Homework question on Cepheids

[arslan]

Hi, I have done this problem multiple times and always seem to come up with the wrong answer.
Any help is greatly appreciated!
Scientists using the Hubble Space Telescope have observed Cepheids in the galaxy M 100. Here are the actual data for three Cepheids in M 100:
Cepheid 1: luminosity = 3.9 x 10^30 watts, brightness 9.3 x 10^-19 w/m^2
Cepheid 2: luminosity = 1.2 x 10^30 watts, brightness 3.8 x 10^-19 w/m^2
Cepheid 3: luminosity = 2.5 x 10^30 watts, brightness 8.7 x 10^-19 w/m^2

Compute the distance to M 100 with data from each of the three Cepheids in light-years (d1, d2, d3)

[antoniseb]

What radius sphere would you need to make 10^30 Watts into 10^-19 Watts per square meter of the surface?

BTW, can you label your threads better, Just calling them all "Difficult Question on Astrophysics, please help" is unhelpful in terms of keeping track of them all.

[arslan]

What radius sphere would you need to make 10^30 Watts into 10^-19 Watts per square meter of the surface?

I still dont understand, can you explain a little more please, thanks.

[arslan]

Ok, so I did a bit of research on line, and turns out, there's a simple relationship between Luminosity, Brightness and Distance.
b = L/(4pi x dē)

b is the brightness in w/mē
L is the Luminosity in Watts
and
d is the distance in meters.

I solved for d for each of the Cepheids, and than averaged out the 3 values to get a distance of 16.8 mpc.
M100 is 16.8 mpc away, which is exactly what the "book value" is.

[baric]

Ok, so I did a bit of research on line, and turns out, there's a simple relationship between Luminosity, Brightness and Distance.
b = L/(4pi x dē)

Grats! Of course, when you're using equations involving Luminosity, Brightness and Distance then I guess we should not be surprised when the light bulb comes on.

[antoniseb]

... b = L/(4pi x dē) ...

Which you might recognize as the formula for the area of the surface of a sphere.
At any distance, a star has the same number of Watts going through that sphere (why would it change?) collectively those Watts were the total Power output of the star N years ago, when the star was N lightyears away. So look at the power through any one square meter, and if you know how much power the star was emitting in the first place (as we can do with Cepheids), you can find the distance.