Download Astronomy 111 Overview of the Solar system

Astronomy 111 Overview of the Solar system
❑ Contents of the solar system
❑ What we can measure and what we
can infer about the contents
❑ How do we know? Initial
explanations of four important facts
about the solar system
❑ Important Units
❑ The Celestial sphere
❑ Working with Angles
This is a composite image of all the planets in our solar
system. From the top is Mercury (taken by the Mariner
10 spacecraft); Venus (taken by the Pioneer Venus
Orbiter); a full disk of the Earth (taken by the Apollo 17
astronauts); the Moon and then Mars (captured from
ground-based telescopes); and Jupiter, Saturn, Uranus
and Neptune (as seen by the Voyager spacecraft). Credit
NASA/JPL.
1
Q: What would an outside
Image by Robert Gendler
Inventory of the Solar
System
observer see if they were
looking at our Solar system?
A: The Sun. The luminosity of the Sun is 4×108 times as
luminous as the second brightest object, Jupiter. The
Sun contains 99.8% of the mass (but NOT most of the
angular momentum).
L◉=4×1026 Watts, M◉=2×1033 g
The solar system is: The Sun + some debris.
2
Aside: observations of other planetary systems
In most other stellar (extrasolar)
systems, all we know about are the stars,
because they are overwhelmingly bright.
– But, planets have been detected around
other stars, with surprising properties
(high eccentricities, small radii from star,
sparse and packed systems).
– Our detailed understanding of the Solar system has
helped us interpret/understand the formation and
evolution of planetary and stellar systems.
– However, what we are finding about extrasolar systems
is challenging previous views of solar system formation
and evolution.
Astronomer-artist’s conception of HD 209458 and its largest planet (Robert Hurt, SSC/Caltech)
3
Components of the “debris”
❑The Giant planets (mostly gas and
liquid)
❑Terrestrial planets and other
planetesimals, (mostly rock and ice)
❑ The Heliosphere (plasma)
Pale Blue Dot" photograph of the Earth taken by the
Voyager 1 spacecraft on July 6,1990
4
Giant Planets
❑ Jupiter dominates with a mass of 10-3 times that of the Sun
(1/1000 M◉ ) or 300 times that of the Earth
❑ Saturn’s mass is 3×10-4 M◉
❑ Neptune and Uranus are about 1/6 the mass of Saturn.
❑ Giant planets at 5, 9, 20, and 30 times further from the Sun than
Earth is (a = 5, 9, 20, 30AU; a is commonly used to denote semimajor axis, covering the possibility of an elliptical orbit).
❑ Saturn and Jupiter have roughly Solar type abundances
(composition) which means mostly hydrogen and helium. Saturn
probably has a rocky core; Jupiter might not.
❑ Neptune and Uranus are dominated by water (H2O) and
ammonia (NH3) and have a larger percentage of their mass in
rocky/icy cores.
❑ Jupiter and Saturn are called gas giants.
❑ Neptune and Uranus are called ice giants.
5
• Earth and Venus,
radius R~6000km,
a=1.0, 0.7 AU respectively
• Mars,
R~3500km, a=1.5AU
• Mercury
R~2500km, a=0.4AU
• Asteroid belt, a~2-5 AU
• Moons and satellites
• Kuiper Belt, including Pluto a>30AU
• Oort Cloud, including Sedna
a~104AU
• Planetary Rings
• Interplanetary dust
Mars Daily Global Image
Mars Global Surveyor MOC April
1999
Terrestrial Planets and Other Debris
Messenger image of lava flooded
craters on Mercury October 6, 2008 6
The Heliosphere
All planets orbit within the
heliosphere, which contains
magnetic fields and plasma
primarily of solar origin.
The solar wind is a plasma
traveling at supersonic speeds.
Where it interacts or merges
with the interstellar medium is
called the heliopause.
Cosmic rays (high energy
particles) are affected by the
magnetic fields in the
heliosphere.
7
Planetary properties that can be determined
directly from observations
❑ Orbit
❑ Age
❑ Mass, mass distribution
❑ Size
❑ Rotation rate and spin axis
❑ Shape
❑ Temperature
❑ Magnetic field
❑ Surface composition
❑ Surface structure
❑ Atmospheric structure and composition
Saturn, Venus, and Mercury, with the European Southern Observatory in the foreground (Stephane Guisard).
8
Other planetary properties that can be inferred
or modeled from the observations
❑ Density and temperature as
functions of position, of the
atmosphere and interior
❑ Formation
❑ Geological history
❑ Dynamical history
These will be discussed in
context with the
observations and
astrophysical processes as
part of this course.
Cut-away view of the Sun’s convection zone
(Elmo Schreder, Aarhus University, Denmark).
9
UNITS
• 1 Astronomical unit AU = 1.5×1013cm
Is the distance between the Sun and Earth.
More precisely is the earth’s semi-major axis
in heliocentric coordinates.
• Time: seconds or years. 1year ~3×107s
• Angles: 360o ~ 2π radians
60 arcminutes per degree, 60’
60 arcseconds per arcminute, 60”
10
Angles on the sky
• One arcsecond, 1”
1'
1o π radians
−6
1"×
×
×
=
4.8
×
10
radians
o
60" 60'
180
• 1” is the angle that we can resolve at optical wavelengths
without atmospheric blurring (seeing).
• d=Dθ d = size of object
d
D = distance to object
θ
(same units as d)
θ = angle in
radians
D
11
Q. How far away could we
resolve an Earth?
Q. Is Neptune resolved?
• Rearth ~ 6500km
• Rneptune ~25,000 km, a~30AU
12
How do we know?
Note that most of what we will say about the planets this semester is
founded upon a lot of very direct evidence, rather than theory or reasonaided handwaving. For example:
1. The Earth is approximately spherical.
Direct observation, and known since about 500 BC:
❑ Lunar phases indicate that it shines by reflected sunlight.
❑ The full moon is nearly on the opposite side of the sky from the Sun.
❑ Therefore lunar eclipses are the Earth’s shadow cast on the moon.
❑ The edge of this shadow is always circular; thus the Earth must be a sphere.
Lunar eclipse (16 Aug 2008) sequence photographed by Anthony Ayiomamitis
13
How do we know? (continued)
2. The planets orbit the Sun, nearly all in the same plane.
Also direct observation.
❑ The planets and the Sun always lie in a narrow band across
the sky: the zodiac. This is a plane, seen edge on.
❑ Distant stars that lie in the direction of the zodiac exhibit
narrow features in their spectrum that shift back and forth in
wavelength by ±0.01% with periods of one year. No such shift
is seen in stars toward the perpendicular directions, or in the
Sun. The shift is a Doppler effect, from which one can infer a
periodic velocity change of Earth with respect to the stars in
the zodiac by ±30 km/sec. Thus the Earth travels in an
approximately circular path at 30 km/sec, centered on the
Sun.
14
15
How do we know? (continued)
The Doppler effect:
Suppose two observers had light emitters and detectors that
can measure wavelength very accurately, and move with
respect to each other at speed v along the direction between
them. Then if one emits light with pre-arranged wavelength λ0 ,the other one will detect the light at wavelength
v#
"
λ = λ0 $ 1 + % ;
c'
&
λ − λ0
that is,
v=c
,
λ0
10
-1
c
=
2.99792458
×
10
cm
sec
where
is the speed of light.
16
How do we know? (continued)
3. The Sun lies precisely 1.50×1013 cm (1 AU) from Earth.
Direct observation: it follows from the previous example, but
we can measure the same thing more precisely these days by
reflecting radar pulses off the Sun or the inner planets,
measuring the time between sending the pulse and receiving
the reflection, and multiplying by the speed of light.
❑ Note that knowing the AU enables one to measure the
sizes of everything else one can see in the Solar system.
❑ Using Venus or Mercury gives the most accurate results, as
the Sun itself doesn’t have a very sharp edge at which the
radar pulse is reflected. It works with Venus or Mercury as
follows:
17
How do we know? (continued)
Sun
Venus
1 AU
θ
Earth
d
Suppose you were to send a
radar pulse at Venus when it
appeared to have a first-or
third-quarter phase, so that
the line of sight is
perpendicular to the VenusSun line. Then
c Δt
d=
2
d
1 AU =
cos θ
= 1.4959787069(3) × 1013 cm
(corrected for planet size and averaged over the orbit)
18
How do we know? (continued)
4. The solar system is precisely 4.6 billion years old.
Direct observation, again, on terrestrial and lunar rocks, and
on meteorites, nearly all of which originate in the asteroid
belt. We will study this in great detail:
❑ When rocks melt, the contents homogenize pretty thoroughly.
❑ When they cool off, they usually recrystallize into a mixture of
several minerals. Each different mineral will incorporate a certain
fraction of trace impurities.
❑ Those trace impurities that are radioactive will vanish, in times that
are measured accurately in the lab.
❑ Thus the ratio of amounts of radioactive trace impurities tell how
much of the tracer the rock had when it cooled off, and how long
ago that was.
❑ The oldest rocks in the Solar system are all 4.567 billion years old,
independent of where they came from, so that’s how long ago the
Solar system solidified.
19
The Celestial Sphere
Astronomy was the first precision science.
For about 200 years, astronomy was considered
mathematics.
Positions of objects can be predicted extremely well
(e.g., eclipses).
To do this we require a good coordinate system.
This we call the celestial sphere. It is a way for us
to specify positions of objects on the sky.
Geocentric reference frame
Rochester is close to 75o W of Greenwich, England or 5h W
of Greenwich England.
So 24h = 360o, or 1h = 15o on the equator.
Mees observatory latitude is 42o 42m.
Relation between time and angle for longitude is not a
coincidence.
Coordinate system tied to rotation axis of the Earth
22
Coordinate system on the
sky
❑ The celestial sphere is an imaginary
sphere of infinite radius with the
earth located at its center.
❑ An astronomer can only a
hemisphere of see the sky at a time,
that is, only half the sky is above the
horizon at any time. The sky moves
as the earth rotates. Just as the sun
rises and sets every day, so do many
stars in the sky each night.
❑ North Celestial Pole (NCP) and the South Celestial Pole (SCP) –
intersections of the north and south pole rotation axes with the
celestial sphere.
❑ Celestial Equator – Intersection of the earth's equatorial plane with
the celestial sphere. The celestial equator is not aligned with the
ecliptic.
❑ The ecliptic is the plane containing the planets.
Declination (DEC, δ)
❑ Declination is the angle
between the celestial equator
and the object. It is similar to
latitude.
❑ The north star has a declination
~+90o , and is approximately
stationary on the sky.
❑ Objects below -15o declination
are difficult to observe from
Rochester.
❑ The circle which contains the
rotation axis of the earth and
the zenith is called the meridian
Objects reach their highest
altitudes (elevations in the sky)
when they are on the meridian.
Sun is in ecliptic!
Sun intersects
celestial equator
twice in the year
Right ascension is similar to longitude. It is
defined with respect to the vernal equinox, (Mar
21). Remember longitude is with respect to
Greenwich England.
Vernal equinox
❑ Vernal equinox is a
moment of time or a
direction. Consider the
the intersection of the
ecliptic with the earth’s
equatorial plane.
❑ The vernal equinox is the
moment in time when the
sun crosses this point.
❑ The sun crosses the vernal
equinox at 21 March,
noon UT (Universal time)
Coordinates on the celestial sphere
Just as latitude and
longitude specify a
position on the glob,
declination and right
ascension specify a
location on the celestial
sphere.
Vernal equinox
❑ The Earth’s equator and the
ecliptic cross at two points on
the celestial sphere or directions.
One of these sets the vernal equinox,
the other the autumnal equinox.
❑ Location of stars given with respect to the vernal
equinox direction.
❑ Orbital elements for orbits of bodies in the solar
system are also given with respect to this direction.
❑ The great circle containing both equinoxes and the
poles defines the zero-point of right ascension.
❑ Note: since the earth’s spin axis precesses, the
angular position of the vernal equinox depends on the
year or epoch.
28
Right Ascension (RA, α)
❑ Right ascension is often given in units of time (hours, minutes
seconds). Similar to longitude on Earth, the Right Ascension of
an object on the celestial sphere is measured eastward along the
celestial equator, from a zero-point (i.e. where α = 0o), defined to
be the vernal equinox – the place where the Sun is on the sky on
March 21.
❑ If you look directly in the opposite direction this means objects at
RA~12h are cresting (rising to the meridian) at midnight on
Mar21.
❑ You can’t look at things that have an RA of 0h in the spring
because the sun is in the way.
❑ In the fall the Earth is on the opposite side of the Sun. You can
observe stars at an RA of 0h in the fall.
❑ 24 hours in RA, and 12 months. This means each month
increases the RA of objects which are on the meridian at
midnight by 2hours.
Local Sidereal Time (LST)
❑ Sidereal is with respect to the locations of stars.
❑ Sidereal time is the RA that is cresting or on the
meridian at a particular time.
❑ To estimate LST you need to know the time and
date as well as your location.
❑ Sidereal Time ST is = the right ascension of a star
on the meridian. Thus ST = 0h at noon during the
vernal equinox (Mar 21). At this time the Sun is
on the meridian.
❑ You cannot observe things with RA=0 during the
vernal equinox. Why not?
❑ At midnight on the vernal equinox, LST=12h.
Objects with RA=12h reach the meridian at
midnight.
Elevation and Hour Angle
❑ The Hour angle, HA is the angular measure in
h,m,s from the meridian westward along the
celestial equator to the foot of the hour circle (like
longitude circle) through an object.
ST = HA + α
Sidereal time = hour angle + right ascension
❑ HA = 0 when an object is on the meridian.
❑ HA<0 before it reaches the meridian.
❑ HA>0 afterwards.
❑ Altitude or Elevation describes how high an
object is above the horizon.
31
What RA is up at midnight?
24 hours in RA
Each month of
movement in
Earth’s orbit
gives 2 hours in RA
RA=0 hours is up
Sept 21 at midnight
RA=2 hours is up
Oct 21 at midnight
RA=12 hours is up
at midnight Mar 21
32
The sidereal and solar day
Careful observation of the sky will
show that any specific star will cross
directly overhead (on the meridian)
about four minutes earlier every day.
In other words, the day according to
the stars (the sidereal day) is about
four minutes shorter than the day
according to the sun (the solar day).
If we measure a day from noon to
noon - from when the sun crosses the
meridian (directly overhead) to when
the sun crosses the meridian again we will find the average solar day is
about 24 hours.
Sidereal day vs solar day
Ps = Sidereal period: Orbital period of a rotating
planet as seen from an external fixed observer
Pd = Solar day: Time between noons as seen by
a person on the surface
Po = orbital period
34
35
Elevation
Q. The elevation of an object at meridian depends on
what?
36
Elevation
Q. The elevation of an object at meridian depends
only on what?
A. The object’s declination and your latitude.
If you are on the equator
the north and south poles
are always on the horizon.
Objects with DEC=0
pass straight overhead.
37
Elevation
Q. What is the maximum elevation of an object that
has a declination of +80o at Mees Observatory
(with latitude +42o 42’)?
38
Elevation
Q. What is the maximum elevation of an object that
has a declination of +80o at Mees Observatory
(with latitude +42o 42’)?
A. Polaris has elevation ~43o
Object has maximum
elevation 10o
higher or 53o
39
EPOCH
o RA is defined with respect to the vernal equinox. However the
earth’s rotation axis precesses with a period of about 26,000 years.
The rotation axis moves in a circle of ~23.5 degrees.
o When you type in an RA and DEC into a telescope computer
system you must specify an epoch for the coordinate system.
Standard epochs include J2000 (Julian 2000). 1950 is also a
popular epoch. Whenever you write down astronomical
coordinates, you need to note the epoch of the coordinates.
o A TCS (telescope control system) computes the position of the
object after precessing the coordinates to the current epoch.
Converting between RA and DEC and
angular distance in radians
Often you want to know the distance between two
points on the sky which are specified in RA and DEC.
RA is typically given in hours, minutes and seconds.
On the equator (DEC=0), 24h=2π=360o. 60m=1h,
60s=1m.
However, for DEC≠0, 24h≠2π radians. You must take
into account the cosine of the DEC.
2π
1hour RA × cos (DEC) =
radians
24
Angular distances
Q. 1 second in RA is how
many arcseconds of angular
distance at a DEC of 45?
Q. 1 second in DEC is
equivalent to many
arcseconds?
42
Angular distances
Q. 1 second in RA is how
many arcseconds of angular
distance at a DEC of 45?
Answer:
24 hours in 2π radians unit of time!!!!!
360 degrees in 2π radians
60 minutes per hour, 60 seconds per minute
60 arcminutes per degree, 60 arc seconds per arc minute
To convert seconds to arcseconds 360/24 = 15
On the celestial equator there are 15 arc
seconds per second of time
43
Angular distances
Q. 1 second in RA is how
many arcseconds of angular
distance at a DEC of 45o?
Answer:
On the celestial equator there are 15 arc
seconds per second of time
Multiply by cos(45o) =1/√2
Answer: 15/√2 =10.6
There are 10.6 arc seconds per second of time in RA
at a DEC of 45 degrees
44
Angular distances
Q. 1 second in DEC is
equivalent to many
arcseconds?
45
Angular distances
Q. 1 second in DEC is
equivalent to many
arcseconds?
Answer: 1
DEC is in degrees, arc
seconds in DEC are true arc
seconds
46
Solid Angles, Spherical coordinates
𝜙 azimuthal angle (like longitude or RA)
𝜃 like latitude or DEC
dφ where φ ∈ [0,2π ] on equator
cos θ dφ off the equator
dθ
# π π$
θ ∈ '− , (
) 2 2*
Integrating Solid Angles
dA = cos θ dθ dφ
just as we needed the
cosine of the dec to
compute an angular
distance from the RA we
need it here to compute
solid angles
Integrating over the sphere
2π
A=
π /2
∫ dφ ∫
0
Area of solid angle
−π / 2
cos θ dθ = 2π × sin θ
A = 4π radians
π /2
]−π / 2 = 2π × 2
Props:
Celestial sphere
Dopper ball or whirly hose
Astroscan for looking at sunspots
49