Frequencies of Spectral Lines

When studying light from distant galaxies, astronomers often observe a phenomenon known as redshift. This occurs because the source of the light is moving away from us, causing the wavelengths to stretch out and the frequencies to decrease. The amount of redshift can provide valuable information about the speed and distance of the source.

Given Information

In this case, the problem states that the frequencies of spectral lines in light from a distant galaxy are two-thirds as great as those of the same lines in light from nearby stars. This means that the light from the distant galaxy has been redshifted by a factor of 2/3.

Calculating the Recession Speed

To find the recession speed of the distant galaxy, we can use Hubble's law, which relates the redshift of an object to its recession velocity. According to Hubble's law, the recession velocity (v) is given by the equation:

v = H0 * d,

where H0 is the Hubble constant and d is the distance to the object.

Using Hubble's Law

In this case, we are given the redshift factor, which is the ratio of the observed frequency to the original frequency:

z = observed frequency / original frequency.

Since the observed frequency is 2/3 of the original frequency, the redshift factor can be written as:

z = 2/3.

We can now rewrite Hubble's law in terms of the redshift factor:

z = H0 * d / c,

where c is the speed of light.

Calculating the Recession Speed (continued)

Now, we can rearrange the equation to solve for the recession speed:

v = z * c / H0.

Plugging in the given redshift factor (z = 2/3), we get:

v = (2/3) * c / H0.

Conclusion

In conclusion, to calculate the recession speed of the distant galaxy, we can use Hubble's law and the given redshift factor. The recession speed is given by the equation v = (2/3) * c / H0, where c is the speed of light and H0 is the Hubble constant.