# Calculating the distance to a star

In summary, the question asks for the distance to star 2 given that star 1 has a surface gravity 10 times higher and is 1pc away. Using equations, it is determined that the ratio of radii is 10^-1, the ratio of fluxes is d*22(R*12/R*22), and the ratio of apparent magnitudes is 0. Therefore, the distance to star 2 is calculated to be 3.16pc, which is feasible considering star 2 has a radius 10 times bigger than star 1.
I have made an effort to answer this question, and would like to know if my thinking is correct. I would appreciate any feedback.

Thank you!

## Homework Statement

Two stars in the sky have similar effective temperatures, masses and apparent brightness. However, star 1 has a surface gravity which is 10 times higher than star 2. If star 1 is 1pc away, what is the distance to star 2?

## Homework Equations

i) g*=GM*/R*2
ii) f*=L*/4πd*2
iii) L*=4πR*2σT*eff4
iv) m*1-m*2=-2.5log(f*1/f*2)

## The Attempt at a Solution

Based upon the question, I can assume that the mass (M*), the effective temperature (T*eff) and the apparent magnitude (m*) of both stars is the same.

First of all, I will start with the gravity which tells me that:

g*1=10g*2

so using equation i) I can say that:

GM/R*12=10GM/R*22

I can then rearrange to get a ratio of radii which will tell me that...

R*12/R*22=10-1

I can then calculate the ratio of fluxes by substituting equation iii) into equation ii),= and doing some cancelling to find that...

f*1/f*2=d*22(R*12/R*22)

I know that the value of R*12/R*22=10-1 so I can sub this value in

as I know that both apparent magnitudes are the same, I can say that m*1-m*2=0 and then sub in my ratio of fluxes to equation 4 to get...

0=-2.5log(d*22/10)

I can then solve this equation for d*2 and I get...

d*2=3.16pc

This seems feasible given that star two would have a radius 10 times bigger than star 1, but I would appreciate any help or advice anyone can offer.

Thank you!

d*2=3.16pc

This seems feasible given that star two would have a radius 10 times bigger than star 1, but I would appreciate any help or advice anyone can offer.

Thank you!
Answer is correct, but it imply radius ratio of 3.16, not 10. 10 is the surface areas ratio.

## 1. How do scientists calculate the distance to a star?

Scientists use a method called parallax to calculate the distance to a star. This involves measuring the change in the position of the star relative to background stars as the Earth orbits the Sun. The greater the parallax shift, the closer the star is to Earth.

## 2. What units are used to measure the distance to a star?

The distance to a star is typically measured in light years. A light year is the distance that light travels in one year, which is approximately 9.46 trillion kilometers or 5.88 trillion miles.

## 3. Can the distance to a star be measured accurately?

Yes, with advancements in technology and more precise instruments, scientists are able to measure the distance to a star with increasing accuracy. However, there is still a margin of error in these calculations due to factors such as the brightness of the star and the accuracy of the measuring instruments.

## 4. How far can scientists accurately measure the distance to a star?

Currently, scientists are able to accurately measure the distance to stars within a range of a few thousand light years. Beyond this range, the margin of error becomes too large to accurately determine the distance.

## 5. Why is knowing the distance to a star important?

Knowing the distance to a star is important for understanding the size and scale of the universe, as well as studying the properties and behavior of stars. It also helps in determining the age and evolution of the universe and can aid in the search for habitable planets outside of our solar system.

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