meridian is a hemisphere and thus it has 180 degrees, and have length of half of the Earths circumference about the poles, ie. 20003.93 km.

180 degrees means 20003.93 km so 24 degrees means (20003.93*24/180) or 2667.19 km.

so tge ship is traveled a distance of 2667.19 km

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