Whiteboard: Angular Measure and Range (Dan MacIsaac, NAU Physics & Astronomy)
Revised 20May01
Activity to accompany M. Thierry Legault's photograph at <http://perso.club-internet.fr/legault/s010113.jpg>
Questions:
1. Examine this picture. Identify the objects in the picture. What unusual
phenomena do you see in this picture?
Describe them.
2. The aircraft in the picture appears to be a MD-11 airliner, of known dimensions
(wingspan 51.8m,
length 61.2m, height 17.7m). Given that the sun subtends a known angle of 33
minutes of arc, can you
use the definition of arc length to determine the range to the aircraft from
the photographer?
3. Given a sun-earth distance of approximately 150 x 106 km, can
you determine the approximate
height of the solar prominence pictured at about 8:30 on the edge of the sun's
disk? Compare the size
of the prominence to the length of the aircraft, and to the radius of the Earth
(approximately 6400 km).
Some Possible Solutions:
The image is of the surface
of the sun through a telescope with an H-alpha filter, showing solar surface
structures (prominences and granules). An airliner is flying in front of the
sun, and its turbulent contrail
is clearly visible, as well as atmospheric turbulence about the aircraft.
The sun is 33 minutes in diameter, or 33 / 60 * 2PI / 360
= 9.6 x 10-3
radians of arc. On my printout of
this image, the aircraft (a/c) measures to be 3.0 cm long and the sun measures
17.5 cm across, so the a/c
subtends an angle of 3.0 / 17.5 * 9.6 x 10-3
rad = 1.7 x 10-3
rad. Assuming a projected a/c length of 60m,
and the arc length formula s = rq ; r = s /
q = 60 m / 1.7 x 10-3
rad. = 35 km slant angle to the aircraft.
The a/c is 35 km away from the observer.
The solar prominence measures 0.4 cm high on my printout
of the picture, so it subtends
0.4 / 17.5 * 9.6 x 10-3
rad = 2.2 x 10-3
rad. Given r = 150 x 108
km;
then s = rq = 150 x 108
km * 2.2 x 10-3
rad = 33,000 km high.
This is more than 5 Earth radii high, or half a million MD-11 lengths in height.
References:
This image was presented, discussed and analyzed in a PHYS-L
interchange by subscribers
Stefan Jeglinski, Skip Kilmer, Rondo Jeffery, John Denker, Tim Sullivan, Dan
MacIsaac, Leigh Palmer
and Bernard Cleyet. Their complete discussion is available at
<http://mailgate.nau.edu/cgi-bin/wa?S2=phys-l&q=&s=interesting+pic&f=&a=&b=>
Many thanks to M. Thierry Legault for taking and sharing this photograph via the internet.
