# Temperature derived from ratio of blackbody radiation

• xSilja
In summary, the ratio of the blackbody fluxes from a star at two different frequencies can be used to determine the surface temperature of the star, even if the star's solid angle on the sky is unknown. This is possible by considering the flux measured on Earth and taking into account the distance of the star and the Stefan-Boltzmann's law.
xSilja

## Homework Statement

Show that the ratio of the blackbody fluxes from a star at two different frequencies (i.e., a color) is measured, then, in principle, the surface temperature of the star can be derived, even if the star's solid angle on the sky is unknown (e.g., if it is too distant to be spatially resolved, and its distance and surface area are both unknown).

Hint:
Remember that the quantity we measure is a flux on the surface of Earth. This will depend on (omega) and distance of a star. Flux in the formula for Stefan-Boltzmann's law is the flux on the surface of a star.

This problem is from Astrophysics In A Nutshell by Dan Maoz.

## Homework Equations

$F=σT^4$

## The Attempt at a Solution

No clue. It seems like no matter how I do ratios the temperature cancels out.

Last edited by a moderator:
You only have Stephan-Boltzman's law there - you also need to factor in the distance to the star (see "hint") and the formula for blackbody radiation (from main question).

## 1. What is blackbody radiation?

Blackbody radiation refers to the electromagnetic radiation emitted by an idealized object that absorbs all incident electromagnetic radiation. This means that the object neither reflects nor transmits any radiation, and therefore appears completely black.

## 2. How is temperature derived from the ratio of blackbody radiation?

The ratio of blackbody radiation, also known as the Planck function, is dependent on temperature. By measuring the intensity of the radiation at different wavelengths and comparing it to the Planck function, we can determine the temperature of the object emitting the radiation.

## 3. What is the relationship between temperature and blackbody radiation?

The relationship between temperature and blackbody radiation is described by the Planck's law, which states that the intensity of radiation emitted by a blackbody is proportional to the temperature of the object raised to the fourth power.

## 4. How is the ratio of blackbody radiation used in scientific research?

The ratio of blackbody radiation is used in various fields of scientific research, such as astrophysics, cosmology, and materials science. It allows scientists to accurately measure the temperature of objects in space, study the early stages of the universe, and characterize the properties of materials.

## 5. What are the limitations of using blackbody radiation to measure temperature?

One limitation of using blackbody radiation to measure temperature is that it assumes the object is an ideal blackbody, which is not always the case. Additionally, factors such as absorption, scattering, and emission of radiation can affect the accuracy of the measurement. Other methods, such as thermometers, may be more suitable for measuring temperature in certain situations.

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