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The history of Universe is essentially a story about the interplay between matter and energy.
We can understand what happens in Universe using physics laws we can test on the Earth (even though the sizes involved are on much bigger scale).
In this Chapter we will discuss laws which govern motion and energy in the Universe;• first we will learn how to describe motion;• we will see what is mass (and what is weight); and then • Newton’s laws of motion, • conservation laws of momentum and energy• and gravity law.
It was Galileo who showed that g is the same for all falling objects, regardless of their mass. He devised experiments (on the leaning
tower of Pisa, the legend says) which proved this to be true (contrary to the experience).
Apollo 15 demonstrationReview: what experiment about the motion done by Galileo do you remember from the last class? (hint: he proved Aristotle was wrong)
• Momentum = mass velocity• Only a net (overall) force can change momentum. It changes
momentum by changing velocity or equally by causing acceleration. • Force actually equals to the rate of momentum change, or the
acceleration caused (times the mass).
• Question: What will happen if a bug, moving with speed of 30km/hr hits your car? What will happen if 2 tone truck, moving at a same speed hits it? Explain why. (hint: which has bigger momentum?)
Whenever there is a change of speed or a direction of motion (whenever there is an acceleration) there is a net (overall) force acting on a body. That force actually equals to the mass of the body times the acceleration caused (which is also a momentum change).
Change of momentum = m change of velocity = = m acceleration (= F)
• Mass never changes, no matter where you are, or how are you moving.
• Weight is actually a gravitational force exerted on you, which you in turn exert on the floor. It depends on:
• Where you are (bigger planets will exert bigger gravity pool on you)• And weather you are accelerating or not (acceleration equals force, so if you are accelerating that is like that something is applying additional force on you).
• Free-fall: if there is nothing to stop you from moving under the attraction of gravity (no floor) you would be weightless, while free-falling.
1. Why is your weight the same while elevator moves with a constant speed? (hint: what is the acceleration of elevator? What does it tell us about the force?)
2. Why your weight changes if the elevator accelerates?3. Would your mass change if the elevator would go with a
Why are astronauts weightless in space? (make a guess…)
• Question: is it true that there is no gravity in the space?• weightlessness is due to a constant state of free-fall:
Let’s imagine you could fall through the Earth. Question: If you would run on the tower and then jump of off it, what would your path be? Now imagine your speed when jumping off the tower is so huge, you actually miss the Earth…
•How do we describe motion?•Speed = distance/time •Speed + direction => velocity (v)•Change in velocity => acceleration (a)•Momentum = mass velocity•Force causes a change in momentum, which means acceleration.
Question: who was the first to discover the basics of this law in his careful experiments? (hint: it helped him as an argument against Earth-centered system)
Published in 1687, under the title “Philosophiae Naturalis Principia Mathematica”
Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.
Force = mass accelerationWhat happens when the force is present…
Question: if you throw away a ball made of plastic and the rock of about the same size, which one would fly further? Why? (hint: what is the force in this example? What is the acceleration?)
What have we learned?• How did Newton change our view of the universe?
• He discovered laws of motion & 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.
Newton used force to describe interactions. We will se now a different approach.
There are three important conservation laws:
• Conservation of momentum• Conservation of angular momentum• Conservation of energy
These laws are embodied in Newton’s laws, but offer a different and sometimes more powerful way to consider motion.
The conservation laws actually show why Newton’s laws are true, by reflecting deeper aspects of nature – conservation of certain quantities.Example: According to Newton’s second law can we actually change
momentum? (hint: how do you change momentum of an object)
What keeps a planet rotating and orbiting the Sun?Conservation of Angular Momentum
As long as Earth doesn’t transfer angular momentum to other objects, its rotation and orbit cannot change.
Question: we have seen this law during the last class already? Do you remember who discovered it? Remember, then it was only an empirical law, here it is explained based on laws of nature.
Conservation of Energy Where do objects get their energy? What is energy?
• Energy makes matter move.Basic Types of Energy• Kinetic (motion): all objects which move have this energy. E=mv2/2.
• Radiative (light): all radiation carries this type of energy, that is why sun-light warms up our planet.
• Stored or potential: energy which can be converted to other two types, I.e., rock on a hill has gravitational potential energy, because if it slips it will start to fall, converting its energy to kinetic energy of his new motion.
Thermal energy is a measure of the total kinetic energy of allthe particles in a substance. It therefore depends both ontemperature AND densityExample:
•Question: In space, does a gas cloud has more gravitational energy when it is spread over a large area or when it closer to the center of gravity? (hint: farther the particles are from the center, is their gravitational potential energy bigger or smaller?)
Subcategory: energy contained in mass itself – “mass-energy”
• Mass itself is a form of potential energy
E = mcE = mc22
• A small amount of mass can release a great deal of energy• Concentrated energy can spontaneously turn into particles (for example, in particle accelerators or in the early Universe)
1 mega tone H bomb converts only about 100 grams (3 ounces) of mass into energy. Enough to destroy a major city.
What have we learned?• What keeps a planet rotating and
orbiting the Sun?• The law of conservation of angular
momentum
• Where do objects get their energy?– Conservation of energy: energy
cannot be created or destroyed; it can only be transformed from one type to another.
– Energy comes in 3 basic types: kinetic, potential, radiative. Some subtypes important in astronomy: thermal energy, grav. Potential energy, mass-energy (E = mc2).
What determines the strength of gravity? The Universal Law of Gravitation (Newton)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
How does Newton’s law of gravity extend Kepler’s laws?
• Newton published Principia in 1687. By that time Kepler’s laws have been well tested (for 70 years) and there was no doubt they were correct. But they were empirical laws (based on observation and it was not clear why they are true.
•Newton used mathematical expression of his law of gravity and derived all three of Kepler laws, showing they are consequence of more fundamental laws. In doing so, he also found that Kepler’s laws are only part of a story of how objects move under the influence of gravity.
Examples:• Calculate mass of Sun from Earth’s orbital period (1 year) and average distance (1 AU).• Calculate mass of Earth from orbital period and distance of a satellite.• Calculate mass of Jupiter from orbital period and distance of one of its moons.
Question: whether the space shuttle and the astronaut outside of it have the same orbital period around the Earth? Why, what determines their periods? Does the astronaut needs to be attached to the shuttle?
• Question: Can orbits change spontaneously? • Let’s define an energy of an object in its orbit: total orbital energy = kinetic energy + gravitational potential energy• Total orbital energy stays constant along an orbit.• Question: Does kinetic energy change along orbit? How about potential
So what can make an object gain or lose orbital energy?1. A gravitational encounter with a third object: for example,
if a comet passes by Jupiter (large planet), comet’s orbit around the Sun can change dramatically.
• Question: where did the energy lost by a comet go (when it went from unbound to the bound orbit)?
Also used by spacecraft to boost orbits. Each of the two Voyagers that visited the outer planets in 1980s was deliberately sent close by Jupiter on a path that caused it to gain orbital energy at Jupiter’s expense.
Examples:• satellites in low-Earth orbit can crash to Earth due to energy loss to friction
with atmosphere
• captured moons like Phobos/Deimos or many moons of Jupiter: they are big and not easy to capture. Capture by Jupiter must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid (now moon) to lose significant amount of its energy.
• Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). Question: Explain this effect using a conservation law? (hint: which quantity describes rotation?)
• Moon once orbited faster; tidal friction caused it to “lock” in synchronous rotation.
To describe motion we use: speed, velocity, acceleration, momentum.
Mass is measure of amount of matter in a body. It is different from weight!
Newton’s laws are:If there is no net force the objects move with constant velocityF=maWhenever there is a net force acting on an object, that object is acting with an equal force in the opposite direction on surrounding.
Conservation laws: angular momentum (mvr) and energy are conserved!