Height of the Aurora

It is required with two observations (photos) from two different locations.

Calculation of the height can be done with or without trigonometric relations.
Simple situation: The two observers and the auroras are in the same vertical plane. Calculation is then done by simple geometry:

a) Let 10 km be equal to 1 cm. Use a protractor to draw the angles "alpha" and "beta" on a paper, and simply measure the height "h" using a ruler.

b) Using trigonometric relations leads to the formula shown in the picture above.

More complex situation: The two observers and the auroras are not in the same vertical plane. We have the situation:

The height in this case will be: .

These two pictures are photographed in Tromsø (Group: Northern Lights II, Franck Pettersen) and at Olsborg (Group: 3FY at Bardufoss videregående skole, Jan Hamre). The distance between the two locations are 57.4 km. The direction from Tromsø to Olsborg is 15.3 degrees west of south. Click on the pictures to get a bigger picture.

Picture 1, Tromsø, Norway

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Picture 2, Olsborg, Norway

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To find the height of the aurora shown on these pictures, just follow this procedure, using the information given in the text and in the pictures:

1. Measure the height above the horizon of one spesific point in the northern lights on the two pictures. We have suggested the point in the middle of the circles.

2. Star A and star B are marked with arrows. Star A is alpha Aquila (Altair), star B is zeta Aquila. The angular distance between them are 12.1 degrees. Calculate the scale of the pictures on your screen in degrees/cm, and find the height of the aurora in degrees.

3. Use the general directions given below each picture and find the angles "alpha" and "beta" from the figure on this page.

4. The northern lights are usually between 85 and 110 km above ground level. We have not taken into account the curvature of the earth in this geometry. Discuss your results.
Franck Pettersen
Last update: Nov 15, 1996