Kepler's third law relates the period of a planet
to its orbital radius r, the constant g in newton's law of gravi-
tation (f = gm1m2/r^2), and the mass of the sun m.. what com-
bination of these factors gives the correct dimensions for the
period of a planet?

√(r³ / (MG))

Explanation:

The dimensions of each variable are:

r = [m]

G = [m³/kg/s²]

M = [kg]

Multiplying M and G eliminates kilograms:

MG = [m³/s²]

The radius cubed divided by MG eliminates meters:

r³ / (MG) = [s²]

The square root gives us seconds:

√(r³ / (MG)) = [s]

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day