Angular Measure and Range


Q1: Examine the above picture. Identify the objects in the picture. What unusual phenomena do you see in this picture? Describe them.

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.

Q2: 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?

The sun is 33 minutes in diameter, or 33 / 60 * 2p / 360 = 9.6 x 10-3 radians of arc. On my printout of this image, the aircraft measures to be 3.0 cm long and the sun measures 17.5 cm across, so the aircraft subtends an angle of 3 / 17* 9.6 x 10-3 rad = 1.7 x 10-3 rad. Assuming a projected aircraft 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 aircraft is 35 km away from the observer.

Q3: 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 6,400 km).

The solar prominence measures 0.4 cm high on my printout of the picture, so it subtends 0.4 / 15 * 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.

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