How does the radius of a star affect the temperature of a planet orbiting it?

  • Thread starter FunkyDwarf
  • Start date
  • Tags
    Temperature
In summary, the conversation discusses deriving an expression for the temperature of a planet orbiting a neutron star, assuming the planet is a perfect black body and the only source of energy is the star. The conversation mentions using the inverse square law and the Stefan-Boltzmann law to calculate the intensity and temperature at the planet's orbit distance. The question of whether the star's radius affects the planet's temperature is also raised, with the conclusion being that it may have a small impact but is generally insignificant.
  • #1
FunkyDwarf
489
0
Hey guys,

Quick question:

Homework Statement


Assume the planet (from a previous question) is a perfect black body and that the only source of energy is the [neutron] star. Derive an expression for the temperature of the planet as a function of the orbit distance, star temperature and star radius.


Homework Equations


Inverse square law (I1/I2)=(d2/d1)^2
I = sT^4 (s = stefan boltzman)


The Attempt at a Solution


Ok now i know how to work out watts per m^2 at a distance, that's cool, but in terms of temperature do we really need the star radius? I did the following. I worked out the intensity at the planet distance and converted that to a temperature, but that only depended on the intial distance and the orbit distance, not star radius, unless they suppose that the former is the star radius which doesn't make sense unless we treat the source of energy as the centre of the star.

Any thoughts?

Cheers
-G
 
Physics news on Phys.org
  • #2
A constant surface temperature would give a constant Intensity of emission at the surface, regardless of the radius of the star. The difference is that the intensity diminishes from this initial intensity as the radius goes from the radius of the star to the radius of orbit of the planet. If the orbital radius is much much bigger than the radius of the star, this becomes an insignificant difference, but it still can put into the formula.
 
  • #3
Sorry I am not sure i understand how the radius of the star comes into it. the only thing is intuitively if you have a larger star, at the same distance, with the same temp you're outputting more power so you'd think the planet would be hotter
 

1. What is temperature at a distance?

Temperature at a distance refers to the measurement of temperature at a specific distance away from an object or heat source. It is affected by factors such as heat transfer and atmospheric conditions.

2. How does temperature change with distance?

The temperature at a distance decreases as the distance from the heat source increases. This is due to the phenomenon of heat transfer, where heat energy is transferred from the source to the surrounding environment.

3. What are some factors that affect temperature at a distance?

Some factors that can affect temperature at a distance include the type and intensity of the heat source, the material properties of the object, and atmospheric conditions such as wind and humidity.

4. Can temperature at a distance be accurately measured?

Yes, temperature can be accurately measured at a distance using instruments such as infrared thermometers or thermal cameras. These devices can measure the infrared radiation emitted by an object or surface and calculate the corresponding temperature.

5. Why is understanding temperature at a distance important?

Understanding temperature at a distance is important in various fields such as meteorology, engineering, and environmental science. It can help predict weather patterns, design efficient heating and cooling systems, and assess the impact of heat sources on the surrounding environment.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Astronomy and Astrophysics
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
7K
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Sci-Fi Writing and World Building
Replies
21
Views
853
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top