The orbit of Halley s Comet

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1 The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758

2 Questions: How close does HC approach the Sun? What is the orbital eccentricity? From Kepler s 3 rd law: P 2 (yr) = a 3 (AU) So, a 3 (AU) = 76 x 76 = 5776 Hence a(au) = (5776) 1/3 = By definition: perihelion distance + aphelion distance = 2a So, we have: Perihelion distance = 2a aphelion distance = 2x Which gives Perihelion distance = 0.58 (AU) Closer than orbit of Venus to the Sun

3 Definition: Eccentricity (e) e = OF / a OF Aphelion (35.3 AU) a Sun 0.58 AU Perihelion distance perihelion a = AU By construction: a = perihelion distance + OF Hence: OF = a perihelion distance = = AU And, accordingly, eccentricity e = / = 0.96

4 From last class Kepler s laws of Planetary Motion 1 st law: The planets revolve around the Sun along elliptical orbits with the Sun at one focus 2 nd law: A line drawn from the planet to the Sun sweeps out equal areas in equal time 3 rd law: The square of a planets orbital period P is proportional to the cube of its orbital semimajor axis a P 2 (yr) = a 3 (AU)

5 Last seen in 1986 back in 2061 OF Perihelion distance Aphelion a Sun perihelion Summing up For Halley s comet Orbital period = 76 years Semi-major axis a = AU Perihelion distance = 0.58 AU Aphelion distance = 35.3 AU Sun displacement from center OF = AU eccentricity e = 0.96

6 Isaac Newton ( ) Mathematician, Alchemist Biblical Scholar Physicist Master of the Mint Basically a spherically clever guy

7 Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light Alexander Pope F gravity G m M 2 R

8 Newton s genius Same physics everywhere in the lab, in the Solar System and anywhere else in the Universe in other words we can measure and understand the physics of the cosmos around us He argued: The rules describing the acceleration of objects falling on the Earth can also describe the motion of the planets Hypothesis: Newton, 1687: There is a gravitational attraction between all of the planets and the Sun

9 Keeping the planets in their place Newton s 1 st law of motion A body will remain at rest or in constant motion along a straight line path unless acted upon by an external force In reality, a planet is continuously accelerated towards the Sun by a gravitational force It is this continuous gravitational interaction that causes a planet to follow an elliptical orbit rather than a straight line path through space

10 Hammer Time When the athlete lets go of the tether, the ball flies off along a straight line path it doesn t keep going in a circle the tether is our gravitational pull analog

11 In each second the Moon falls 1.4 mm towards the Earth (away from straight line path) and moves 1 km around its orbit the Moon is continuously falling towards Earth, or more correctly from the straight line path it would otherwise have if there were no gravity Moon Path of Moon without gravity F g Path of Moon with gravity (orbit) Earth Not only does gravity explain planetary orbits, it also explains Kepler s 2 nd and 3 rd laws

12 Kepler s 3rd law. Newton style Cutting to the chase - Newton showed: P 2 /a 3 = K = 4p 2 / G(M Sun + M Planet ) In other words, Newton found that the constant K in K3 is related to the system mass Units are now kilograms, meters and seconds (the SI units of measure) G is the universal gravitational constant

13 The Moons of Mars: Phobos and Deimos

14 Phobos Period = hours Orbital radius = 9400 km Moon diameter is about 20 km Discovered by Asaph Hall in 1877

15 Weighing Mars M Mars + M phobos = (4p 2 ) a 3 / G P 2 Kepler s 3 rd law with Newton s modification Can safely assume M Mars >> M Phobos so, using SI units (meters, sec., kg) M Mars = (4p 2 ) (9.4x10 6 ) 3 / G (7.656 x 3600) 2 = 6.6 x kg = 1/10 th M Earth

16 Not just for planets Provided a measure of the size of the orbit (a) and the orbital period (P) can be made K3 as formulated by Newton can be used to find the masses of astronomical objects.. Later on we will weigh the stars as well as the entire Milky Way Galaxy using K3

17 We now have a set of tools and laws to describe: 1. Motion on the sky the celestial sphere (ecliptic) 2. The distances to the planets and the scale of the Solar System Copernicus s method for inferior planets and the Big Result formula 3. Orbital shape semi-major axis and eccentricity 4. Planetary motion Kepler s three laws 5. The mass of a planet if it has a moon Newton s refinement to K3 Our next task is to take an inventory of the Solar System what exactly is it and what kind of objects does it contain?

18 The contents The Solar System is a dynamic collection of many hundreds of thousands of objects: The Sun, planets, dwarf planets, moons, asteroids, comets, Kuiper-belt objects, meteoroids, dust grains. Also: magnetic fields, radiation (light), cosmic rays The planets are the largest objects (next to the Sun) in the Solar System but the definition for planetary status is not simple (or even agreed upon) Eight classical planets are recognized: Mercury Neptune and five dwarf planets: Ceres, Pluto, Eris, Makemake & Haumea

19 Inner solar system planets Outer solar system planets Dwarf planets

20 From last class Discussed Newton s result WRT Kepler s 3 rd law observations of period and orbit size enable derivation of system mass our astronomical weigh scale Discussed the scale and extent of the Solar System - Introduced the Kuiper Belt and Oort Cloud regions of the outer Solar System Kuiper belt = disc-like distribution of small ice/rock worlds beyond Pluto stretches out to ~ 20,000 AU Oort cloud = outer most boundary of the Solar System (where gravity of the Sun is less than the other stars in the rest of the galaxy) - located at ~ 100,000 AU from the Sun

21 200,000 AU The scale of the Solar System Oort Cloud KB Oort Cloud named after Jan Oort (1950) vast reservoir of comets surrounding Sun (spherical halo of objects) Comets can enter the inner solar system at any angle Kuiper Belt Sun Pluto 40 AU 20,000 AU Kuiper Belt named after Gerald Kuiper (1951) disk like distribution of large ice / rock objects - with Pluto being the first such object discovered (1930)

22 Light travel time across the Oort Cloud Kuiper belt distance velocity time OOTETK Velocity = speed of light Distance ~ 200,000 AU Meters in 1 AU Time = distance / velocity = 200,000 x x / 3 x 10 8 = 9.97 x 10 7 seconds = 3.16 years The solar system is BIG!!... Way big

23 By any other name. Conditions for planetary status: IAU (August 2006) definition: International Astronomical Union 1. Object must orbit the Sun 2. Large enough to be spherical through its own gravity (this is a size / mass constraint) 3. Must have cleared its region of the solar system of other smaller objects i.e., it is the dominant gravitational object in its region

24 Dwarf Planets Minor planet designation An object that satisfies conditions 1 and 2 for a planet but not condition 3 Dwarf planets presently recognized: Ceres formerly the largest asteroid» (historically a former planet) Pluto formerly a planet (discovered 1930) Eris discovered 2003 Makemake - discovered 2005 Haumea discovered 2004 Let s just have his head and be done with it

25 Moon Planets Haumea Dwarf planets Pluto Makemake Ceres Eris

26 The Solar System Ceres (dwarf planet) Pluto Eris Makemake Haumea Physical properties

27 The Main Components Are: Sun The nearest star to us. ~ 8% of all stars are Sun-like stars Accounts for 99.9% of the mass of the solar system Planets Terrestrial planets: Mercury Mars Small, rocky (metal core) worlds with orbits less than 2 AU from the Sun Jovian planets: Jupiter Neptune Large, mostly gas-giant planets with orbits greater than 5 AU from the Sun

28 Outer Solar System Inner Solar System Terrestrial planets: closely packed orbits Small, rock/iron worlds Jovian planets: widely spaced orbits Large, gas giant worlds

29 Dwarf Planets Ceres aside DPs have orbits beyond Neptune Pluto is essentially the first of the Dwarf Planets Have orbits beyond 35 AU Also called Made predominantly of rock and ice Plutoids Sizes smaller than Earth s Moon (< 3000 km) It is possible that large (Earth-sized) DPs exist but none have so far been detected Move in the Kuiper Belt region and can undergo collisions with KBOs producing cometary fragments Presently 5 Dwarf Planets officially recognized, dozens, even many hundreds more awaiting discovery

30 2390 km Greek Goddess Ruler of the underworld Hawaiian Gods of childbirth and fertility Roman Goddess

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