Module 3 The Celestial Sphere Activity 2 Tracking

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. 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 1 mm, then the Sun’s diameter would need to be 30 cm, 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 site, you can visit a “virtual Orrery” at Solar System Live at http: //www. fourmilab. ch/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. 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 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: depending on where Mercury and Venus are in relation to the Earth and 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/

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 half 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, then, at some stage, it will appear to “loop the loop”

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 of passing 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). inferior conjunction superior conjunction orbit of interior planet They then “over take” 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 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). In this case the Earth “over takes” 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 that 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 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:

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 from the neighbourhood of 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/2 moons. 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 STSc. I-PRC 95 -16, 95 -HC-114) http: //nssdc. gsfc. nasa. gov/image/planetary/venus/hst_venus 95. 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. Hit the Esc key (escape) to return to the Module 3 Home Page