A line in star's spectrum lies at 400.0 nanometers. In the laboratory, that same line lies at 400.2 nanometers. How fast is the star moving along the line of sight; that is, what is its radial velocity? Is it moving toward or away from us?

Since the wavelength shift is to shorter wavelengths (from 400.2 in the lab to 400.0, the star is moving toward observer (Earth).

The speed of approach along the line of sight, V, is given by
(400.2 - 400.0)/400.0 = 0.2/400 = V/c
Solve for V.

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400.2+400.0=800.2

To solve for V (the speed of approach along the line of sight), we need to rearrange the equation:

V/c = (400.2 - 400.0)/400.0

Let's simplify the equation step by step:

1. Subtract 400.0 from 400.2:

0.2/400.0 = V/c

2. Divide both sides by 400.0:

0.2/400.0 = V/c

3. Simplify the division:

0.0005 = V/c

4. Multiply both sides by the speed of light (c):

V = 0.0005 * c

Now, to find the value of V, we need to know the speed of light. The speed of light is approximately 299,792,458 meters per second. Therefore:

V = 0.0005 * 299,792,458

Calculating the value:

V ≈ 149,896.229 m/s

So, the star is moving toward the observer (Earth) with a speed of approximately 149,896.229 meters per second along the line of sight.