<p>The only star subtending an angle of 32 arcminutes at the Earth is the Sun!</p>
<p>The angular size combined with the orbital separation of the Earth from the Sun gives its radius. The peak wavelength gives <em>an estimate</em> of the effective temperature based on <a href="https://en.wikipedia.org/wiki/Wien%27s_displacement_law" rel="noreferrer">Wien's law</a>. Application of the <a href="https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law" rel="noreferrer">Stefan-Boltzmann law</a> then gives the luminosity.</p>
<p>The only way to get the mass would be to use a calibrated mass-luminosity relationship assuming that the &quot;star&quot; is on the main-sequence. Given that these are usually scaled from the solar luminosity, this is a bit nonsensical - the Sun is a star of one solar mass. You can of course use the period of the Earth's orbit and the size of that orbit in <a href="https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law" rel="noreferrer">Kepler's Third Law</a> to estimate what that solar mass is.</p>

CC BY-SA 4.0
2022-08-18T13:00:02.347Z
2022-08-18T13:00:02.347Z
ProfRob
<p>For example if a certain star subtends an angle of 32 arcminutes at the Earth’s orbit and it's light has a peak wavelength of 500 nm, how can I find the luminosity and mass of that star?</p>

CC BY-SA 4.0
2022-08-18T12:53:51.820Z
You are talking about the Sun right?
ProfRob
CC BY-SA 4.0
2022-08-18T13:20:39.603Z
Yeah, this kind of has the feel of an astronomy quiz "extra credit" question.
notovny
<orbit><orbital-mechanics><spectroscopy><luminosity>
How can I calculate the luminosity and mass of a star only knowing it's peak wavelength and it's subtended angle?
R-802
# How can I calculate the luminosity and mass of a star only knowing it's peak wavelength and it's subtended angle?

(Asked by: username_0 on 2022-08-18)

For example if a certain star subtends an angle of 32 arcminutes at the Earth’s orbit and it's light has a peak wavelength of 500 nm, how can I find the luminosity and mass of that star?

**Tags:** orbit, orbital-mechanics, spectroscopy, luminosity

> **Comments:**
> **username_1**: You are talking about the Sun right?  
> **username_2**: Yeah, this kind of has the feel of an astronomy quiz "extra credit" question.  

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## 1 answers

### Answer by username_1 on 2022-08-18. Score: 8 | Accepted answer

The only star subtending an angle of 32 arcminutes at the Earth is the Sun!

The angular size combined with the orbital separation of the Earth from the Sun gives its radius. The peak wavelength gives *an estimate* of the effective temperature based on [Wien's law](https://en.wikipedia.org/wiki/Wien%27s_displacement_law). Application of the [Stefan-Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law) then gives the luminosity.

The only way to get the mass would be to use a calibrated mass-luminosity relationship assuming that the "star" is on the main-sequence. Given that these are usually scaled from the solar luminosity, this is a bit nonsensical - the Sun is a star of one solar mass. You can of course use the period of the Earth's orbit and the size of that orbit in [Kepler's Third Law](https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law) to estimate what that solar mass is.


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