Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
PHY2083 ASTRONOMY Tides THE DIMENSIONS OF THE SOLAR SYSTEM Using Kepler’s Laws, we can construct a model of the solar system with the correct shapes of the orbits, and correct relative sizes. The actual sizes cannot be obtained from Kepler’s laws => What is 1 AU? 1 AU = ? Early measurements from transiting inner (i.e. Mercury or Venus) planets + geometry Transit times can be measured very accurately from different locations on the Earth Transit of Mercury (2003) Extreme UV λ 1 AU = ? If we know the distance to Venus, we can work out the value of 1 AU. Aim to measure the distance to Venus when it is closest to the Earth using Radio Detection And Ranging (RADAR) 0.3 AU = 45 x 106 km => 1 AU = ? Why can’t we use RADAR to measure the distance to the Sun? Kepler’s laws were derived empirically i.e. from an analysis of Tycho’s observational data. Newton’s Laws + Gravity Isaac Newton Kepler’s laws do not explain why the planets revolve around the Sun and do not fly off into space. Planet Found in Nearest Star System to Earth M ~ 1.14 M_Earth d ~ 4 light-years radial velocity ~ 51cm/s P ~ 3.2d 1 AU 0.04 AU 0.4 AU SUMMARY Kepler’s 3 Laws: I Orbits are ellipses II The rate of change of area swept by a line connecting a body to the focus of its elliptical orbit = constant ∝ (semi-major axis)3 and Period ∝ 1/(total mass) III (Period)2 Orbital velocity ∝ 1/(semi-major axis)1/2 Black Hole Orbits The solar system Terrestrial (Earth-like) planets Jovian (Jupiter-like) planets TERRESTRIAL JOVIAN Basic Form Rock Gas/Ice/Rock Mean orbital dist. (AU) 0.4-1.5 5.2-30 Mean surface temp. (K) 215-733 70-165 Mass (Earth-masses) 0.055-1.0 14.5-318 Equatorial radius (Earth-radii) 0.38-1.0 3.88-11.2 Mean density kg/m3 3933-5515 687-1638 Rotation period (equator) 23.9h--243d 9.9h-17.2h No. of moons 0-2 13-63+ Ring systems no yes Rotation axes: why? Tidal Forces For Kepler’s laws, we treated the stars etc. as point masses, and assumed that they were spherically symmetric. Tidal Forces One side of the moon is closer to the Earth than the opposite side. Newton’s 3rd law => same must happen on Earth => differential forces => non-spherical shape m M dr r Lunar and Solar Tides Sun also exerts a force on Earth => 2 tidal bulges: one pointing towards the moon, and one towards the Sun. Sun x375 further away, but 27 million times more massive! Lunar and Solar Tides • Tidal bulges not directly aligned with the moon, because rotation period of Earth slightly shorter than rotation period of the moon. • Frictional forces drag the bulge axis ahead of the Earth-Moon line. Dissipative force => rotational KE being lost => Earth’s spin rate is being slowed down 0.0016s / century • Frictional forces drag the bulge axis ahead of the Earth-Moon line. Dissipative force => rotational KE being lost => Earth’s spin rate is being slowed down 0.0016s / century • Some of this energy transferred to the moon c.f. fairground ride (faster spin, larger force outwards) • => Moon is moving away from Earth at the rate of ~3.8 cm per year • Newly-formed Earth: 1 day ~ 5 hours • Moon much closer to the Earth • Braking force due to moon over 4.5bn years => 1day = 24h • Coral records • Slow-down of Earth’s rotation => same side of Earth will face the moon => travel half-way around the world to see the moon! “synchronous rotation” (c.f. Martian moons) • Consequences for humans?! • Triton giant moon of Neptune is in synchronous rotation, but retrograde orbit => tidal bulges are causing it to spiral inwards • ---> Roche limits The Big Bang Theory (excerpt) Summary from last lecture: Tidal forces: • Gravitational force proportional to r • This results in a differential force (and therefore a -2 differential acceleration). Proportional to r-3 • For the Earth-Moon system, energy is lost through tidal friction => rotation rate of Earth slowing down • Conservation of angular momentum => moon is being pushed further away from Earth Summary cont’d: • Synchronous orbit: orbiting body (e.g. moon) has a period equal to the body that it is orbiting (e.g. Earth) • This results in tidal-locking i.e. same side of body faces the other. • Interesting case of Triton, the giant moon of Neptune which is in a retrograde orbit. Tidal bulges such that Triton is slowly spiralling inwards towards Neptune. (c.f. recent Earth-mass planet) Summary cont’d: Prograde vs Retrograde Roche Limits R r µ d At some distance, the tidal force lifting the rock from the surface F (tidal) = F(grav.). Remember: differential force goes as r-3 so as r decreases, tidal forces get more severe R r µ d Example 1: Interacting Binary Star “Spaghettification” Ma gra teria vit l di ati rec on al ted a for ce long ve cto r Example 2: Tidal forces near a black hole Example 3: Comet Shoemaker-Levy 9 Example 4: Saturn’s Rings RP 2.5RP Example 4: Saturn’s Rings Average density of Saturn ~ 687 kg/m3 Radius (Saturn) ~ 6 x 107 m For a typical moon density ~ 1200 kg / m3, can calculate Roche limit. => Ring system lies within this limit, larger moons are further out.