CAIE Physics (9702)

The brightness of some stars varies regularly. These stars are called variable stars. Fig. 2.1 shows the variation of luminosity with time for a variable star. luminosity period time A student determines the period T and mean luminosity L of the star. The student repeats the process for different variable stars. It is suggested that L and T are related by the equation L = SKT where S is the luminosity of the Sun, and a and K are constants. gradient =

Values of T and L are given in Table 2.1. Table 2.1 T / days L / 10 W lg (T / days) lg (L / 10 22 2.9 ± 0.2 32 4.9 ± 0.2 42 6.9 ± 0.2 54 9.8 ± 0.2 78 16 ± 2 97 21 ± 2 Calculate and record values of lg (T / days) and lg (L / 10 W) in Table 2.1. Include the absolute uncertainties in lg (L / 10 W).

(i) Plot a graph of lg (L / 10 W) against lg (T / days). Include error bars for lg (L / 10 W).

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = [2] 0.4 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 lg (L / 10 lg (T / days) answer.

Using your answers to

, determine the values of a and K. Include the absolute uncertainties in your values. You need not be concerned with units. Data: S = 3.85 × 10 a = K =

A variable star has a period of 5.0 days. Determine the luminosity L of this star. L = W [1] [Total: 15] Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.