Transcript The Sun: Ruler of the Solar System

Swinburne Online Education Exploring the Solar System
Module 19: The Sun
Activity 2:
The Sun:
Ruler of the
Solar System
© Swinburne University of Technology
Summary:
In this Activity, we will investigate
(a) the composition of the Sun...
(b) the mass of the Sun ...
(c) how the Sun “works” ...
What is the Sun
made of?
What shape is it,
and why?
... and the masses
of other stars and
planets
… how the mass
of the Sun can
be measured
…at least, how people used to think that
the Sun produces energy
(a) What the Sun is made of ...
We’ll start by learning what the Sun is composed of.
The composition of the Sun will help to explain why the
Sun is the shape it is, and (in the next Module) how the
Sun manages to emit such an enormous amount of
energy over such an incredible length of time.
Composition of the Sun
The average density of the Sun is 1410 kg m-3 (kilograms
per cubic metre), ranging from 160,000 kg m-3 at the core
to almost nothing at the corona.
For comparison:
Sun
1410 kg m-3
Jupiter 1400 kg m-3
Saturn
690 kg m-3
H H
H HO
HHe
HC
H
HHeH C O
HH He
H HHHe
Earth
Mars
Moon
Why is it so?
The diagram to the left might
give you a hint …
5520 kg m-3
3900 kg m-3
3340 kg m-3
What do the H,
He, O and C
mean?
The reason: some objects in the Solar System are mostly solid and
comprised of heavier elements, while other objects are comprised
entirely or almost entirely of gas.
Even if that gas is sometimes extremely compressed, it is far less
dense than a solid made of heavier elements.
It is pretty obvious which of the bodies listed below consist mostly of
gas.
“Jovian”,
mostly
gas
Sun
1410 kg m-3
Mercury 5440 kg m-3
Jupiter 1340 kg m-3
Venus 5240 kg m-3
Saturn
690 kg m-3
Earth
5497 kg m-3
Uranus 1190 kg m-3
Moon
3360 kg m-3
Neptune 1660 kg m-3
Mars
3940 kg m-3
Pluto
(uncertain: 2000?)
“Terrestrial”,
mostly
solid
The density of water is (by definition) 1000 kg m-3.
The planet Saturn (690 kg m-3) is less dense than water.
If you had an ocean large enough, Saturn would float on it!
The Sun is made up almost entirely
of hydrogen (72%) and helium
(26%), while other elements make
up the remaining 2%.
He
26%
other
2%
H
72%
For example, for every million hydrogen atoms in the Sun,
there are about 90,000 helium atoms … and only about
690 oxygen
420 carbon
87 nitrogen
45 silicon
40 magnesium
37 neon
32 iron
(and traces of
many others)
(b) Mass of the Sun
The mass of the Sun is 1.989 x 1030 kg, or about 300,000
times that of the Earth.
However, the radius of the Sun is about 100 times that of
the Earth; therefore, its volume is about 1,000,000 times
that of Earth.
The reason: the Sun is made up mostly of light
elements such as hydrogen and helium, while
the Earth is made mostly of heavy elements
such as iron.
Measuring the Mass of the Sun
How on Earth can we measure the mass of
the Sun?
It is not possible to “weigh” the Sun, but its
effect on the planets can be used to estimate
its mass.
To understand this further, we will have to
have a look at gravitational force and how it
depends on mass.
Newton’s Law of Gravitational Attraction
Isaac Newton discovered an important fact about
gravitational force a long time ago.
If two bodies share a gravitational attraction,
the force of attraction depends on both of their
masses.
Show
me the
equation!
On Earth, we call this gravitational attraction “weight”. It
depends on the masses of both the planet and the object
you are weighing.
Weight depends on where you are
m
M
2m
600 N
Chris feels a
gravitational force
of 600 N on Earth.
M
m
1200 N
If Chris doubles in
mass, the gravitational
force will double:
1200 N.
1/80M
100 N
0.27R
If, on the other hand,
Chris moves to the Moon,
which has a smaller mass
and radius, the
gravitational force will
decrease by 5/6 to 100N.
To remind you again: if any two bodies share a gravitational attraction, that
attraction depends on the masses of both of them and their separation (in
fact its another inverse square law).
Interesting, but … we need more!
Now, this principle is very useful in astronomy.
If we know
In practice astronomers combine Newton’s
lawthe
of distance
gravitation
to the Sun, the velocity
with his other laws, like F=ma (Force is equal to mass times
of the Earth and Newton’s
acceleration) and the fact that in order
to stay
circular
motion
Constant
we in
can
calculate
the force required is mv2/R where m, the
v and
R are
the
mass,
mass
of the
Sun
!
velocity and distance to an object.
Force
to
The basic idea is that the
gravitational
force between
Gravitational
a
objects
must equal theremain
force in
required
to keep the objects
Force
circular
in their orbits. If one star orbit!
is very much heavier than the
other:
Kepler’s Third Law
Kepler discovered that the planets travel around the
Sun in such a way that the time required to complete
one orbit was independent of their mass, and only
dependent upon their distance from the Sun.
The same is true for the orbit of satellites around the Earth,
i.e. it depends only on the mass of the Earth and the satellite
distance — and not on the mass of the satellite at all!
R = radius of orbit, the distance
between the planet and the star
T = period of orbit, the time taken to
complete one revolution (i.e. a “year”)
Kepler’s third law states
is constant.
Same radius, same period
Astronauts in satellites and their lunches have very different masses, but that
doesn’t matter. Because they are at the same radius, they have the same
period of revolution.
Just as well: otherwise astronauts would lose their lunch (and anything else
they didn’t hang on to) quick smart.
Comment: The relationship between the orbit of a planet and the mass of its “parent” star
is promising.
Therefore, measuring the orbits of the planets (that is,
radius R and period T) can allow us to calculate the
mass of the Sun (provided that you know what the
constant G is)
This is why scientists in the 18th century were
so keen to measure the distance to
the Sun! Newton’s laws, coupled
with an accurate distance to
the Sun, led to the first measurements
of its mass of 2x1030 kg.
The Sun is so much more massive than anything else in
the Solar System.
1 Earth
mass
Jupiter:
318 Earth
masses
Sun:
300 000 Earth masses
(and not to scale!)
Masses of other bodies: binary systems
If the masses of two bodies orbiting each other are not
too different (e.g. in a binary star system, or the Earthand-Moon system) the masses of the two bodies can be
compared by measuring “perturbation” in their motions.
Click on the
corresponding picture
below to view animation.
Two possible ways to measure mass
In summary:
The period and radius of orbit
of a planet about a star
depend only on the mass of
the star.
This fact is useful in the Solar System,
as period and radius of orbit are not too
hard to measure.
If two bodies aren’t too different in mass, each clearly
revolves around the other. Comparing the radii of their
orbits allows you to compare their masses.
This fact is one of the key factors that helped astronomers
measure the masses of other stars - more later.
Shape of the Sun
Some ancient peoples
believed that the Sun
was round ...
… because it was a huge
ball of dung being rolled
across the sky by a beetle!
There are actually three forces
affecting the shape of the Sun,
causing it to be an oblate spheroid:
that is, a sphere or ball that is slightly squashed.
The three things that define the Sun’s shape are:
The gravitational forces between the
atoms in the Sun, causing it to collapse ...
(these forces will decrease as the Sun loses mass)
The pressure of gas within the Sun,
causing it to expand…
(this will depend on the temperature of the Sun)
The rotation of the Sun on its axis,
causing it to “belly out” around its equator.
(this should stay about the same during the Sun’s main
sequence lifetime)
(c) The Sun as a source of energy
The Sun emits enormous amounts of energy (including
energy in the form of matter) in many forms …
… so of course we humans, being curious, cold, and afraid of
the dark, have always wondered how it manages to do that.
protons, ions
visible light
electrons
other
electromagnetic
radiation
neutrinos
“solar wind”
How the Sun works
Many humans thought for thousands of
years that the Sun was actually a ball
of flame:
that is, that the heat and light from the
Sun came from chemical reactions,
just like the heat and light from a fire.
This cannot be so.
It can be shown that if the Sun were
fuelled by chemical reactions it could
never have survived for anything
approaching 5 billion years. It would
have burned up long ago.
Later on, when people became
more familiar with gases and the
relationship between volume,
temperature and pressure, they
thought that the Sun was radiating
heat and light because of
gravitational contraction.
Squeeze a ball of gas ...
… and it gets hotter
However,if this were so, the Sun could have managed to
radiate heat and light for only 15 million years …
and radioactive dating and other evidence suggests
that our Solar System is already about 5 billion years old.
Neither chemical combustion nor
gravitational collapse could
account for the enormous energy
output and the extended lifetime of
the Sun.
It was only very recently (in terms of the history of
science) that people came up with another, newer idea
to explain how the Sun works…
… and that deserves just about a whole chapter to itself.
So we’ve continued the story in the next Activity,
Solar is Nuclear.
The Sun in Summary 1
Distance from Earth
1 astronomical unit (AU)
Angular size from Earth
Radius
Mass
Surface temperature
Central temperature
100 x Earth's radius
300 000 x Earth's mass
20 x Earth's temperature
1.5 x 1011 m
32 arc minutes
(~0.5 degrees)
700,000 km
1.989 x 1030 kg
6000K
7
1.5 x 10 K
The Sun in Summary 2
Period of
rotation
Age
25 Earth days at
Equator
4.5-5 billion years
Surface
Composition
72% hydrogen,
26% helium, 2%
"heavy" elements
gas throughout
3.8 x 10 26 W
1370 watts/m 2
Interior
Luminosity
Flux at top of
Earth's
atmosphere
Image Credits
Burning pallets (reproduced with permission)
http://flame.cfr.nist.gov/fire/fires/pall/pa_840.gif
Johannes Kepler (reproduced with permission)
http://antwrp.gsfc.nasa.gov/apod/ap970913.html
Solar disk in broadband K Ca lines
Data courtesy of J. Harvey, National Solar Observatory (Tucson/Kitt Peak,
AZ).
http://www.hao.ucar.edu/public/slides/slide2.html
NASA: Blue sun
http://sohowww.nascom.nasa.gov/bestofsoho/
NASA: Transition Region and Coronal Explorer (TRACE) recording of the
Sun at 171 Angstrom, 24/8/98
http://sohowww.nascom.nasa.gov/data/synoptic/gif/980824/stra_00171_fd_19980824_1203.gif
HST: Saturn (colour-enhanced)
http://oposite.stsci.edu/pubinfo/pr/1998/18/content/9818x.jpg
Now return to the Module home page, and read
more about the Sun in the Textbook Readings.
Hit the Esc key (escape)
to return to the Module 19 Home Page
Chemical symbols
An element is a pure substance,
containing only one kind of atom (that
is, all atoms in this substance have the
same number of protons).
H = hydrogen
He = helium
O = oxygen
When astronomers, chemists, biologists
and other people working in the sciences
want to write about particular elements
such as hydrogen, helium, oxygen and so
on, they use a letter or letters which relate
to the Latin name for the substance.
C = carbon
Example:
CO2 = carbon dioxide
Back to
“Composition
of the Sun”
Gravitation: the equations
The equations that describe the gravitational force between two objects
with mass were first developed by Sir Isaac Newton (late 1600s).
Under most circumstances these well-established laws are perfectly adequate in
describing what we observe; it is only when extremely massive or fast-moving
objects are involved that we have to use the relativistic equations of Albert
Einstein instead.
Force between two objects with mass
Isaac Newton’s law of gravitation: The gravitational
force between two objects separated by a distance R,
one with mass M and the other with mass m, is given by:
G is the Universal
Gravitational Constant
Johannes Kepler’s third law: There is a fixed relationship
between the cube of the radius of a planet’s orbit and the square of
its period of orbit.
G and 4p2 are
constants
M is the mass of
the Sun
The ratio will depend only on the mass of the Sun (and some
universal constants).
A similar relationship holds in any star system, although if the
masses of the stars are comparable, it is slightly more complicated.
Johannes Kepler
Kepler lived from 1571 to 1630,
completing most of his most profound
and useful work after 1601, in Prague.
First Law: The orbits of planets are
ellipses, with the Sun at one focus.
Second Law: A line from a planet to
the Sun sweeps out equal areas in
equal times.
Third Law: The cube of the radius of a
planet’s orbit is directly related to the
square of its period of orbit.
[Alternatively, the quotient of these is
constant, within one solar system.]
G and 4p2 are
constants
M is the mass of
the Sun
Back to
“Measuring
the Mass”