Let us use all the information accumulated to calculate the physical properties of Denebola (beta Leo). Its

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Let us use all the information accumulated to calculate the physical properties of Denebola (beta Leo). Its spectral classification is A3.

IMPORTANT! The steps (i) - (vii) below show you how the stellar properties will be determined. All the calculations for Denebola are shown. Please work your way through this example. It will be worth the effort! The calculations are summarized in the second column of the table.

i. Denebola is A3 and from the H-R diagram x-axis, you can estimate that Denebola's temperature is between 9,000 and 10,000 K. Let's choose it to be 9,400 K.

Temperature (T₁in Kelvin) = 9,400 K

ii. Temperature as compared to the Sun = T₁/ 5800 = 9,400 /5800 = 1.6

T = 1.6 (this value will be used in step vi)

iii. Let's check luminosity of Denebola from H-R graph. If you draw a line from A3 up to the main sequence line you plotted, and then read the corresponding luminosity, it turns out to be about 20 times that of the Sun. Therefore, L = 20

(Note this value may be different since it depends on where you drew your H-R line. Since we are doing approximate calculations, it is more important for you to understand the process than get the exact answer).

iv. From the mass-luminosity graph on page 4, a luminosity of 20 corresponds to 2 solar masses. M = 2 (solar mass)

M = 2(2 x 10³⁰kg) = 4 x 10³⁰kg

v. Radius R

Radius = 1.75 (7 x 10⁸m) = 1.23 x 10⁹m

vi. Lifetime t = Mass/Luminosity = 2/20 = 0.1 solar lifetime

Lifetime = 0.1 (10 billion years) = 1 billion years.

D. You will be doing calculations for two stars, 61-Cygnus and 78-Ursa Major. The table on the next page shows all the calculations for Denebola and the equations used. Follow the example carefully.

The table below shows all the calculations for Denebola and the equations used. Follow the example carefully.

E. Estimate the temperature of each star using its given spectral type and the table on page 1. Also calculate the temperature as compared to the Sun.

F. Use your HR graph and on it draw a vertical line from the spectral type to the line you have drawn, and then a horizontal line to read the luminosity of these stars. Pleasedrawthese lines! Record the luminosity value in the table.

G. Next use the mass-luminosity graph to read the mass using the luminosity value you have determined in the step above. Do the calculations