Rising Sun [;)]

GiveATry · 发表于 2007-10-30 05:02:51

City A, is approximately 120 miles due west of City B. They are in the same time zone and at the same elevation. How much sooner would a person in City B see the rising sun than a person in City A?

salmonfish · 发表于 2007-10-30 06:12:01

R(earth)=3950 miles; Treat sun as a point farfar away from earth. Earth spin angular rate= 2pi/(24x3600) (弧度/秒），then,

angle A=120/3950=0.03038 (弧度）

therefore, delay time=(0.03038x24x3600)/2pi=418 秒~7 分钟。

只看该作者 · 发表于 2007-10-30 06:19:13

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salmonfish · 发表于 2007-10-30 06:35:56

你是对的。但是题中未给出这些条件。我假设了两点都在赤道上，且地球自转轴与地球到太阳的方向相垂直（春季）。最简单情况。

GiveATry · 发表于 2007-10-30 22:48:04

The speed of the rotation of the earth is 1 revolution per day.
1 revolution = the perimeter of the earth = 2 Pi r
r =6.4x10³ km is the radius of the earth
=> 1 revolution = 2 x 3.14 x 6.4x10³ = 40192 km

Therefore the speed of the earth is:
t = (40192/ 24) km/hr=1675 km/hr = (1675/1.609) mile/3600 second = 0.2891 mile/sec www.ddhw.com

1 mile = 1.609 km; 1 hour = 3600 second.
We are given that the distance between this two cities is 120 miles, so after T seconds the person on the west side (city A) will see the sunrise:
T= 120 miles / 0.2891 mile/sec ~ 415.08 seconds ~ 6.9 mintes

So the person on the east side (city B) will see the rising sun about 6.9 minutes sooner than the one on the west side.

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Rising Sun [;)]

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