Chapter 2: The Solar System
in Perspective
NOTE: These slides are highlights that I want
to discuss together - you are responsible for
the other material covered in homework and
activities.
Intro Astrophys
Chapter 2
1
Wien’s Law
•
For a blackbody, the
peak wavelength
(λ max) is related to
the blackbody
temperature, T, by:
"max = 0.002898m /T
or
!
"max T = 0.2898cm # K
Intro Astrophys
Chapter 2
2
!
Stefan’s Law
•
Relates flux output (F = energy/s/area) of a
blackbody with its temperature:
F = "T 4
where
•
•
!
σ = 5.67 x 10-8 W m-4 K-4
To calculate the luminosity, L, of a
blackbody of temperature T, multiply Stefan’s
Law by the surface area of the blackbody.
Intro Astrophys
Chapter 2
3
1
Observed Flux
•
To calculate the flux of a blackbody a
distance r away, use
F=
!
Intro Astrophys
L
4 "r 2
Chapter 2
4
Example Problem (2.11)
•
The albedo of Venus is about 0.77 because
of the cloudy atmosphere. What would the
noontime temperature be? (The measured
temperature is 750 K.)
Intro Astrophys
Chapter 2
5
Example Problem (2.11)
•
•
The energy flux from the Sun at Venus is:
Energy received by Venus is the flux times
the area that receives solar radiation:
Intro Astrophys
Chapter 2
Appropriate for
planets w/atmospheres
6
2
Example Problem (2.11)
•
The amount of energy absorbed is
where A, the albedo, is the fraction of
incoming radiation that is reflected. (1-A) is
therefore the amount of incoming radiation
that is absorbed.
Intro Astrophys
Chapter 2
7
Example Problem (2.11)
•
The absorbed energy is re-radiated over the entire
surface of Venus. Therefore, the emitted flux is the
energy absorbed divided by the surface area of
Venus:
Cancelling yields:
Intro Astrophys
Chapter 2
8
Example Problem (2.11)
•
We can rewrite the luminosity of the Sun as
•
Substituting into the flux equation gives:
Intro Astrophys
Chapter 2
9
3
Example Problem (2.11)
•
We can now use Stefan’s law to solve for the
temperature of Venus:
Intro Astrophys
Chapter 2
10
Example Problem (2.11)
•
You can find constants in Appendices:
•
From appendix 3 (pg A-7 - A-8)
•
From appendix 7 (pg A-17)
•
•
•
•
•
aV = Semimajor Axis of Venus = 108.2E6 km
Radius of Sun = 6.96 E 5 km
Temperature of the Sun = 5780 K
Plugging in
• T = (1-.77)**0.25*(6.95e5/108.2e6)**0.5 *5780
Tvenus = 227 K.
•
•
Actual surface T = 750 K.
Where did we go wrong??
Intro Astrophys
Chapter 2
11
Total Energy of Gravitating System
•
Escape speed occurs when TE = 0.
•
Example: let Earth = m1
•
•
v1 = 0, solve for v2
Escape speed:
Intro Astrophys
Chapter 2
12
4
Conservation of Energy
•
For a bound system
where
•
•
•
a = semi-major axis
r = radius at some point in elliptical orbit
Can use this to calculate launch speed of
least-energy orbit.
Intro Astrophys
Chapter 2
13
5