Oleg Zabluda's blog
Tuesday, June 12, 2012
 
Two Sunsets On the Same Day from the same building is the brouhaha of the day, and is minboggling to some people.
Two Sunsets On the Same Day from the same building is the brouhaha of the day, and is minboggling to some people.

Sun is 1/2° across. Let's calculate how high we have to climb to look 1/2° and 1° below the horizon:

(1/cos(1/2°)-1)*6,371=0.24 km
(1/cos(1°)-1)*6,371=0.97 km [1]

It takes Earth (24*60)/360=4 min to turn 1°, or 2 min for 1/2°.  So if we can get to 0-240m-970m fast enough, we would indeed see two or even three complete sunsets.  To just keep up with the Sun and see one long sunset, your average velocity 0-240m will be leisurely 7.5 kph and 240-970m will be easy 22 kph. This speed increases as a square of height, starting from 0, because derivative of derivative of arccos(1+h/R) is infinity at h=0. This gives us 2 ideas.

Idea one: who says you need to see complete sunset. Astronomical sunset is when the trailing edge of the Sun crosses horizon. 

(1/cos(3 minute)-1)*6,371=0.0024 (=2.4m)
(1/cos(6 minute)-1)*6,371=0.0097 (9.7m)

so, simply standing up from lying on a beach while Sun sets, allows one to see 3 arcmin below the horizon, which is 10% of Sun's diameter. Easily qualifies as seeing 2 astronomical sunsets. How romantic. And you can easily double the effect by climbing a 10m hill or structure.

Idea two:

Who says you need to watch 2 sunsets. What about 2 sunrises? Trivially done by BASE jumping.

[1] So you have to be 970m high. Burj Khalifa is 830m. arccos(1+0.830/6371)=0.9248°. Close, but no cigar.

The brouhaha originated with this silly article:
http://gizmodo.com/5917230/did-you-know-that-the-burj-khalifa-is-so-tall-that-you-can-watch-two-sunsets-on-the-same-day

In contrast, the video it references is excellent:
How High Can We Build?
http://gizmodo.com/5917230/did-you-know-that-the-burj-khalifa-is-so-tall-that-you-can-watch-two-sunsets-on-the-same-day

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