Watch the Sun Rise: Detlef Palm

I received a stack of envelopes; each contains a challenge. I must only open a new envelope once the previous task is completed. This time I had to watch the sun rise. 

Here we need to add meaning.  For a genuine experience, the sun has to rise above the horizon, and not simply peek over the roof of your neighbor's house. We had to get up in the dark, drive into the hills, take a brisk walk to a point with unobstructed views facing east. And then wait for the spectacle to unfold.

Huge, reddish and covered in Sahara dust

Unfortunately, I am one of those people who wake up long before the alarm rings because I worry of missing it. To fall back asleep, I started mentally calculating how far we would have to see to catch the sunrise over the horizon and not just over the trees of a nearby forest..

In the diagram, 

• R is the radius of earth at about 6,378,000 meter. 
• h is the eye-level height of the observer. 
• x is the distance to the horizon - where we expect the sun to appear.

According to Pythagoras: 

(R+h)² = R² + x²

x = √(2Rh + h²)

We ignore the term h², because it is negligibly small compared to the radius of the earth. This simplifies the equation to

x ≈ √(2Rh)

For a 2 meter tall person standing on the beach, the horizon is 5000 meter away, or 5 km. For a person sitting in a lighthouse 20 meter above ground, the horizon is 16 kilometer away.

We are not living on a beach. The Earth's surface is not a billiard ball, but resembles a shriveled orange. Our landscape is undulating and hilly. One must find a prominent point that allows an unobstructed view as far and beyond as required by the (calculated) distance to its (theoretical) horizon.  

Based on my calculations during the night, I concluded that our chosen location would meet this condition. In the image below, taken exactly at the predicted time of the sunrise, the horizon is more than 70 kilometers away. 

The sun rises as a tiny sliver of light and instantly disappears into some haze. This is not what we expected. The weather-app had predicted a cloudless sky.

Half an hour later the sun reappears, magnified, huge and reddish, as in our photo at the top. On the way back in our car, we hear on the news that a massive Saharan dust cloud has reached Germany.

Broaden your horizon. Go and watch the sun rise. 

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For other real life puzzles, visit:

The UNICEF Field Trip

The Cannonball Puzzle

The Europe Puzzle

The Yellow Submarine

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More Insights from Outside the Bubble, by Detlef Palm

Detlef can be contacted via detlefpalm55@gmail.com