Question

Do the algebraic solution first before plugging in the values.

5. It has been found that galaxies are moving away from the Milky Way (i.e., the Earth) at a speed that is proportional to their distance from the earth. This discovery is known as Hubble's law. The speed of a galaxy a distance r away is given by: V = Hr, where H is Hubble's constant, which is about
2.33 X 10 -18 s^-1. What is the speed of a galaxy 5 X 10²² m from the Milky Way and 2 X 10²⁵ m from the Milky Way?
THE REAL QUESTION IS THIS: If each of these galaxies has traveled with constant speed, how long ago were they both located at the same place as the Milky Way?

Answer 1

The speed of a galaxy at distance 'r' away which is given by -

v = H r

where, H = Hubble's constant = 2.33 x 10^-18 s^-1

At r = 5 x 10²² m, then we get

v₁ = [(2.33 x 10^-18 s^-1) (5 x 10²² m)]

v₁ = 1.165 x 10⁵ m/s

At r = 2 x 10²⁵ m, then we get

v₂ = [(2.33 x 10^-18 s^-1) (2 x 10²⁵ m)]

v₂ = 4.66 x 10⁷ m/s

If each of these galaxies has traveled with a constant speed, how long ago were they both located at the same place as the Milky Way?

t_total = t₁ + t₂

t_total = [(5 x 10²² m) / (1.165 x 10⁵ m/s)] + [(2 x 10²⁵ m) / (4.66 x 10⁷ m/s)]

t_total = [(4.291 x 10¹⁷ s) + (4.291 x 10¹⁷ s)]

t_total = 8.58 x 10¹⁷ s