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.

Homework #1 is due this Friday Homework #2 is online Access to the website of the textbook: www.masteringastronomy.com. The course ID is EART8FALL17. It will need your student ID. You have to register on that web site to finish the homework online and in-class quiz. Buy the textbook package (the code including the access to the website and learning catalytics) from the bookstore. If you get a used book, you still need to purchase access to the website and the quiz tool. You can do this online.

Outline of this week Basic physics review Newton’s laws Gravity, light, matter Spectra

Which phase is it?

Which phases is it?

Kepler’s Laws

Kepler's First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

Kepler's Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times. This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

Kepler's Third Law The square of the orbital period of a planet is proportional to the cube of the semi-major axis of the ellipse. p2 = a3 p = orbital period in years a = Semi-major axis of the ellipse (avg. distance between the body and the sun) It might be noted here that a is also equal to the semi-major axis of the orbit.

Today’s Outline Motion, Energy, Gravity Newton’s laws of motion and gravity Conservation laws Chap. 4

Motion, Energy, and Gravity 12

How to describe motion? Precise definitions to describe motion: Speed: Rate at which object moves Example: 10 m/s Velocity: Speed and direction Example: 10 m/s, due east Acceleration: Any change in velocity units of speed/time (m/s2), also has direction. speed = distance time units of m s Basic vocabulary of motion. Emphasize that turning, slowing, and speeding up are all examples of acceleration.

The Acceleration of Gravity All falling objects accelerate at the same rate (not counting friction of air resistance). On Earth, g ≈ 10 m/s2: speed increases 10 m/s with each second of falling.

Momentum and Force Momentum = mass × velocity A net force changes momentum, which generally means an acceleration (change in velocity). Rotational momentum of a spinning or orbiting object is known as angular momentum. Angular Momentum = mass × velocity × length of the spinning arm

Mass is different from weight? Mass – the amount of matter in an object Weight – the force that acts upon an object Mass is different from weight? You are weightless in free-fall!

Why are astronauts weightless in space? There is gravity in space. Weightlessness is due to a constant state of free- fall.

Speed = distance/time Speed and direction => velocity Change in velocity => acceleration Momentum = mass × velocity Angular Momentum = mass × velocity × length of the spinning arm Force causes change in momentum, producing acceleration. Mass = quantity of matter Weight = force acting on mass Objects are weightless in free-fall.

Isaac Newton Realized the same physical laws that operate on Earth also operate in the heavens Discovered three laws of motion Newton’s law of gravity Much more: experiments with light, first reflecting telescope, calculus… Sir Isaac Newton (1642–1727)

"Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light". --Alexander Pope "Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced…Mortals rejoice that there has existed such and so great an ornament of the human race! …”. https://www.youtube.com/watch?v=8yis7GzlXNM

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.

Newton's first law of motion An object moves at constant velocity unless a net force acts to change its speed or direction.

Newton's second law of motion There are two equivalent ways to express Newton's Second Law of Motion Force = mass × acceleration (F=m×a, m is mass and a is the acceleration) acceleration: change in velocity Also can be shown as: Force = rate of change in momentum because: Change in velocity => acceleration Momentum = mass × velocity

Quiz How does the gravitational force on the star due to the planet orbiting compare to the gravitational force on the planet due to the star it orbits?

Newton's third law of motion: For every force, there is always an equal and opposite reaction force. Newton's third law of motion:

How did Newton change our view of the universe? He discovered laws of motion and gravitation. He realized these same laws of physics were identical in the universe and on Earth. What are 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.

Why do objects move at constant velocity if no force acts on them? Objects continue at constant velocity because of conservation of momentum. The total momentum of interacting objects cannot change unless an external force is acting on them. Interacting objects exchange momentum through equal and opposite forces (e.g. Billiards!).

What keeps a planet rotating and orbiting the Sun?

Conservation of Angular Momentum Angular momentum = mass × velocity × radius The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it. Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely.

Angular momentum conservation also explains why objects rotate faster as they shrink in radius. Discuss astronomical analogs: disks of galaxies, disks in which planets form, accretion disks…

Basic Types of Energy Kinetic (motion) Potential (stored) Radiative (light) Energy can change type, but cannot be created or destroyed.

Thermal Energy The collective kinetic energy of many particles (for example, in a rock, in air, in water) Thermal energy is related to temperature but it is NOT the same. Temperature is related to the average kinetic energy of the many particles in a substance.

Temperature Scales Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends on both temperature AND density. Example:

Gravitational Potential Energy On Earth, depends on: object's mass (m) strength of gravity (g) distance object could potentially fall

Gravitational Potential Energy In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. A contracting cloud converts gravitational potential energy to thermal energy.

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)

Gravitational Waves 36 + 29 - 62 = 3 solar mass = wave energy! On 11 February 2016, the Laser Interferometer Gravitational-Wave Observatory (LIGO) collaboration announced the detection of gravitational waves, from two black holes merging about 1.3 billion light years away. During the final fraction of a second of the merge, it released more power than 50 times that of all the stars in the observable universe combined. 36 + 29 - 62 = 3 solar mass = wave energy!

Conservation of Energy Energy can be neither created nor destroyed. It can change form or be exchanged between objects. The total energy content of the universe was determined in the Big Bang and remains the same today.

Why do objects move at constant velocity if no force acts on them? Conservation of momentum What keeps a planet rotating and orbiting the Sun? Conservation of angular momentum Where do objects get their energy? Conservation of energy: energy cannot be created or destroyed but only transformed from one type to another. Energy comes in three basic types: kinetic, potential, radiative. Mass is a form of energy