How can you calculate the power intercepted by a planet from a distant star?

R^2.In summary, the conversation discusses a physics problem involving a star with radius R and surface temperature T, and a planet with radius r at a distance d from the star. The problem involves calculating the ratio between the total power output of the star and the power received by the planet. The solution involves using Stefan's law and considering the power to be isotropic, resulting in a formula that takes into account the distance and radii of the objects. The conversation ends with one person offering a potential solution and asking for confirmation.
  • #1
haki
161
0
Hi,

I found one very interesting physics problem but I have no idea how to solve it.

Lets say we have a star with radius R and the surface temperature T. Now we wish to know, what is the ratio between the total power output of the star and the power that the distant planet receives from that star. The planet has a radius r and the distance between the center of the objects is d. We idealise the problem and say that both object have e=1.

I know that the trick is in the Stefan's law. I can calculate the power output of the star by

P=Stefan's constant*area of a spheare of radius R*temperature of star T on the 4th power,

now the funny thing is how can you calculate how much of that power is intercepted by the planet?

Any help would be apprichiated.
 
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  • #2
Got an idea. Maybe the correct way to go is by saying that the ratio

area of a spheare of radius d(distance from the two object) / half the area of the spheare of radius r(radius of the planet) = total output of the sun / power gotten by the planet?
 
  • #3
Assume the power P of the star is isotropic, i.e. same in all directions.

At the distance R from the star, i.e. the radius of the planet's orbit, the flux, [itex]\Phi[/itex] (power per unit area) = P/(4[itex]\pi[/itex]R2).

If the planet has radius r, then the fraction of power intercepted is simply the product of the power and the ratio of the areas, or the product of the flux and area subtended by the planet, i.e.

[itex]\Phi[/itex] * [itex]\pi\,r^2[/itex]
 

1. What is black body radiation?

Black body radiation is the electromagnetic radiation emitted by a perfect black body, which is an object that absorbs all radiation that falls on it and reflects none. This type of radiation is given off by any object that has a temperature above absolute zero, and its intensity and wavelength distribution depend on the temperature of the object.

2. How does black body radiation relate to temperature?

The intensity and wavelength distribution of black body radiation are directly related to the temperature of the object. As the temperature increases, the peak intensity of the radiation shifts to shorter wavelengths, and the overall intensity of the radiation increases.

3. What is the significance of black body radiation in physics?

Black body radiation is significant in physics because it is used to explain the emission of light from objects at different temperatures, as well as the spectrum of light emitted. It also played a crucial role in developing the theory of quantum mechanics and understanding the behavior of atoms and molecules.

4. How is black body radiation measured?

Black body radiation can be measured using a spectrometer, which detects the intensity of radiation at different wavelengths. The data collected can then be compared to the theoretical black body radiation curve, known as the Planck curve, to determine the temperature of the object emitting the radiation.

5. What are some practical applications of black body radiation?

Black body radiation has many practical applications, including in thermal imaging cameras, which use the infrared radiation emitted by objects to produce images. It is also used in astronomy to study the temperature and composition of stars and other celestial bodies. Additionally, the concept of black body radiation is essential in the development of technologies such as solar panels and incandescent light bulbs.

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