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 ecliptic too, which is why they seem to follow the Sun’s path from east to west across the sky.

(This is not to scale! For example, Pluto’s average distancefrom the Sun is actually 100 times that of Mercury.)

planetary orbits

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.

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!

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Thus Orrerys are not built to scale in distance or in size, but the periods of revolution of the planets are represented to scale.

Or visit the Build a Solar System site athttp://www.exploratorium.edu/ronh/solar_system/index.htmlwhere 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.

On the Internet site, you can visit a “virtual Orrery” at Solar System Live at http://www.fourmilab.ch/solar/solar.html

Astronomers define a convenient unit of length:The AU (astronomical unit) = average distance between Sun and Earth = 1.496 x 1011 m

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 ofthe average Earth–Sun separation.

1 AU

In order of distance from the Sun, the planets are (not to scale!):

Mercury, 0.39 AU from the Sunon average

Venus, 0.72 AU from the Sunon average

Earth, 1.00 AU from the Sunon average (by definition!)

Mars, 1.52 AU from the Sunon average

Jupiter, 5.20 AU from the Sunon average

Saturn, 9.54 AU from the Sunon average

Uranus, 19.2 AU from the Sunon average

Neptune, 30.0 AU from the Sunon average

Pluto & its companion Charon, 39.5 AU from the Sunon average

Pluto is usually the furthest planet from the Sun, but itseccentric orbit brings it closer than Neptune on occasion- for example, between Jan 21, 1979 and Mar 14, 1999.

(b) Phases of the innermost planets

The innermost planets, Mercury and Venus, never stray very far from the Sun from our vantage point on Earth.

The Sun illuminates one side of each planet: dependingon where Mercury and Venus are in relation to the Earthand the Sun, they exhibit phases just like the phases of the Moon.

For example, here is Venus viewed “side-on” from the Sun, 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/

To see how this comes about, follow this link to a simulation which demonstrates the phases of Venus.

Earth

gibbous gibbous

crescent crescent

halfhalf

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.

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 inthe sky at the same time each night, over a period of many months, it will appear to move along the ecliptic, then, at some stage, it will appear to “loop the loop”

(c) Retrograde Motion

Retrograde motion caused great difficulties in the past to natural philosophers who tried to model the Solar System as being centred on 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.

Then retrograde motion is analogous to the effect ofpassing another car travelling on the inside lane of a freeway - the other car appears to be going backwards.

To see how retrograding comes about, click here to see an animation illustrating the retrograde 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).

They then “over take” the Earth and temporarily appear to have an east to west motion relative to the background stars.

orbit of interior planet

inferior conjunction

superior conjunction

Apparent retrograde motion of Venus

VenusEarth

Background stars

Retrograde motion of an inferior planet near inferior conjunction as the planets “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).

orbit of superior planet

opposition

conjunction

In this case the Earth “over takes” the planet.

Apparent retrograde motion of Mars

MarsEarth

Background stars

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 that on Earth:

In order of distance from the Sun, the planets are (again, not to scale):

On Mercury, the length of the sidereal dayis 59 Earth days.

On Venus, the length of the sidereal dayis 243 Earth days.

On Earth, the length of the sidereal dayis (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 dayis 1.03 Earth days .

On Jupiter, the length of the sidereal dayis 0.41 Earth days.

On Saturn, the length of the sidereal dayis 0.43 Earth days.

On Uranus, the length of the sidereal dayis 0.72 Earth days.

Note the angle of the rotation axis of Uranus- as we will see in a later Module, Uranus rotateson its side, which gives it very unusual days & nights!

On Neptune, the length of the sidereal dayis 0.67 Earth days.

On Pluto & its companion Charon, the length of the sidereal dayis 6.4 Earth days.

(Pluto rotates almost on its side too.)

As you can see, there is no particular pattern in the length of days on 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:

Planet (Sidereal) Year

If we express each planet’s orbital period as multiples of Earth years ...

Mercury 0.241

Venus 0.615

Earth 1.00

Mars 1.88

Jupiter 11.9

Saturn 29.5

Uranus 84.0

Neptune 165

Pluto 249

Planet Orbital Speed (km/s)

… and also compare their average orbital speeds ...

Mercury 47.9

Venus 35.03

Earth 29.79

Mars 24.13

Jupiter 13.06

Saturn 9.64

Uranus 6.81

Neptune 5.43

Pluto 4.73

… we can see that the length of planetary years increases and the orbital speed decreases as one moves out from the neighbourhood of the Sun.

We’ll investigate this trend in the next Activity.

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

Image Credits

Now return to the Module home page, and read more about planetary motion in the Textbook

Readings.

Hit the Esc key (escape) to return to the Module 3 Home Page