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Physics 312
Introduction to
Astrophysics
Lecture 14
James Buckley
[email protected]
Lecture 14: Extrasolar Planets
Kepler
Circular acceleration
(wikipedia!)
•
1.4m mirror, 95 Mpixel camera
Named after Johannes Kepler, launched March 7 2009. Monitors brightnes of 145,000
• As of January 2015, Kepler has found >1000 (confirmed) exoplanets and more
stars.
than 400 stellar systems.
∆⃗v
⃗a =
•
∆tEarth-sized planets in the
Based on Kepler data could be as many as 40 billion
habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy.
The nearest such planet could be 12 light years away!
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Results
ofacceleration
Extrasolar Planet Searches
Circular
•
⃗a =
∆⃗v
∆t
• (Almost) habitable exoplanets
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Potentially
Habitable Planets
Circular
acceleration
•
⃗a =
∆⃗v
∆t
• Update - habitable planets!
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Brightness, B (W/m2)
Transits acceleration
Circular
•
⃗a =
∆⃗v
∆t
f ⇥B
B
Time, t (days)
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Transits acceleration
Circular
Fraction of light blocked by planet =
cross sectional area of planet
cross sectional area of star
f=
R⇤
⇡Rp2
⇡R⇤2
For a jupiter sized planet passing in front of
a sun-sized star:
R⇤ ⇡ 10 ⇥ Rp
• R
p
⃗a =
∆⃗vf
∆t
⇡
1
= 1%
100
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Kepler Data
Circular acceleration
•
⃗a =
∆⃗v
∆t
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Brightness, B (W/m2)
Transit time jitter
Circular acceleration
•
⃗a =
∆⃗v
∆t
Jitter in transit time indicates
gravitational effect of other planets
Time, t (days)
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Orbital Velocity
and Doppler Shift
Circular
acceleration
• We’d like to get the planet’s velocity from the Doppler shift, but it is
important to note that the star is MUCH brighter than the planet; we can
only measure the Doppler shift of the star light not the planet light. How
do we relate the velocity of the planet (that we get from Kepler’s law) to
the velocity of the star?
vp
•
Since momentum is conserved
throughout the orbit, the star and planet
must always have equal and opposite
momenta
mp
r
⃗a =
∆⃗v mp vp = ms vs
∆t
vs
ms
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Doppler
Shift
Circular
acceleration
•
⃗a =
=
∆⃗
vv
∆t
c
As an example, let’s calculate the redshift of a Jupiter mass planet in a mercury like orbit
around a star with the same mass as our sun
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Putting
it
all
together
Circularm acceleration
p
If the mass of the planet is comparable to the mass of
the star, we need to use a slightly modified version of
Kepler’s third law
vp
a
P2 =
r
4⇡ 2
a3
G(mp + ms )
But for many cases, the mass of the star is
much larger than that of the planet and we
can use the approximation
vs
ms
•
∆⃗v
ms
mp
✓ 2 ◆
4⇡
2
P ⇡
a3
Gms
We can measure the period (transits or Doppler ⃗
shifts)
a = and can determine the mass of the star from
its spectral properties. This gives the orbital radius a, ∆t
which can be used to dermine the velocity
vp ⇡
distance
circumference
2⇡a
=
=
time
period
P
mp vp = ms vs
And if we also have a Doppler shift measurement of the star’s velocity, we can determine the mass
of the planet and, with the transit data giving radius, determine density - terrestrial vs. Jovian
Physics 125, J. Buckley
Physics 312 - Lecture 1
=
4⇡
d2
No-Greenhouse Temperature
Circular acceleration
Incident Flux, F = L/A =
L
4⇡d2
A
re
a,
A
Absorptivity averaged over solar spectrum:
R
↵⌫ F⌫ d⌫
↵visible = R
F⌫ d⌫
L
albedo ⌘ reflectivity of visible light
 Z
avis = exp
↵vis ds
d
Absorbed Flux, Fabs =
Pabs = Fabs · ⇡R2 =
•
⃗a =
∆⃗v
Emitted Power Pem = (
∆t
✓
L
⇡
◆1/4 
(1
a)
d2
1/4
L(1 avis )
4⇡d2
L(1
avis )R2
4d2
T 4 ) · 4⇡R2
avis )R2
= 4⇡ T 4 R2
4d2

1/4
(1 a)
For our sun : T = 280 K
d2
In equilibrium Pabs = Pem
1
T =
2
– p. 25/27
L(1
Physics 312, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
How good
is the approximation?
Circular
acceleration
• Earth:
- Earth’s albedo (optical reflectivity) is a=0.3
- Earth is at a distance of 1 a.u= 1.5 x 1011 m
- No-greenhouse temperature is T=256K. Actually, the average
temperature of the Earth’s surface is 288K, so there is some
greenhouse effect
• Venus:
- •Venus’ albedo a=0.8 (less visible light is absorbed)
∆⃗v
∆t
⃗a the
= Earth).
- d=0.723 a.u (not too different from
- No Greenhouse temperature is T=220K, but the temperature of
Venus is 730K!!! More greenhouse gases!
- Early on, water was vaporized - runaway greenhouse effect more CO2 released from rocks, high density CO2 atmosphere
Physics 312, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
The Greenhouse
Effect
Circular
acceleration
•
⃗a =
∆⃗v
∆t
Source: OSTP
Physics 312, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
ses interact
Greenhouse
gases?
Circular
acceleration
• A greenhouse gas is defined as a gas that efficiently absorbs (and re-
emits) Why
IR radiation.
do certain gases interact
Molecules with more than two
with radiation?
Molecules
more
twomuch lessatoms
a gas
can than
absorb
efficiently
• Suchwith
tend at
tooptical
absorbwavelengths,
radiation more
radiation
impinges
on
a
atomswithout
tend toWhen
absorb
radiation
more
violating Kirchoff’s laweffectively
since this only
demands
of
than diatomicequality
molecules
molecule,
it
can
excite
the
molecule,
effectively
than
diatomic
molecules
absorption and emission at a given
wavelength.
such
as N2 and O2. This is because
such as N2 and
O2. by
This
is because
either
vibrating
(vibrational
of the net balance of their electron
of the net balance
of their
electron(rotational
energy)
or rotating
What makes
a greenhouse
gas aconfiguration.
good IR absober? Typicallydiatomic
these are
•
configuration.energy)
That is it.
whyMolecules
diatomic of a particular That is whyCH
molecules
withare
vibrational
and rotational
energy
levels that are 4separated
nitrogen and
nitrogen
and oxygen
not
CH4 oxygen are not
kind
of
gas
have
a
different
shape
by energies
wavelengths gases.
- need a dipole moment so
greenhouse
gases.corresponding to IRgreenhouse
frommolecules
molecules
of
another
type
of
• symmetric
are not as good.
gas, and so are excited by radiation
∆⃗v
⃗a2 =
in different ways. N2, O
N2, O2
H2O
H2O
∆t
nges on a
ite the molecule,
vibrational
rotational
es of a particular
different shape
nother type of
ited by radiation
CO2
CH
CH
4 4
CO2
CO2
N2, O2
H
2O
CO
Physics 312, J. Buckley
2
Physics 312 - Lecture 1
– p. 25/27
Solar
Constant
Circular
acceleration
H2O
• L⊙ = 3.826 × 1033 erg s−1
• Earth is at a distance d = 1 AU = 1.496 × 1013 cm
• Radiant flux incident on earth is
F =
L⊙
= 1.360 × 106 erg s−1 cm−2
2
4πd
• Converting to more familiar units:
•
F
∆⃗v−2
= 1.360 × 106 erg⃗as−1
= cm ×
∆t
= 1.36 kW m
-2
−1
!
100 cm
1m
"2
×
1 joule
107 erg
Physics 125, J. Buckley
PhysicsPhysics
312 - Lecture
1 – p.525/27
312 - Lecture
– p.12/16
CH4
The
Magnitude
Scale
Circular
acceleration
M=1
M=2
M=3
M=4
M=5 M=6
• Hipparchus (followed by Ptolemy) created a catalog of about
1000 stars that were grouped into six Magnitude groups. Ptolemy
called the brightest stars first magnitude or M = 1, the second
• brightest stars second magnitude M = 2 and so on.
∆⃗v
• In the early 19th century, William
Herschel devised a method to
⃗a =
∆t
make quantitative measurements of magnitude.
Physics 125, J. Buckley
Physics 312 - Lecture 1 – p. 25/27
Physics 312 - Lecture 5 – p.3/16
Friedrich
Wilhelm
Herschel
Friedrich
Wilhelm
Herschel
Circular acceleration
•
Born in•Hanover
Germany,
1738.Germany
Unsuited for
Army life, 15,
left Germany
Born in
Hanover,
November
1738 for England in 1757 and
took up music then transitioned to astronomy.
•
Built a 48” reflector telescope with a 4000 pound grant from King George III. Eventually,
used a•20”
refractorteacher,
(picturedcomposer,
above) for many
of his observations.
• Music
bandmaster
•
Discovered
Uranus,
moons reflector
of planets, telescope
binary⃗
and orbits.
nebulae
(his son
• Built
astars
= with
48-inch
4000Catalogued
pound grant
from
∆t
continued work in the southern hemisphere). Believed nebulae were clusters of stars he called
King George
``island nebulae’’
- close toIII
the modern concept of galaxies.
•
20-foot
refractor
(above)
forWilliam,
most observations
Sister, Caroline
Lucretia
Herschel
workedused
with Sir
discovered a number of comets,
was inducted into the Royal Astronomical Society, and was awarded thePhysics
Prussian
Gold
of
312 - Lecture
5 – Medal
p.5/16
Science shortly before her death at 97.
Physics 312, J. Buckley
• Unsuited for army life, left Germany for England in 1757
∆⃗v
•
Physics 312 - Lecture 1
– p. 25/27
Herschel’s Method
Circular acceleration
Star 1
To find the relative brightness of a bright star
(star 1) to a dim star (star 2), you can stop down
the aperture of one telescope until the two stars
appear to be equally bright.
Star 2
Stars appear equally bright if
F 1 · A1 = F 2 · A2
A2
A1
F1
A2
=
F2
A1
•
∆⃗v
∆t was able to determine that
Herschel
⃗a =
two stars di↵ering in magnitude m = 1
had relative brightness of F1 /F2 = 2.5
Physics 312, J. Buckley
Physics 312 - Lecture 1
– p. 25/27
Magnitude Scale
Circular acceleration
•
In modern times, we define magnitude so that a difference of 5
magnitudes corresponds exactly to a factor of 100 in brightness
• i.e., a difference in magnitude of ∆m = 1 corresponds to
1001/5 = 2.512
• Or we can write:
F2
= 100(m1 −m2 )/5 = 2.512m1 −m2
F1
•
⃗a =
∆⃗v
∆t
Physics 125, J. Buckley
Physics 312 - Lecture 5 – p.7/16
Physics 312 - Lecture 1 – p. 25/27
Absolute
magnitude
Circular acceleration
F10
F
(1/10pc)2
=
1/d2
!
"2
d
=
10 pc
100(m−M )/5 =
d = 10(m−M +5)/5 pc
•
m−M
∆⃗v
=⃗a =5 log
∆t 10
!
d
1pc
"
−5
Physics 125, J. Buckley
312 - Lecture
PhysicsPhysics
312 - Lecture
1 – p. 525/27– p.8/16
Absolute
magnitude of the Sun
Circular acceleration
• The apparent magnitude of the sun is msun = −26.81 and is at a
distance of d = 1 AU = 4.848 × 10−6 pc
• Calculate the absolute magnitude of the sun:
Msun = msun − 5 log10 (4.848 × 10−6 ) + 5 = 4.76
•
⃗a =
∆⃗v
∆t
Physics 125, J. Buckley
312 - 1Lecture
5 – p.9/16
Physics Physics
312 - Lecture
– p. 25/27
1.2 Host star
Radius
(r)
0.52 −0.04 R
1.3 Orbit
Temperature
(T)
3748 (± 112) K
2 Habitability
Metallicity
+0.06
[Fe/H] 0.16 (± 0.14)
+0.8
Age
3 Discovery and follow-up studies
4.4 −0.7[3] Gyr
Physical characteristics
4 See also
Mass
(m)
1.3 −0.7 M⊕
5 References
Radius
(r)
1.12 (± 0.16) R⊕
+2.6
6 External links
Stellar flux
Kepler-438b - Wikipedia
18h
Coordinates:
Kepler-438b
46m
35.000s,
+41° 57ʹ 03.93ʺ
(F⊙)
+0.67
1.40 −0.77 ⊕
From Wikipedia, the free encyclopedia
Kepler-438b (also known by its Kepler Object of Interest
designation KOI-3284.01) is a confirmed near-Earth-sized
exoplanet, likely rocky, orbiting on the inner edge of the
habitable zone of the red dwarf as it receives 1.4 times our
Kepler-438b[1][2][3]
Exoplanet
List of exoplanets
or nearly 4.5 × 1015 km) from Earth in the constellation
Lyra.[1][2] The planet was discovered by NASA's Kepler
spacecraft using the transit method, in which the dimming
effect that a planet causes as it crosses in front of its star is
measured. NASA announced the confirmation of the
exoplanet on 6 January 2015.[1] Although it is not habitable,
as of June 2015, it has the highest index on the Earth
Similarity Index, with a rating of 0.88.[6]
Kepler-438b is approximately 470 light years from Earth, so
travelling there is presently impossible within a human
lifetime. The German-designed Helios probes, notable for
having set the current speed record among spacecraft at
252,792 km/h, would take some two million years to travel
to Kepler-438b.[7]
(mV) 14.467
Mass
1.2 Host star
1.3 Orbit
+0.06
0.544 −0.04 M
Radius
(r)
0.52 −0.04 R
Temperature
(T)
3748 (± 112) K
+0.06
[Fe/H] 0.16 (± 0.14)
+0.8
4.4 −0.7[3] Gyr
Physical characteristics
Mass
(m)
Radius
(r)
Stellar flux
(T)
1.12 (± 0.16) R⊕
276 K (3 °C; 37 °F)
Mass, radius and temperature
Semi-major
axis
(a)
0.16600 AU
Kepler-438b is an Earth-sized planet, an exoplanet that has a
mass and radius close to that of Earth. It has a radius of 1.12
R⊕, and
a mass of 1.3 M⊕. It has an equilibrium temperature
Kepler-442b - Wikipedia
of 276 K (3 °C; 37 °F), close to that of Earth.
Eccentricity
(e)
+0.01
0.03 −0.03[3]
Orbital
(P)
35.23319 d
physics
and chemistry,
with 1.00studies
being the most similar,
Distance
ly
ww.openexoplanetca 1120
Kepler-438+b)
3 Discovery
and follow-up
Kepler-438b has an index of 0.88, the highest known to date, talogue.com)
(342[3] pc)
making
currently the most Earth-like planet in terms of
4 Seeitalso
6 External links
old,[3]
200 or
million
than
(342only
parsecs,
nearlyyears
1.0553younger
× 1016 km)
Sun.[8]
[1][7] The planet
andinthe
has a surface
of
Earth
theSun
constellation
Lyra.temperature
the from
5778
was
K.[9]discovered by NASA's Kepler spacecraft using the transit
method, in which the dimming effect that a planet causes as
crosses
in frontmagnitude,
of its star is or
measured.
NASA
announced
The itstar's
apparent
how bright
it appears
from
[7]
the perspective,
confirmation of
exoplanet
on 6 January
2015.
Earth's
is the
14.467.
Therefore,
it is too
dim to be
seen with the naked eye.
Contents
Orbit
Characteristics
Kepler-442b is a super-Earth, an exoplanet with a mass and
radius bigger than that of Earth, but smaller than that of the
ice giants Uranus and Neptune. It has an equilibrium
m 27.98s, +39° 16ʹ 48.30ʺ
(i)
19h 0189.860°
Discovery information
The planet orbits a (M-type) red dwarf star named Kepler[1][2][7]
known
its Kepler
Object
of
438.Kepler-442b
The star has a mass(also
of 0.54
M by and
a radius
of 0.52
Interest designation KOI-4742.01) is a confirmed near-EarthR , sized
both exoplanet,
lower thanlikely
thoserocky,
of the
Sun bywithin
almost
It has a
orbiting
thehalf.
habitable
surface
3748 K and isstar
estimated
to be about
about
[8] Kepler-442,
zonetemperature
of the K-typeofmain-sequence
2015[4]
temperature of 233 K (−40 °C; −40 °F).[5] It has a radius of
1.34 R⊕. Because of its radius, it is likely to be a rocky
planet with a solid surface. The mass of the exoplanet is
Transit
List of exoplanets
Discovery status
star.[10]
KOI-3284.01; Kepler-438 b; KOI-3284 b;
1.2 Host star
1.3 Orbit
Habitability
Host star
has a mass of 0.61 M and a radius of 0.60 R . It has a
temperature of 4402 K and is around 2.9 billion years old,
with some uncertainty. In comparison, the Sun is 4.6 billion
somewhat metal-poor, with a metallicity (Fe/H) of −0.37, or
Database references
42% of the solar amount.[2] Its luminosity (L ) is 11% that
Extrasolar
Planets
data of(http://exoplanet.eu/plan
of the Sun.
Approximate
size comparison
a hypothetical
Encyclopaedia
et.php?p1=Kepler-438&p2=b
superhabitable planet
with Earth.
The star's apparent magnitude, or how bright it appears from
)
Parent star
Habitability
The planet 2was
announced as orbiting within the habitable
zone of Kepler-438,
a region
where liquid
3 Discovery
and follow-up
studieswater could exist
on the surface of the planet. In the Earth Similarity Index
(ESI), which
measures
4 See
also how similar are planets to Earth as to
physics and chemistry, with 1.00 being the most similar,
5 References
Kepler-438b
has an index of 0.88, the highest known to date,
making it currently the most Earth-like planet in terms of
6 External links
radius and stellar flux.[1][2] However it has been found that
Apparent
https://en.wikipedia.org/wiki/Kepler-438b
Mass, radius and temperature
pac.caltech.edu/cgi-bin/Displ
112.3 days and an orbital radius of about 0.4 times that of
(δ) +39° 16ʹ 48.30ʺ
ayOverview/nph-DisplayOve
Earth's (a little larger than the distance of Mercury from the
(mV) 14.976[2]
rview?objname=Kepler-438+
Sun, which is about 0.38 AU).[1][7] It receives about 70% of
b)
the sunlight that Earth receives from the Sun.
magnitude
Distance
1120 ly
Open Exoplanet (342[3]
data )(http://www.openexopla
pc
Catalogue (http://w netcatalogue.com/search/?id=
Spectral type
K?V[4]
ww.openexoplanetca Kepler-438+b)
Mass
The planet was announced as being located within the
talogue.com) (m) 0.61 (± 0.03)[2] M
Radius
Metallicity
(r)
0.60 (± 0.02)[2] R
(T)
4402 (± 100)[2] K
habitable zone of its star, a region where liquid water could
exist on the surface of the planet. It was described as being
one of the most Earth-like planets, in terms of size and
temperature, yet found.[1][7] It is outside of the zone (around
0.02 AU) where tidal forces from its host star would be
[Fe/H] −0.37 (± 0.10)[2]
2.9+8.1[2] Gyr
Age
enough to tidally lock it.[9]
−0.2
Physical characteristics
Kepler-442b is a super-Earth, an exoplanet with a mass and
radius bigger than that of Earth, but smaller than that of the
ice giants Uranus and Neptune. It has an equilibrium
temperature of 233 K (−40 °C; −40 °F).[5] It has a radius of
1.34 R⊕. Because of its radius, it is likely to be a rocky
planet with a solid surface. The mass of the exoplanet is
(r)
0.60 (± 0.02)[2] R
Temperature
(T)
4402 (± 100)[2] K
Metallicity
[Fe/H] −0.37 (± 0.10)[2]
2.9+8.1[2] Gyr
Age
−0.2
Mass
(m)
Radius
(r)
Mass
(m)
Radius
(r)
2.3+5.9[5] M⊕
−1.3
1.34+0.11[2] R⊕
https://en.wikipedia.org/wiki/Kepler-442b
−0.18
Stellar flux
(F⊙) 0.73 (± 0.11)[6] ⊕
estimated to be 2.34 M⊕.[9] The surface gravity on Kepler442b would be 30% stronger than that of Earth, assuming a
Temperature
(T)
233 K (−40 °C; −40 °F)
rocky composition similar to that of Earth.[10]
Semi-major
axis
(a)
0.409+0.209[2] AU
Host star
Eccentricity
(e)
0.04+0.08[2]
The planet orbits a (K-type) star named Kepler-442. The star
has a mass of 0.61 M and a radius of 0.60 R . It has a
temperature of 4402 K and is around 2.9 billion years old,
Orbital
period
(P)
112.3053+0.024
(i)
89.94+0.06[2]°
−0.12
Orbital elements
Inclination
−0.060
−0.04
−0.0028
[2]
d
2.3+5.9[5] M⊕
−1.3
1.34+0.11[2] R⊕
−0.18
10/19/16, 11:17 AM
Stellar flux
(F⊙) 0.73 (± 0.11)[6] ⊕
(T)
233 K (−40 °C; −40 °F)
Orbital elements
(a)
0.409+0.209[2] AU
Eccentricity
(e)
0.04+0.08[2]
−0.04
Orbital
period
(P)
112.3053+0.024
(i)
89.94+0.06[2]°
−0.12
Inclination
−0.060
−0.0028
[2]
d
Discovery information
Discovery date
6 January 2015[2][3]
Discoverer(s)
Kepler spacecraft
Discovery method
Transit
Discovery status
Published referred article
Other designations
KOI-4742.01; Kepler-442 b; KOI-4742 b;
K04742.01; WISE J190127.98+391648.2 b; KIC
4138008 b; 2MASS J19012797+3916482 b
Database references
Extrasolar Planets
Encyclopaedia
data (http://exoplanet.eu/plan
et.php?p1=Kepler-442&p2=b
)
SIMBAD
data (http://simbad.u-strasbg.f
r/simbad/sim-id?Ident=Keple
r-442+b)
Exoplanet Archive
data (http://exoplanetarchive.i
pac.caltech.edu/cgi-bin/Displ
ayOverview/nph-DisplayOve
rview?objname=Kepler-442+
b)
Habitability
Temperature
Characteristics
data (http://simbad.u-strasbg.f
seen with the naked eye.
Kepler-442
(KOI-4742)
r/simbad/sim-id?Ident=Keple
Lyra[1]
Orbit
r-438+b)
Right
(α) 19h 01m 27.98s
Exoplanet Archive data (http://exoplanetarchive.i
ascension
Kepler-442b orbits its host star with an orbital period of
Declination
0.61 (± 0.03)[2] M
Radius
Semi-major
axis
K03284.01; WISE J184634.98+415704.0 b; KIC
years old[11] and has a temperature of 5778 K.[12] The star is
6497146 b; 2MASS J18463499+4157039 b
Constellation
(m)
rocky composition similar to that of Earth.[10]
Earth's perspective, is 14.97. Therefore, it is too dim to be
1 Characteristics
Kepler-438b
orbits its parent star once every 35.2 days.[1][2]
It is likely tidally1.1
locked
to its
distance to its
Mass,due
radius
andclose
temperature
K?V[4]
Mass
Temperature
Published refereed article The planet orbits a (K-type) star named Kepler-442. The star
Other designations
SIMBAD
Star
Spectral type
estimated to be 2.34 M⊕.[9] The surface gravity on Kepler442b would be 30% stronger than that of Earth, assuming a
Discoverer(s) Kepler-442b
Kepler spacecraft
Discovery method
Exoplanet
data (http://simbad.u-strasbg.f
r/simbad/sim-id?Ident=Keple
Kepler-442
r-438+b) (KOI-4742)
Physical characteristics
period
Discovery date
SIMBAD
Constellation
Exoplanet Archive Lyra
data[1](http://exoplanetarchive.i
h 01m 27.98s
Right
(α) 19pac.caltech.edu/cgi-bin/Displ
ayOverview/nph-DisplayOve
ascension
rview?objname=Kepler-438+
The planet
announced as orbiting within the habitable
Declination
(δ) +39° 16ʹ 48.30ʺ
1.3was
Orbit
b)
zone of Kepler-438, a region where liquid water could exist
Apparent
(m ) 14.976[2]
on2theHabitability
surface of the planet. In the Earth Similarity Index
Open Exoplanet V
data (http://www.openexopla
(ESI), which measures how similar are planets to Earth as to magnitude
Catalogue (http://w netcatalogue.com/search/?id=
Mass, radius and temperature
Orbital elements
Inclination
Coordinates:
Extrasolar Planets data (http://exoplanet.eu/plan
Encyclopaedia
et.php?p1=Kepler-438&p2=b
Approximate size comparison
of a hypothetical
superhabitable) planet with Earth.
1.1 Mass, radius and temperature
(F⊙)
Temperature
From Wikipedia, the free encyclopedia
+0.01
Habitability
1.2 Host star
+0.67
Kepler-442b
Host
star
0.03 −0.03[3]
Discovery information
radius and stellar flux.[1][2] However it has been found that
5 References
+2.6
1.3 −0.7 M⊕
1.40 −0.77 ⊕
Characteristics
0.16600 AU
(e)
Eccentricity
FromHost
Wikipedia,
star the free encyclopedia
https://en.wikipedia.org/wiki/Kepler-438b
6 External links
(a)
axis
star.[10]
M?V
Age
5 References
Semi-major
Kepler-438b orbits its parent star once every 35.2 days.[1][2] Parent star
It is
tidally locked due to its close distance to its
1 likely
Characteristics
Star
(m)
Metallicity
4 See also
Orbital elements
Kepler-442b
Contents
470[2] ly
Spectral type
1.1 Mass, radius and temperature
3 Discovery and follow-up studies
276 K (3 °C; 37 °F)
Orbital
(P) 35.23319 d
period
Coordinates:
19h 01m 27.98s, +39° 16ʹ 48.30ʺ
Inclination
(i) 89.860°
Orbit
(145 pc)
2 Habitability
(T)
[4]
Distance
1 Characteristics
Mass, radius and temperature
Temperature
Discovery date
2015
[1][2][7]
The planet
orbits(also
a (M-type)
star named
Kepler-442b
knownred
bydwarf
its Kepler
ObjectKeplerof
Kepler-442b
Approximate size comparison of Kepler-438b (right) withInterest
438.designation
The star hasKOI-4742.01)
a mass of 0.54isMa confirmed
and a radius
of 0.52
Discoverer(s)
Kepler spacecraft
near-EarthEarth
, both lower
than
thoseorbiting
of the Sun
by almost
half. It has a Exoplanet
sizedRexoplanet,
likely
rocky,
within
the habitable
List of exoplanets
Discovery method
Transit
temperature
of 3748 K and
is estimated
to be
about
zone surface
of the K-type
main-sequence
star[8]
Kepler-442,
about
Parent star
Discovery status
Published refereed article
[3]
billion years
onlyor200
million
years×younger
than
1,1204.4
light-years
(342old,
parsecs,
nearly
1.0553
1016 km)
Star
Kepler-438
Other designations
[8] and the Sun has a surface
Sun.
5778
from the
Earth
in the
constellation Lyra.[1][7]temperature
The planet of
was
KOI-3284.01; Kepler-438 b; KOI-3284 b;
Constellation
Lyra[2]
[9]
K.
discovered
by NASA's Kepler spacecraft using the transit
K03284.01; WISE J184634.98+415704.0 b; KIC
Right
(α) 18h 46m 35.000s
method, in which the dimming effect that a planet causes as
6497146 b; 2MASS J18463499+4157039 b
The star's
apparent
or howNASA
bright announced
it appears from
it crosses
in front
of its magnitude,
star is measured.
ascension
Earth's perspective, is 14.467. Therefore, it is too dim
to be
Database references
the confirmation
the exoplanet
on 6 January 2015.[7]
Declination
(δ) +41° 57ʹ 3.93ʺ
seen with theofnaked
eye.
Apparent
magnitude
Contents
Characteristics
Kepler-438b is an Earth-sized planet, an exoplanet that has a
Kepler-442b
mass- Wikipedia
and radius close to that of Earth. It has a radius of 1.12
R⊕, and a mass of 1.3 M⊕. It has an equilibrium temperature
of 276 K (3 °C; 37 °F), close to that of Earth.
solar flex.[5] Kepler-438, about 470 light-years (145 parsecs,
4.4 billion
years
1,120 light-years
10/19/16, 11:16 AM
Open Exoplanet
data (http://www.openexopla
Catalogue (http://w netcatalogue.com/search/?id=
ww.openexoplanetca Kepler-442+b)
talogue.com)
Page 1 of 3
Exam Questions
Circular
acceleration
•
Consider a planet orbiting a star with twice the mass, and twice the luminosity
of the sun. If the orbital period is 2 solar years, what is the surface temperature
of the planet? How could one determine the mass of the planet (if you
measure the Doppler shift of the star)?
•
Consider a star with some RA and DEC, viewed at some sidereal time, plot the
appearance of the night sky. Draw and label RA and DEC lines
•
⃗a =
∆⃗v
∆t
Physics 125, J. Buckley
Physics 312 - Lecture 1
– p. 25/27