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A math question about the moon and an airplane

Hans

Philosopher
Hans
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May 10, 2007
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Math disabled person here asking for assistance.

If an observer is on the ground and the moon is full and at its apex in the sky and an aircraft moving at 400 kph passes in front of on the observers line of sight to the Moon. How do you calculate how long it will be visible while passing said Moon, assume an aircraft of 747 size 1/2 kilometer up?

Thanks in advance to the math smart people.
 
The angular size of a full moon varies, but let's take 31 arc minutes =0.51666°
An aircraft travelling at 400kph is moving at 111.1 m/s.
At 500m altitude (this is very low), the aircraft is moving at 25.46°/s, and thus will pass across the moon in 0.516666/25.46 = 0.02029 seconds.

This ignores the length of the aircraft itself.
 
Half a kilometer (1650 feet) up is very low for a 747; that would only be part of a take off or landing, which may account for the surprisingly low answer.

An object that is twice as far away as another object will appear half as big The moon is 238,900 miles away, or about 764,480 times as far away from the observer as the jet. The moon's diameter is about 2159 miles. If we divide that by 764,480, we get that the apparent size of the moon at the same point as the plane is only .00282 miles or about 14 feet. Since the plane itself is about 232 feet, the question becomes how long does it take the plane to travel 246 feet. At 400 KPH the answer appears to be around 2/3rds of a second.
 
If what Belgian thought is suggesting is right, and you are looking for a photo of a 747 silhouetted against the eclipsed Moon, and for them to be the same apparent size, then the 747 will need to be 8.4 km distant. Further if you want it to be smaller than the Moon.

If directly overhead, this is approaching typical maximum cruising altitude (about 11km I think: warning, this is not a topic I know anything about) for a jet aircraft. At 400kph, an 8.4km distant aircraft is moving at about 1.52°/sec and would appear to cross the moon in 0.34 sec.


Last year, I was looking at the Sun for the first time through a newly-acquired eclipse filter mounted on a telescope. I was nervous about it not working and blinding myself. Suddenly, I leapt backwards from the eyepiece because something had happened. It turned out to have been an aircraft flying directly across the face of the Sun. Had I had a camera attached, what a picture that would have been. It crossed the Sun in a blink of an eye, consistent with the back-of-the-envelope calculations above.
 
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Thanks all for the answers - very helpful - well mostly the humour was much appreciated too!
 
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