SME
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
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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