Question

you find that a distant galaxy is moving away from us a 407 km/s. what is the distance to the galaxy (in mpc)?

Answer 1

Approximately
`6\; {\rm Mpc}` (assuming that
`H_(0) \approx 70\; {\rm km \cdot s^(-1) \cdot Mpc^(-1)}`.)

Step-by-step explanation:

The speed at which a distant object moves away from the observer is known as recessional velocity.

By Hubble's law, the recessional velocity
`v` of a distant galaxy would be proportional to the distance
`D` from the observer:

`v = H_(0)\, D`,

Where
`H_(0)` is Hubble's Constant.

The value of Hubble's Constant varies over time. Assuming that
`H_(0) \approx 70\; {\rm km \cdot s^(-1) \cdot Mpc^(-1)}`. Rearrange Hubble's Law to find distance
`D`:

`\begin{aligned}D &= (v)/(H_(0)) \\ &\approx \frac{407\; {\rm km\cdot s^(-1)}}{70\; {\rm km\cdot s^(-1) \cdot Mpc^(-1)}} \\ &\approx 6\; {\rm Mpc}\end{aligned}`.