# Using parallax and magnitudes.

• C.E
In summary, the conversation is about a question related to astronomy. The question involves calculating the distance and absolute magnitude of two stars, Rigel and Betelgeuse, using their apparent magnitudes and parallaxes. The question also asks for the determination of the luminosity of Rigel in terms of solar luminosities. The person asking the question is unsure of their answers, as they seem unrealistic. They also mention using a formula involving the Sun's absolute magnitude to calculate the luminosity of Rigel. In response, the other person suggests checking Wikipedia and mentions a special homework section.

#### C.E

Hi, I am quite new to astronomy and was wondering whether I had done the following question correctly (some of my answers seem unrealistic). Plus, how many significant figures should questions like these be answered to?

The star Rigel in the constellation of Orion has an apparent magnitude of 0.1 mag,
its parallax is 4.22 milli-arc seconds (mas). Betelgeuse, also in Orion, has an
apparent magnitude of 0.58 mag and a parallax of 7.63mas.

(i) Compute the distance from Earth to Rigel and Betelgeuse.

my attempt: distance to Rigel= 1/(4.22 x 10^-3) = 237 pc

distance to Betelgeuse = 1/(7.63 x 10^-3) = 131 pc

(ii) Using the above information, compute the absolute magnitude of both stars.
Which star has the higher luminosity?

I used M=m- 5log(d/10)

For Rigel M=0.1-5log(23.7)= -6.77 (this seems too low to me).

For Betelgeuse M=0.58 - 5log(13.1)=-5.0 (again I was not expecting a value this low)

Hence Rigel is brightest.

(iii) The Sun has an absolute magnitude of 4.83 mag. Determine the luminosity of
Rigel in solar luminosities.

L=L(sun)10^(M(sun)-M(R))/2.5 so L= 43700 L(sun) (again this does not seem realistic to me).

Any ideas?

Any ideas?
BTW, there's a special homework section.

## 1. What is parallax and how is it used in astronomy?

Parallax is the apparent change in the position of an object when viewed from different perspectives. In astronomy, parallax is used to determine the distance of a celestial object from Earth. By measuring the angle of the object from two different points on Earth's orbit, astronomers can calculate the object's distance using trigonometry.

## 2. How do astronomers measure parallax?

Astronomers use a technique called triangulation to measure parallax. This involves measuring the angle of an object from two different points on Earth's orbit around the sun. The larger the angle, the closer the object is to Earth.

## 3. What is the significance of parallax in determining the distance of stars?

Parallax is essential in determining the distance of stars because it allows us to measure distances that are too vast to be measured directly. By measuring parallax, we can determine the distances of stars up to a few thousand light-years away.

## 4. How does parallax affect the apparent brightness of a star?

The apparent brightness of a star is affected by its distance and the inverse square law, which states that the intensity of light decreases as the distance from the source increases. This means that a closer star will appear brighter than a more distant star, even if they have the same intrinsic brightness.

## 5. How are magnitudes used in astronomy?

Magnitudes are used to measure the brightness of celestial objects, such as stars and galaxies. The magnitude scale is logarithmic, meaning that a difference of 5 magnitudes represents a difference of 100 times in brightness. Lower magnitudes correspond to brighter objects, with the brightest objects having negative magnitudes.