# Shift in wavelength of photons from the Sun using energy argument

• etotheipi
In summary, the conversation discusses the method for calculating the change in wavelength of a photon between being emitted from the sun and arriving at Earth. This involves calculating the GPE of the photon at the start and end points, and equating the change in GPE to the change in energy of the photon, resulting in an approximate expression for the change in wavelength. The concept of energy conservation is also mentioned. However, for a more rigorous argument, General Relativity should be used.
etotheipi
I came across a question recently which involved calculating the change in wavelength of a photon between being emitted from the surface of the sun and arriving at the Earth.

The method that was implied involved calculating the GPE's of the photon (assuming the photon to have a mass h/[c lambda]) at the start and end points in order to calculate the overall decrease in its GPE, with Mph, Me and Ms being the photon, Earth and Sun masses respectively and rs, re and rse being the Sun's radius, Earth's radius and Earth-Sun distance respectively. This turns out to be: $$\Delta U = GM_{ph}[-\frac{M_{e}}{r_{e}}-\frac{M_{s}}{r_{se}}+\frac{M_{s}}{r_{s}}+\frac{M_{e}}{r_{se}}]$$ Since the term Ms/Rs is substantially larger than the others, we omit all of the other terms and find the following approximate expression for change in GPE: $$\Delta U = GM_{ph}\frac{M_{s}}{r_{s}}$$The last step is to equate this change in GPE to the change in energy of the photon from which we can approximate the change in wavelength of that photon:$$\Delta E_{ph} \approx hc \frac{\Delta \lambda}{\lambda^{2}} = \frac{GM_{s}}{r_{s}}\frac{h}{\lambda c}$$ This yields the result $$\frac{\Delta \lambda}{\lambda} = 2.1\cdot10^{-6}$$Whilst I can understand the mathematical steps, I have trouble understanding the intuition for this last part. Why can we equate the increase in the photon's GPE to the decrease in the energy associated with its wavelength? Thanks a bunch.

Energy is conserved. So if the photon gains GPE as it climbs out of the sun's gravitational well, it must lose energy from somewhere. Since the photon's energy is hc/λ, and h and c are constants, λ must increase.

etotheipi
phyzguy said:
Energy is conserved. So if the photon gains GPE as it climbs out of the sun's gravitational well, it must lose energy from somewhere. Since the photon's energy is hc/λ, and h and c are constants, λ must increase.

Thanks for the really quick reply! That makes sense. I was also wondering how rigorous is this argument considering that the photon only really has an effective GPE?

I think what you have outlined is a heuristic argument which is not completely rigorous. To do it properly, you need to use General Relativity. This Wikipedia article has a description of how you do that, as well as experimental tests. I find the Pound-Rebka experiment really fascinating. They were able to measure the increase in wavelength of light propagating from the basement of their lab up to the roof, as it climbed out of the Earth's gravitational field.

etotheipi

## 1. What causes the shift in wavelength of photons from the Sun?

The shift in wavelength of photons from the Sun is caused by the Doppler effect, which is the change in frequency or wavelength of a wave due to the relative motion between the source and the observer. In this case, the shift is due to the relative motion between the Sun and the Earth.

## 2. How does the energy argument explain the shift in wavelength of photons from the Sun?

The energy argument states that as the source of a wave moves towards the observer, the energy of the wave increases and the wavelength decreases. Conversely, as the source moves away from the observer, the energy decreases and the wavelength increases. This explains the shift in wavelength of photons from the Sun as it moves towards or away from the Earth.

## 3. Is the shift in wavelength of photons from the Sun significant?

Yes, the shift in wavelength of photons from the Sun is significant. The Doppler effect causes the wavelength of light from the Sun to shift by a small amount, but this shift is measurable and has important implications in fields such as astronomy and remote sensing.

## 4. How does the shift in wavelength of photons from the Sun affect our perception of color?

The shift in wavelength of photons from the Sun does not have a noticeable effect on our perception of color. This is because our eyes are able to adjust and perceive the same color despite changes in wavelength. However, specialized instruments and technologies may be able to detect these shifts in wavelength.

## 5. Can the shift in wavelength of photons from the Sun be used to measure the speed of the Sun?

Yes, the shift in wavelength of photons from the Sun can be used to measure the speed of the Sun. By measuring the amount of shift in wavelength, scientists can calculate the speed at which the Sun is moving towards or away from the Earth. This information is useful in understanding the motion and dynamics of celestial bodies.

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