Understanding Rigel's Velocity Relative to Us

How can you solve Rigel's velocity relative to us?

The observed frequency in Rigel's spectrum is shifted downward by 4.26 * 10¹⁰ Hz compared to the stationary frequency. This difference is called the redshift.

The Doppler shift formula relates the observed frequency (f obs), the stationary frequency (f 0), and the velocity (v) of the source:

f_obs = f₀ * (1 - v/c)

where c is the speed of light (approximately 3 * 10⁸ m/s).

We can rearrange the formula to solve for the velocity:

v = c * (1 - f_obs / f₀)

v = 3 * 10⁸ m/s * (1 - (6.17 * 10¹⁴ Hz - 4.26 * 10¹⁰ Hz) / 6.17 * 10¹⁴ Hz)

v = 3 * 10⁸ m/s * (1 - 5.744 * 10¹⁰ Hz / 6.17 * 10¹⁴ Hz)

Answer:

Rigel's velocity relative to us is approximately -20713.13 m/s. The negative sign indicates that Rigel is moving away from us.

The give values are:

Observed frequency, F = 4.26 * 10¹⁰ Hz

Original frequency, F₀ = 6.17 * 10¹⁴ Hz

Let the velocity of Rigel be = V m/s

As we know,

F₀ = F * √((C + V)/(C - V))

On putting the values, we get:

((6.17 * 10¹⁴) / (4.26 * 10¹⁰)) = √((C + V)/(C - V))

((C + V)/(C - V)) = (14483.56808)²

((C + V)/(C - V)) = 209773744.2

C + V = 209773744.2 * C - 209773744.2 * V

V = (209773743.2 / 209773745.2) * C

V = 0.99C

So, Rigel's velocity will be "0.99C".

Calculating further,

V = 0.99 * 3 * 10⁸ = 2.97 * 10⁸ m/s