Chapter 21 Origin of Modern Astronomy
Answer to Review Questions
Hopefully Eratosthenes made his calculations more carefully than did the authors If there are 5,000 stadia between the post at
Alexandria and the Well at Syene, then to calculate the circumference of the Earth you multiply that distance by 360 degrees and divide by the angle he measured which was 7 degrees.
This gives you 257,142 stadia for the circumference, not 250,000 as the authors claim. This makes the estimate for the circumference to be 40,525.71 km rather than the 39,400 km which the authors calculated by truncating down the estimate of the circumference to 250,000 from 257,142. If they wanted to round the value it should have been up not down. So if the angle had been 10 degrees, the estimate for the circumference would have been 180,000 stadia or 28,368 km which is much smaller than the modern estimate.
2. a) 10 years b) 5 A. U. (Astronomical Units) c) It has noting to do with the size of the planet. They would move around the sun at the same speed.
3. a) You only see slivers (crescent phase) of the planet Venus illuminated. You never see a full illumination (similar to seeing a full moon). b) You see the full range of illuminations including a full illumination. (like the phases of the moon) c) When he never saw a full illumination of Venus he correctly assumed that Venus had to revolve around the Sun, not the Earth.
4. Asteroid B will have 4 times less gravitational acceleration by the parent on the left. Asteroid C will have exactly the same as A because it is at the same distance.
5. The asteroid pair A are 3 times closer than the asteroid pair
B. So if the asteroid pair B are 9 times larger they could have the same gravitational force pulling them together.
6. 48 hours.
7. The definition of a solar day is from position A in the sky to the next time the Sun appears at position A in the sky. So if the rotation were reversed the solar day would still be 24 hours.
8. Figure 21.A is on page 623. a) Virgo, b) Aquarius, c) Leo because the Earth would have rotated 180 degrees and you would be looking opposite of location of the Sun.

9. Since the sun appears in that constellation. No you would not be able to see that constellation as the sun would be in the way and would be too bright.
10. a) Waning, b) Before sunrise
11. The Earth will be in the phase "New Earth", that is with no direct illumination from the sun. The Earth would be bathed only by moonlight, no sunlight
12. a) 6 solar eclipses and 6 lunar eclipses (one of each per month). b) the same as a).