January 2011 Mock: Question 18

a) 4.6 days
(x distance from peak to peak)

b) The relationship between a Cepheid variable's period and its luminosity is almost directly proportional. So, if you know the period of a Cepheid variable star, you can work out the luminosity using the period-luminosity law (luminosity is essentially the same as absolute magnitude). Then, using its apparent magnitude, you can use the distance modulus equation, M=m+5 - (5 log d), to calculate the distance to the star in parsecs.

Or: Where I=intensity of light observed from Earth, L = the star's luminosity and D = the distance to the star,
I=L/4piD^2
Rearranging this equation gives us:
D=sqrt(L/4piI)

c) The heliocentric parallax method can be used to determine the distance to a star, if the star in question is relatively nearby. The position of a star against the fixed background stars is noted, then measured again 6 months later, when the earth is on the opposite side of the sun. The star's shift in position is used to calculate the parallax angle, and then trigonometry can be used to calculate the distance to the star.

*Suitable diagram*