How fast must we be approaching a distant galaxy emitting yellow light (590nm) for it to appear green (520nm)?

I believe it uses doppler effect, but how?

for non-relativistic speeds, we can use the approximation.

c/520 = (1+v/c) * c/590
520(1+v/c) = 590
1+v/c = 59/52
v/c = 7/52
v = 7/52 c

Is that relativistic? Generally, less than 0.1c is considered non-relativistic, so we may be a bit off, but if that matters, use the exact formula, which you can find with a quick web search.

Not being sure just how the Doppler effect is calculated, I just did some online searches. You could also have done this.

To calculate the change in wavelength due to the Doppler effect, we need to use the formula:

Δλ/λ = v/c

where Δλ is the change in wavelength, λ is the original wavelength, v is the velocity of the source/object relative to the observer, and c is the speed of light (which is approximately 3 x 10^8 m/s).

In this case, we want to find the velocity (v) at which the galaxy must be approaching us for its yellow light (590 nm) to appear green (520 nm).

Let's rearrange the formula to solve for v:

v = (Δλ/λ) * c

Now, let's plug in the values:

Δλ = 520 nm - 590 nm = -70 nm (negative because the light is shifting towards shorter wavelengths, indicating an approaching source)
λ = 590 nm
c = 3 x 10^8 m/s

First, convert the change in wavelength from nanometers (nm) to meters (m):

Δλ = -70 nm = -70 x 10^-9 m

Now we can calculate the velocity:

v = ((-70 x 10^-9 m) / (590 x 10^-9 m)) * (3 x 10^8 m/s)

Simplifying:

v = -0.1186 * (3 x 10^8 m/s) = -3.558 x 10^7 m/s

Therefore, for the distant galaxy emitting yellow light (590 nm) to appear green (520 nm), it must be approaching us at a velocity of approximately 3.558 x 10^7 m/s.