Abell's Exploration of the Universe
7th ed. Answers to questions.

3.5 Did Newton need to know the size of the Earth (in miles) to test his theory of the fall of the apple and the fall of the Moon, ie, gravity?

3.11 Where is the barycenter in a double-star system where M1=3, M2=1 and a=4

(units are solar masses, au, year).

3.12 What is the period of the binary star described above (3.11)?

3.13 What would Earth's orbital period and speed (29.8km/s) be if the sun had eight times its present mass and the Earth were 2au distant?

3.5 No, he just needed to know the Moon's distance in terms of the Earth's radius (about 61 earth radii to the Moon) a quantity well determined by the ancient Greek astronomers.

3.11 Lever law: M1R1=M2R2 so R2/R1=3 and R1+R2=4 so R2=3au and R1=1au.

3.12 (3+1)P^2=4^3, P=sqrt(64/4)=4 years.

3.13 First the period. 8P^2=2^3 so P=sqrt(1)=1 year. Boo!

Speed? Twice as fast since we have twice as far to go.