Xi Zhang E&MS A261 <xiz@ucsc.edu> Planetary Discovery in the era of Spacecraft Exploration Xi Zhang E&MS A261 <xiz@ucsc.edu> TA: Szilard Gyalay <sgyalay@ucsc.edu>

Lecture notes will be posted before and after each lecture. Course Website: http://es.ucsc.edu/~xiz/file/EART8 Lecture notes will be posted before and after each lecture. Xi’s Office Hours: Monday/Friday, 4:00-5:00 p.m. or by appt. Discussion Sections (Mandatory, E&MS D258): (1) Tuesday, 6:00-7:00 p.m. (2) Thursday, 2:00-3:00 p.m.

Newton's three laws of motion 1. Object moves at constant velocity if no net force is acting. 2. Force = mass × acceleration 3. For every force there is an equal and opposite reaction force. Sir Isaac Newton (1642–1727)

Mass = Energy E = mc2 Mass itself is a form of energy: A small amount of mass can release a great deal of energy (for example, an A-bomb, an H- bomb, the sun). Concentrated energy can spontaneously turn into particles (for example, in particle accelerators). E = mc2 Albert Einstein (1879-1955)

Today’s Outline The universal law of gravitation Newton’s version of Kepler’s laws Gravity: Escape Velocity and Tides Nature of matter and light Chap. 4 and 5

The universal law of gravitation 1. Every mass attracts every other mass. 2. Attraction is directly proportional to the product of their masses. 3. Attraction is inversely proportional to the square of the distance between their centers. Two object actually apply the same gravitational force on each other. That means the earth feels the same gravitational force that you feel on the surface! But because we are so much less massive than the Earth, the acceleration we experience is much greater.

Kepler’s Laws 1. Planets move around the Sun in ellipses, with the Sun at one focus. 2. The line connecting the Sun to a planet, sweeps equal areas in equal times. 3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of the ellipse.

Newton and Kepler’s First Law Newton Revised Kepler’s 1st Law to describe the mutual motion of two objects as they orbit each other. Because of momentum conservation, orbiting objects orbit around their center of mass. pluto/charon: center of mass is outside of Pluto!

Newton's Law of Gravity Extends Kepler's laws Kepler's laws apply to all orbiting objects, not just planets. Ellipses are not the only orbital paths. Orbits can be: bound (ellipses) unbound parabola hyperbola

Kepler's Second Law As a planet moves around its orbit, it sweeps out equal areas in equal times. Conservation of angular momentum: Mass × Velocity × Distance = constant mass is constant => v × r = constant After time Δt, sweeping Area (like a triangle) A ≈ v × Δt × r/2 Therefore, A = constant A rigorous proof requires calculus. r v × Δt area r

Kepler's Third Law p = orbital period Gravitational Force Centrifugal Force p = orbital period a = average orbital distance (between centers) M= sum of object masses

Energy view of orbits The concept of orbital energy is important to understanding orbits. Total orbital energy (gravitational + kinetic) stays constant if there is no external force. Orbits cannot change spontaneously.

Escape Velocity If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit). Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr). Does not depend on the mass of that escaping object. Can use this to discuss how adding velocity can make a spacecraft move to a higher orbit or ultimately to escape on an unbound orbit.

Gravity causes tides Use this figure to explain the origin of the tidal bulges. Gravitational pull decreases with (distance)2, the Moon's pull on Earth is strongest on the side facing the Moon, weakest on the opposite side. The Earth gets stretched along the Earth-Moon line. The oceans rise relative to land at these points. The combined effects of gravitational forces exerted by the Moon, Sun, and rotation of the Earth. Moon's gravity pulls harder on near side of Earth than on far side. Difference in Moon's gravitational pull stretches Earth..

Tidal Friction Tidal friction gradually slows Earth's rotation (and makes the Moon get farther from Earth). The Moon once orbited faster (or slower); tidal friction caused it to ''lock'' in synchronous rotation.

Tidal Heating Ice fountains of Saturn’s moon Enceladus and plume on Jupiter’s moon Europa suggest they may have a subsurface ocean. Encelauds’ geothermal heat is enormous, a result of tidal interaction between the satellite and Saturn. © 2014 Pearson Education, Inc. Europa

How do gravity and energy together allow us to understand orbits? Change in total energy is needed to change orbit Add enough energy (escape velocity) and object leaves. How does gravity cause tides? The Moon's gravity stretches Earth and its oceans. Tidal heating might be important for icy satellites.

Today’s Outline Gravity: Escape Velocity and Tides Nature of matter Nature of light Chap. 5

Structure of matter Use this figure to define the nucleus; protons, neutrons, electrons; scale of atom and "electron cloud."

Phases of matter Most familiar phases: Solid (ice) Liquid (water) Gas (water vapor) Phases of same material behave differently because of differences in chemical bonds. Use this figure to define the nucleus; protons, neutrons, electrons; scale of atom and "electron cloud."

Phase changes Ionization: stripping of electrons, changing atoms into plasma Dissociation: breaking of molecules into atoms Evaporation: breaking of flexible chemical bonds, changing liquid into vapor Melting: breaking of rigid chemical bonds, changing solid into liquid © 2014 Pearson Education, Inc.

Today’s Outline Gravity: Escape Velocity and Tides Nature of matter Nature of light Chap. 5

Interaction between light and matter Transmission Transparent objects transmit light. Opaque objects block (absorb) light. Reflection/scattering Emission Absorption

Quiz Why is rose red? The rose absorbs red light. The rose transmits red light. The rose emits red light. The rose reflects red light. William Wallace Denslow's illustrations for "Roses are red”