3.5  In 1920, a NYT editor would not publish an article based on rocket pioneer R. Goddard's paper that predicted space flight, saying that "rockets could not work in outer space because they have nothing put push against" (a statement the Times did not retract until July 20, 1969).  You, of course, know better.  What was wrong with the editor's logic?

The rocket exhaust pushes against the rocket, propelling it forward while the exhaust goes backward.

3.7   Imagine a planet moving in a perfectly circular orbit around the Sun and, because the orbit is circular, the planet is moving at a constant speed.  Is this planet experiencing acceleration?  Explain.

Yes, change in direction is acceleration.

3.13   During the latter half of the 19th centruy, a few astronomers thought there might be a planet circuling the Sun inside Mercury's orbit.  They even gave it a name, Vulcan.  We now know that Vulcan does not exist.  If there were such a planet with an orbit 1/4 the size of Mercury's, what would be its orbital period relative to that of Mercury?

P² = A³, compare the orbits of Vulcan and Mercury

P_Mercury ²            A^{_Mercury 3}                 1 ³  
------   =   ----------  = ---------   = 64,    so the orbital period of Mercury is 8 (the square root of 64) times
P_Vulcan ²             A_Vulcan ³                (1/4) ³                 longer than the orbital period of Vulcan