Solving Brightness Equation with Procyon: 7L☉ and 11.41 light years

[vbillej]

In a question is says that Brightness = Luminosity/4πr₂ (for a star).

Procyon = 7L☉ and 11.41 light years as distance.

the equation in B= 7L☉/ 4π(11.41)₂

the answer turned out to be 0.004 L☉ watts per square light year (its a textbook question). What i don't understand is what is 7L☉, what's its value. I read that L☉ is approx the suns luminosity so i did 7(3.839 × 10^26). but still getting the wrong answer.

Thanks

vbillej

 

[Sorry!]

In a question is says that Brightness = Luminosity/4πr₂ (for a star).

Procyon = 7L☉ and 11.41 light years as distance.

the equation in B= 7L☉/ 4π(11.41)₂

the answer turned out to be 0.004 L☉ watts per square light year (its a textbook question). What i don't understand is what is 7L☉, what's its value. I read that L☉ is approx the suns luminosity so i did 7(3.839 × 10^26). but still getting the wrong answer.

Thanks

vbillej

I don't exactly understand what the problem is.

 

[vbillej]

I just don't get what 7L☉ is, i looked up L☉ but i still don't really understand how the answer was 0.004 L☉.

Like how would i put 7L☉ into a calculator.

 

[Nabeshin]

L☉ is just a unit, specifically, the unit solar luminosity. Its value is defined to be the luminosity of the sun. You don't put 7L☉ into a calculator any more than you put 7 meters or 7 seconds into a calculator, you only calculate the numbers, the units are your responsibility.
The equation you mentioned has units of L☉/ly^2, which is exactly what you wanted, is it not?

 

[Sorry!]

I just don't get what 7L☉ is, i looked up L☉ but i still don't really understand how the answer was 0.004 L☉.

Like how would i put 7L☉ into a calculator.

Read the answer carefully.
7 is the AMOUNT L_☉ is the UNITS. This means how luminous the object is compared to the currently accepted luminosity of our Sun. You are correct in your conversion from solar luminosity to just get the luminosity for the star but you don't need to do that.

The stars brightness or its flux is given by the equation:

$$f=\frac{L}{4\pi d^2}$$

So you are given the stars luminosity and its distance plug that into the equation and you get appox. 0.00428092 (using google to calculate). Your units would be L_☉ Watts per squared light year... which is what is in the back of the textbook.

and I've noticed that while I was fixing some problems with my latexing Nabeshin had already answered you :P

 

[vbillej]

Thanks guys, i found out that i put 7L☉/ 4π(11.41)₂ as a fraction in the calculator... -_- haha


thank your very much for your help

vbillej