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Grade 12 Science · Earth & Space Science

The sun and stellar evolution: fusion, the H-R diagram, nucleosynthesis and black holes

Use this for “A star is 1.71 times the Sun’s radius at 9,940 K. How many times brighter than the Sun is it?”

Diagram

supergiantsgiantswhite dwarfsmain sequence0.01 R☉1 R☉100 R☉Sun40,00020,00010,0005,0002,50010⁻⁴10⁻²110²10⁴10⁶Surface temperature (K): hot on the leftLuminosity (Sun = 1)Sirius A
Sirius A: 9,940 K and 25.7 times the Sun’s luminosity, so about 1.71 times its radius.
It lies on the main sequence.
This is an example. Type your own values to start a new problem.
L (L☉)
=
(
R (R☉)
)
2
×
(
T (K)
÷
5,772
K)
4

Formulas

L
=
R
2
×
(
T
5,772
)
4
25.7
=
1.71
2
×
(
9,940
5,772
)
4

Assumptions

•
A bigger or hotter star gives off more light.
•
Main-sequence stars fuse hydrogen in their cores; mass sets where they sit.
•
Giants are cool but huge; white dwarfs are hot but tiny.

Step-by-step

WE KNOW
T = 9,940 K, R = 1.71 R☉
FIND
luminosity (L)
Step 1 · Find luminosity (L)
Use L = R² × (T ÷ 5,772)⁴
Surface
area
grows
as
R
2
;
each
square
meter
shines
as
T
4
,
compared
with
the
Sun.
L
=
1.71
2
×
(
9,940
5,772
)
4
L
=
1.71
2
×
1.7221
4
L
=
2.9241
×
8.795
L
=
25.7
L☉
Check
Put the numbers back in. Both sides should match.
25.7
≈
1.71
2
×
(
9,940
5,772
)
4
✓
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