Calculating Luminosity of a Star at Different Stages

In summary: Remember, the apparent magnitude is how bright the star appears to us on Earth, while the absolute magnitude is how bright it would appear at a standard distance of 10 pc. So if we know the ratio of the luminosity, we can use that to find the ratio of the apparent magnitude. And then we can use that to find the ratio of the distance. Does that make sense?In summary, the conversation discusses the changes in a main sequence star as it ascends the red giant branch. The star's surface temperature decreases by a factor of 3 and its radius increases by a factor of 50. Using the formulas L~R^2*T^4 and apparent magnitude - absolute magnitude = 5 log(base 10) (
  • #1
kelseymclean
6
0
The question is A main sequence star is barely visible at a distance of 20 pc with a certain telescope. The star subsequently
ascends the red giant branch, during which time its surface temperature drops by a factor of 3 and its radius increases by a factor of 50.
a) Determine the how luminous the star is now compared to its original luminosity, that is, determine
LRED GIANT/LORIGINAL
b) Determine how far away this star could be seen now by the same telescope.

So far, I have, L=R^2 * T^4. and that Radius is proportional to [tex]\sqrt{luminosity}[/tex]/temperature.
and Apparent magnitude - absolute magnitude = 5 log(base 10) (Distance/ 10 pc).
I am stuck at determining the radius and luminosity of the star before it ascends.
Any hints/ help would be greatly appreciated.
 
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  • #2
You don't need to know the radius and luminosity before it goes red giant. You are only asked to determine the ratio of the luminosity after it expands to the luminosity before it expands. The formulas you wrote have everything you need. If the radius increases by 50 and the temperature decreases by 3 and L~R^2*T^4, what happens to the luminosity?
 
  • #3
The luminosity increases by 50^2/(3^4) Because temperature drops by a factor of 3?
 
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  • #4
Sounds good to me!
 
  • #5
So this value, 30.86 is LRedGiant/ L original? how do i go about finding out how far it can be seen from?
 
  • #6
Do you know how to relate luminosity, distance, and magnitude?
 

What is luminosity and why is it important in studying stars?

Luminosity is the total amount of energy that a star emits per unit time. It is an important factor in studying stars because it gives us information about a star's size, temperature, and age. Luminosity also affects a star's evolution and can indicate the presence of planets or other objects orbiting the star.

How do scientists calculate the luminosity of a star?

Scientists calculate the luminosity of a star by using the star's brightness, distance from Earth, and temperature. They use a formula called the inverse-square law, which states that the luminosity of a star is inversely proportional to the square of its distance from Earth. They also take into account the star's apparent magnitude, or brightness as seen from Earth, and its absolute magnitude, or brightness at a standard distance.

Can the luminosity of a star change over time?

Yes, the luminosity of a star can change over time. As a star ages, it goes through different stages of fusion, which can affect its luminosity. Some stars, like the Sun, have a relatively constant luminosity during their main sequence stage, while others, like red giants, can have significant changes in luminosity as they expand and evolve.

How does the luminosity of a star change during its life cycle?

The luminosity of a star changes during different stages of its life cycle. During the main sequence stage, a star's luminosity remains relatively constant as it fuses hydrogen into helium. As a star runs out of hydrogen, its core contracts and heats up, causing it to expand and become a red giant. This leads to an increase in luminosity. Eventually, the star's core will fuse heavier elements, and its luminosity will decrease as it becomes a white dwarf or supernova.

Can the luminosity of a star vary within the same stage of its life cycle?

Yes, the luminosity of a star can vary within the same stage of its life cycle. For example, a star may have periods of increased or decreased luminosity due to changes in its internal processes or interactions with other stars. Additionally, some stars may have pulsations or eruptions that cause temporary increases in luminosity. These variations are important to study in order to better understand the life cycle and behavior of stars.

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