Wednesday 11 February 2009

Asteroids and comets in inner solar system I "Snapshot" of the positions of several thousand asteroids (dots) and a few dozen comets (arrow heads) at some particular time. The two groups of asteroids 60 degrees on either side of Jupiter are the Trojan asteroids. These are located around the L4 and L5 Lagrange points of the Sun- Jupiter system. The Trojans need not be located exactly at the L4 or L5 points- they can wander around the L points quite a bit, but still be in 1:1 resonance with Jupiter (that is, have same period around Sun as Jupiter.) This explains the extended nature of the two Trojan "clouds" of objects.

The vast majority of the asteroids are located in the main asteroid belt between the orbits of Mars and Jupiter, but you can see some located interior to the Earth's orbit- these are called Earth Crossing Asteroids (ECAs).

Asteroids and comets in inner solar system II Similar to previous, but only for region out to inner region of main asteroid belt. The Sun is at center (we all know stars have 5 points, right??) The first ellipse is orbit of Mercury (note it is significantly non-circular), then Venus, Earth and Mars. Green dots are main belt asteroids. Red dots are asteroids that have perihelia less than 1.3 Au. These are often called "Near Earth Asteroids" (NEAs).

Now, of course, the size of the dots are not in scale to the distances! Otherwise, the objects would be touching! Sizes of asteroids ranges up to 1000 kilometers (50 km is a "typical" size) but the typical distances between asteroids are millions of kilometers.

Asteroids and comets in inner solar system III Similar to previous, but also highlighting the Hildas (dots in orange). See plot after next for more info Hildas.

Hildas The Hildas are objects in 3:2 resonance with Jupiter- that is, they each have an orbital peiod about 2/3 that of Jupiter, or about 7.9 years. Each object orbits the Sun in 7.9 years, but the triangular PATTERN rotates along with Jupiter- every 11.9 years.

Lagrange points of Sun-Earth system.. In a system consisting of a very massive object and a moderately massive object (like a star and an orbiting planet) there are 5 points where a low mass body can orbit the massive body with the same period as the moderate mass body. These are called Lagrange points. The L4 and L5 points are stable- the Jovian Trojan asteroids are located around the L4 and L5 points of the Sun-Jupiter system. There was a famous space society (well, famous to space geeks!) called the L5 Society which was formed in 1975 to promote space colony ideas. The L1 and L2 points of Earth-Sun system have been used as places to "park" satellites for special purposes (e.g. SOHO, a satellite to study the Sun, is at L1, and WMAP, a satellite to study the cosmic microwave background, is at L2). The L1 and L2 (and L3) points are unstable, but a satellite can be made to stay near one of these points by occasional corrections using small thrusting jets on the satellite. Satellites at L1 and L2 stay in the same place relative to Earth, making communication easier, but are far enough from Earth that the Earth doesn't block much of the sky (and L1 of course offers a continuously unobstructed view of the Sun). As far as we know, there are no natural objects at the Earth's L3 point, but it always behind the Sun as seen from Earth (also the point is unstable, so we would not expect objects to stay there if they got there). Because it would be hard to observe anything that is located at L3, the L3 point is a place where science fiction authors (and occasionally other forms of wacky folks!!) like to place "alien planets" etc.

In this diagram, the sizes of the Earth, Sun and Moon, size of Moons orbit around the Earth and the distance from Earth to the L2 point are NOT to scale with the Sun-Earth distance. The diameter of the Moons orbit around Earth is about 1/200 of the Earth-Sun distance, and the Earth-L2 distance is about 1/60 the Earth-Sun distance. (And the size of the spacecraft is *SERIOUSLY* NOT TO SCALE with Earth-Sun distance- or the size of Earth!!)

Further readable info on Lagrange points can be found here.

Kirkwood gaps.. A histogram of the semi-major axes of asteroids show gaps at periods which are a small integer ratio to the period of Jupiter. These are called Kirkwood gaps. They are caused by resonant effects of Jupiter preferentially removing asteroids at these periods. Note that the gaps do NOT show up in a snapshot of the positions of asteroids at any time (see asteroid position image above). This is because the eccentricity of asteroid orbits means that the distance from the Sun of an asteroid at any one time is not equal to its semimajor axis. IF all asteroids had circular orbits with the a distribution as given in the diagram, then we WOULD see "gaps" in asteroid position "snapshot" (like we see gaps in Saturns rings due to resonant effects- see image below).

Pluto and Neptune orbits Pluto's orbit has a=39.5AU, e=0.25, i = 17 degrees. Neptune's has a=30.1AU, e=0.01, i=2 degrees. The high (for a planet) e of Pluto means that it spends part of its orbit closer to Sun than Neptune!!

Pluto - Neptune resonance Pluto has a rather eccentric orbit (eccentric for a planet, that is, not eccentric for a minor body such as an asteroid) that comes closer to the Sun than the orbit of Neptune. This sounds like a recipe for disaster- if relatively low-mass Pluto comes close to Neptune, it will collide with the much larger Neptune or be gravitationally scattered out of its orbit. So how can Pluto continue in its orbit? The answer is that Pluto and Neptune are in resonance. Pluto orbits the Sun 2 times for every 3 times that Neptune orbits the Sun. Carefully follow the diagram of the positions of Pluto and Neptune and you will see that, because of the resonance, Neptune is never near the position of Pluto when Pluto is near perihelion. The positions of Pluto (black dot) and Netune (blue dot) are shown at successive time steps differing by 0.5 times the length of Plutos orbit (which is equal to 0.75 times the length of Neptunes orbit).

Cassini Division in Saturns rings Even a small telescope will show the rings of Saturn. The rings look like a flat washer with a dark ring in it. This "gap" is called the Cassini Division. The position of the gap is at the 2:1 resonance with the Saturnian moon Mimas (The Death Star moon).

We will see *MUCH* better pictures of Saturn and its ring system later in course!