Star luminosity . The luminosity L of a star is the power output at a star’s surface (measured in watts). The star’s apparent brightness b is the wattage received on Earth’s surface. The apparent magnitude m of a star depends on its absolute magnitude M (related to L ) and its distance D in parsecs ( 1 parsec ≈ 3 .36 light years) by the formula: m − M = 2.5 log L b = 5 log D 10 . a. Given m and M for a star, show that its distance D from Earth is D = 10 1 + ( m − M ) / 5 parsecs b. For the star Alpha Centauri, m = 0 and M = 4.39 . How far is it from Earth? c. Compare the luminosity and brightness of Alpha Centauri.
Star luminosity . The luminosity L of a star is the power output at a star’s surface (measured in watts). The star’s apparent brightness b is the wattage received on Earth’s surface. The apparent magnitude m of a star depends on its absolute magnitude M (related to L ) and its distance D in parsecs ( 1 parsec ≈ 3 .36 light years) by the formula: m − M = 2.5 log L b = 5 log D 10 . a. Given m and M for a star, show that its distance D from Earth is D = 10 1 + ( m − M ) / 5 parsecs b. For the star Alpha Centauri, m = 0 and M = 4.39 . How far is it from Earth? c. Compare the luminosity and brightness of Alpha Centauri.
Solution Summary: The author calculates the apparent magnitude of a star based on its absolute magnitude M and its distance D from Earth.
Star luminosity. The luminosity
L
of a star is the power output at a star’s surface (measured in watts). The star’s apparent brightness
b
is the wattage received on Earth’s surface. The apparent magnitude
m
of a star depends on its absolute magnitude
M
(related to
L
) and its distance
D
in parsecs (
1
parsec
≈
3
.36
light years) by the formula:
m
−
M
=
2.5
log
L
b
=
5
log
D
10
.
a. Given
m
and
M
for a star, show that its distance
D
from Earth is
D
=
10
1
+
(
m
−
M
)
/
5
parsecs
b. For the star Alpha Centauri,
m
=
0
and
M
=
4.39
. How far is it from Earth?
c. Compare the luminosity and brightness of Alpha Centauri.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY