Our projects for the beginning of summer on 21^st June 2004

Determination of the circumference of the earth according to Eratosthenes

· Measuring at place A

a) Measure at local noon time the length l_A of a vertical pole with height h_A

b) Determine the angle g_A between the sunbeams and the pole

· Measuring at place B

a) Measure at local noon time the length l_B of a vertical pole with height h_B

b) Determine the angle g_B between the sunbeams and the pole

· Calculation of the angle m = g_A - g_B

· Determination of the distance d_AB of A and B with the aid of atlas

· Calculation of the circumference of the earth according to U_Erde = 360°/m * d_AB

· Calculation of the radius of the earth according to r_Erde = U_Erde /(2*p)

Determination of the latitude of the observation place

1. From the measurings of the Eratosthenes project

· Determination of the angle g

· Calculation of the latitude j of the observation place according to

j = 23,5° + g or j = 23,5° - g or j = g - 23,5° (depending on the position of

the observers location)

2. From the high of culmination a of the sun

· Determination of the high of culmination a of the sun (shadow measurement or with sextant)

· Calculation of the latitude j of the observation place according to

j = 23,5° + (90° - a) or j = 23,5° - (90° - a)

3. From shadow measurement and the angle of the ecliptic e

· Determination of the angle g

· Calculation of the latitude j of the observation place according to

j = g_21.06. + e = g_21.06. + 23,5°

4. From the length of the day or half of day's length t

· Determination of local noon time

· Determination of local time of sunset

· Calculation of half of the length of a day t (as angle)

· Calculation of the latitude j of the observation place according to

j = arctan(cos t /(-tan 23,5°))

5. From the distance between the west-point and point of sunset

· Determination of the distance between west-point and point of sunset w

· Determination of azimuth a

· Calculation of the latitude j of the observation place according to

j = arccos(- sin 23,5°/cos a) with a = 90° + w

Determination of the angle of ecliptic

· Determination of the angle g_S between the sunrays and the pole on 21^st June 2004 (beginning of summer), g_A on 22^nd September 2004 (beginning of autumn), g_W on 21^st December 2004 (beginning of winter)

· Determination of the angle of ecliptic e

by drawing and measuring of the angle e

or calculating according to

e = g_A - g_S and e = g_W - g_A with g_S = arctan l_S/h, g_A = = arctan l_A/h, g_W = arctan l_W/h