Rowan introduction to astronomy activity #3: eratosthenes, mercury, kepler name: seore . in 240 bc. eratosthenes (c. 276 bc-c. 194 bc) measured the earth's circumference and came within 95% of the modern alue. using the diagram, calculate the cireumference of the 1. earth in stadia. then, convert stadia to kilometers. show your work in the box. measurements (known values): syene to alexandria is a distance 5,000 stadia. the angle 7 also, agreek stadium is 1/6 km. [hint convert lo* krn to a decima. round this yalue to 4 decimals.] the moderm value of earth's eircumference is 40,100 km. compare your (eratosthenes? answer to this. note this proportion: 360 5000 stadia/circumference of earth in stadia cicumerence of the earth ancilent stadium could vary from 157 m (515 t) to 209 m (686 ft). circumference in stadia: round to a whole mumber. t0 p circumference in kilometers: round to a whole number. 0pts 2. with only naked eye observation and a simple measuring instrument, you can determine the relative distance of the inner planets to the sun (in terms of astronomical units, au) a measurement of the greatest eastern elongation of mercury (the maximum angle in degrees between the earth-sun line and the earth- planet line) shows it to be 22.8. calculate mercury's distance from the sun. from geometry, we know that sp rand se-. (by definition, the distance se from earth to sun is 1 au-1.496 × 10s kn.) the angle c-22.8". one of the properties of a right triangle is r sin (e) in au. (you need your scientific calculator to determine sin e.) also, convert mercury's distance in au to kilometers. right briangle 1 au e earh s sun caution! make sure that your scientific calculator's mode is set for sci (not eng). you want degrees (deg), not radians (rad). show your work in the box. mercury's distance: au mercury's distance: km (use scientific notation) round to 2 decimails [i0pts (round to 1 decimal.)