Newton’s law of gravitation says that the force, F, between two objects of mass m1 and m2, a distance d apart, is given by F =

Gm1m2 d

2

, where G = 6.674×10−11 N m2

/kg2 is the gravitational constant.

a. Calculate ∂F

∂m1

,

∂F

∂m2 and ∂F

∂d

. Which of these are positive and which are negative? Explain why your answers are scientifically sensible.

b. If F has units of newtons, what are the units of m1, m2 and d?

c. If m1 = m2 = 1000±0.2 g and if d = 2.0±0.01 mm, what is F (in newtons)?

d. What is the relative uncertainty in the value of F

c. Plot some examples of c(x, t) for t = 0.01, t = 0.1, t = 2 and t = 10. What is the solution doing? Can you predict what the solution will do for even larger values of time?