Transcript Tracking the Planets - Lincoln

Module 3:
The Celestial Sphere
Activity 2:
Tracking the Planets
Summary
In this Activity, we will investigate
(a) planetary distances,
(b) phases of the innermost planets,
(c) retrograde motion of the outer planets, and
(d) orbital and rotational periods.
(a) Planetary Distances
The apparent motions of the planets (or “wanderers”)
across our nighttime sky does not coincide with the
regular rotation of the stars around the celestial poles.
Instead their motions fall in a narrow band around the
ecliptic, which, as we saw in the Activity Star Patterns,
is the Sun’s path across the sky.
Remember that the plane of the ecliptic is an imaginary
planar surface in space containing the Earth’s orbit and
the Sun:
The other planets’ orbits are in, or close to, the plane of
the ecliptic too, which is why they seem to follow the
Sun’s path from east to west across the sky.
planetary orbits
(This is not to scale! For example, Pluto’s average distance
from the Sun is actually 100 times that of Mercury.)
If mechanical Orrerys like this
were built to scale, then even if
the diameter of Mercury was
chosen to be only 1mm, then the
Sun’s diameter would need to be
30cm, and the distance from the
Sun to Saturn would be
approximately 29 metres!
© Brian Greig 1998
It’s very difficult to draw a scale model of planetary orbits in our
Solar System, because of the vast extremes of scale. For
example, the orbits of the outer five planets occupy a radius of
about 19 times that occupied by the four inner planets.
Thus Orrerys are not built to scale in distance or in size, but the
periods of revolution of the planets are represented to scale.
On the Internet, you can visit a “virtual Orrery” at Solar
System Live at http://www.fourmilab.ch/solar/solar.html
Or visit the Build a Solar System site at
http://www.exploratorium.edu/ronh/solar_system/index.html
where you can build your own scale model of the Solar
System. You will be asked to nominate a size for the Sun,
and the Solar System builder will then work out for you the
sizes of and distances to all the planets to scale.
Distances in the Solar System are in fact very large!
To compare the average distances between the Sun and
each of the planets, it’s convenient to do it in terms of
the average Earth–Sun separation.
As we saw before, astronomers define a convenient
unit of length:
The AU (astronomical unit)
= average distance between Sun and Earth
= 1.496 x 1011 m
1 AU
In order of distance from the Sun, the planets are (not to
scale!):
Mercury,
0.39 AU from the Sun
on average
Venus,
0.72 AU from the Sun
on average
Earth,
1.00 AU from the Sun
on average
(by definition!)
Mars,
1.52 AU from the Sun
on average
Jupiter,
5.20 AU from the Sun
on average
Saturn,
9.54 AU from the Sun
on average
Uranus,
19.2 AU from the Sun
on average
Neptune,
30.0 AU from the Sun
on average
Pluto & its companion Charon,
39.5 AU from the Sun
on average
Pluto is usually the furthest planet from the Sun, but its
eccentric orbit brings it closer than Neptune on occasion
- for example, between Jan 21, 1979 and Mar 14, 1999.
(b) Phases of the innermost planets
From our vantage point on Earth, the innermost planets,
Mercury and Venus, never stray very far from the Sun.
The Sun illuminates one side of each planet and,
depending on the position of Mercury and Venus in
relation to the Earth and the Sun, they exhibit phases,
just like the Moon.
For example, here is
Venus illuminated from
the side by the Sun.
This image was captured
by the Hubble Space
Telescope in ultraviolet
light.
For images and a movie of the phases of Venus, visit:
http://www.calvin.edu/academic/phys/observatory/images/venus/
When Venus is on the same side of the Sun as the Earth,
we see it in crescent phase with a large angular size.
When Venus is on the opposite side of the Sun, in gibbous
or nearly full phase, its angular size is small.
gibbous
gibbous
half
half
crescent
crescent
Earth
To see how this comes about, follow this link to a
simulation which demonstrates the phases of Venus.
(c) Retrograde Motion
Mars, Jupiter, Saturn (& Uranus, Neptune and Pluto)
wander far from the Sun, always appearing close to ‘full’
phase, but showing, at times, retrograde motion.
For example, if we keep track of the position of Mars in
the sky at the same time each night, over a period of
many months, it will appear to move along the ecliptic.
But, at some stage, it will appear to “loop the loop”:
Retrograde motion created headaches for the natural
philosophers who tried to model the Solar System as
being centred on the Earth.
However, retrograde motion is easily explained in the
heliocentric model, where the planets travel in elliptical
(& nearly circular) orbits around the Sun with each planet
travelling more slowly as we move out from the Sun.
Retrograde motion is then analogous to the effect of
passing another car travelling on the inside lane of a
freeway - the other car appears to be going backwards.
To see how retrograde motion comes about, click here to
see an animation illustrating the motion of Mars.
What about the inner planets - Venus and Mercury? Do
you think that they too can exhibit retrograde motion?
It turns out that they can. The
inferior planets (meaning those
planets inside the orbit of the
Earth – Venus and Mercury)
exhibit apparent retrograde
motion when at inferior
conjunction (passing between the
Earth and the Sun).
inferior
conjunction
superior
conjunction
orbit of interior planet
They then “overtake” the Earth and temporarily appear to
have an east to west motion relative to the background stars.
Apparent retrograde motion of Venus
Background stars
Venus
Earth
Retrograde motion of
an inferior planet near
inferior conjunction as
the planet “overtakes
the Earth on the inside
lane”.
The superior planets (with orbits outside that of the Earth
– so Mars, Jupiter & Saturn) appear to move “backwards”
at opposition (when both planets are on the same side of
the Sun).
In this case the
Earth “overtakes”
the planet.
opposition
conjunction
orbit of superior planet
Apparent retrograde motion of Mars
Background stars
Mars
Earth
Retrograde motion
of a superior planet
near opposition,
as the Earth
“overtakes on the
inside lane”.
(d) Orbital & Rotational Periods
Just as the Earth rotates
around a rotational axis ...
… so do the other planets. This rotation produces day
and night on these planets too, but as we will see, the
length of the day - the rotational period - can be quite
different on other planets to what we have here on
Earth!
In order of distance from the Sun, the planets are
(again, not to scale):
On Mercury,
the length of the sidereal day
is 59 Earth days.
On Venus,
the length of the sidereal day
is 243 Earth days.
On Earth,
the length of the sidereal day
is (almost) 1 Earth day.*
* In the last Activity we saw that a sidereal day is
about 4 minutes shorter than a mean solar day on Earth.
On Mars,
the length of the sidereal day
is 1.03 Earth days .
On Jupiter,
the length of the sidereal day
is 0.41 Earth days.
On Saturn,
the length of the sidereal day
is 0.43 Earth days.
On Uranus,
the length of the sidereal day
is 0.72 Earth days.
Note the angle of the rotation axis of Uranus
- as we will see in a later Module, Uranus rotates
on its side, which gives it very unusual days & nights!
On Neptune,
the length of the sidereal day
is 0.67 Earth days.
On Pluto & its companion
Charon,
the length of the sidereal day
is 6.4 Earth days.
(Pluto rotates almost on its side too.)
As you can see, there is no particular pattern in the
length of the days for the planets in our Solar System.
However, the lengths of planetary sidereal years
- their orbital periods - do show a general trend, and so
do the speeds with which they orbit the Sun:
If we express each planet’s orbital period as multiples of
Earth years ...
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
(Sidereal) Year
0.241
0.615
1.00
1.88
11.9
29.5
84.0
165
249
… and also compare their average orbital speeds ...
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Orbital Speed (km/s)
47.9
35.03
29.79
24.13
13.06
9.64
6.81
5.43
4.73
… we can see that the length of planetary years
increases and the orbital speed decreases as one
moves out in distance from the Sun.
We’ll investigate this trend in the next Activity.
Image Credits
NASA: Mercury
http://pds.jpl.nasa.gov/planets/welcome/thumb/merglobe.gif
NASA: Venus
http://pds.jpl.nasa.gov/planets/welcome/thumb/venglobe.gif
NASA: Earth
http://pds.jpl.nasa.gov/planets/welcome/earth.htm
NASA: Mars
http://pds.jpl.nasa.gov/planets/welcome/thumb/marglobe.gif
NASA: Jupiter
http://pds.jpl.nasa.gov/planets/welcome/thumb/jupglobe.gif
NASA: Saturn
http://pds.jpl.nasa.gov/planets/welcome/thumb/2moons.gif
Image Credits
NASA: Uranus
http://pds.jpl.nasa.gov/planets/welcome/thumb/uraglobe.gif
NASA: Neptune http://pds.jpl.nasa.gov/planets/welcome/thumb/nepglobe.gif
NASA: Pluto & Charon
http://pds.jpl.nasa.gov/planets/welcome/thumb/plutoch.gif
NASA: Ultraviolet image of Venus' clouds as seen by HST's Wide-Field
/Planetary Camera 2. (NASA Photo Numbers STScI-PRC95-16, 95-HC-114)
http://nssdc.gsfc.nasa.gov/image/planetary/venus/hst_venus95.jpg
A Brian Greig Orrery © Brian Greig 1998 (used with permission)
www.planetariums.com
Now return to the Module home page, and read
more about planetary motion in the Textbook
Readings.
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