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Gravity, Orbits, Energy, Forces
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Upon completion of this lesson, the student will be able to
Correct the misconception: "There is no gravity in space."
Relate Kepler's Laws to physical laws.
Solve a variety of problems using the equation for the force of gravity where the independent variables are changed in small amounts.
Define gravitational potential energy and kinetic energy, giving an example of each; explain how under the conservation of energy one kind of energy changes to another.
Define radiative energy and explain its importance to the study of planets.
State the difference between a planet's rotation and its revolution.
Meet the objectives set out in the activities for this lesson.
Take the Quiz == page down to the bottom of these lecture notes.
Gravity is one of the 4 fundamental forces of the Universe.
Gravity is the weakest of the 4 fundamental forces of the Universe.
Gravity is always attractive never repulsive.
Gravity operates over long, long distances.
Gravity results in weight
Gravity causes precession of the Earth's axis
Gravity causes tides
Gravity explains orbits
We can determine the mass of an object if it has an orbiting body
Gravity leads to our detection of other planetary systems
| Try out your smarts with the Two Little Gravity Quizzes. |
For the orbital animations I showed in class, go to: http://csep10.phys.utk.edu/, click on "sample chapter" link shown in left-hand frame, click on "The Modern Synthesis," "Universal Gravitation," "Kepler's 3rd Law." Scroll down a bit in this sub-window, and see a side-bar that says "Effect of the Center of Mass." You should see a link to a Java applet that demonstrates Newton's modified form of Kepler's third law. Play around with the eccentricity of the orbit and the masses of the bodies. There are other very good illustrations and animations of the fundamentals of gravity, motions, and discoveries.
Orbits of planets are ellipses, with the Sun at one focal point.
The planets sweep out equal areas in equal time.
The square of the period of the planet is proportional to the cube of its distance from the Sun.
After you visit these three sites, see if you can answer the following questions:
Check this site out:
Newton's Universal Law of Gravitation
and
Newton's Three Laws.
The (equal and opposite) force of gravity felt by two objects is proportional to product of the two masses divided by their distance apart squared.
For someone on the surface of a planet, F = GMm/R2, where M is mass of that world, m is person's mass, and R is the radius of the world.
For two worlds in orbit about each other, the force is F = GMm/d2, where d now represents the distance between (the centers) of the two worlds.
Law of inertia
Force = mass x accleration
or
acceleration of an object = Force exerted on that body
divided by its mass
a = F/m
For every action there is an equal and opposite reaction.
Gravitational mass is the property of an object that determineshow strongly it attracts other objects through gravity:
Inertial mass is the property of an object which determines how fast it accelerates when acted upon by a force:
As far as could be determined, the value of the gravitational mass of an object is equal to the value of its inertial mass. This suggests that there may be some connection between gravity and acceleration.
More on Gravity and Orbits
An interesting and fun site with Orbital simulations.
Most of this is fundamental reading; some of it is more advanced. Pull what you can from it.
We have a good sense of matter and energy from our everyday experience.
We measure energy in units of Calories, kilowatt-hours, or joules (the
favored unit in science). Energy comes in three basic forms: kinetic
energy, which is energy of motion; potential energy, which represents
energy stored for later conversion into kinetic energy; and radiative
energy, which is energy carried by light. Energy is what makes matter move.
Terms you should know:
Potential energy is energy being stored for later conversion into
kinetic energy. Kinetic energy is energy of motion. A ball
has gravitational potential energy when it sits on a ledge. When it
rolls off, that potential energy is gradually converted to kinetic
energy as it falls. When the ball hits the floor, all of its energy
is in the form of kinetic energy. Where does that energy go? Into
thermal energy heating the ball as it compresses and heating the floor.
If the ball is elastic, some of the kinetic energy is stored as the
ball bounces. As the ball rises, the kinetic energy is converted back
to potential energy. (Click on "Reload" if the animation is stopped at
the left.)
The gravitational potential energy of an object (the type of potential
energy we will be most concerned with here), depends on its mass,
the strength of the gravity, and the distance the object falls. It
doesn't take a rocket scientist to convince you that it hurts much,
much more if you fall from a 10-story building versus falling out of
a chair! That gravitational potential energy was converted to kinetic
energy which is converted to thermal energy and breaking-bone energy
as you hit the pavement!
Scientists calculate the energy of any moving object using the simple formula:
or, the kinetic energy of an object equals one-half times the mass of that object times the velocity of the object squared. The more massive the object, the more kinetic energy it has. The higher the velocity of an object, the more kinetic energy it has: 2 times the velocity, 4 times the KE; 3 times the velocity, 9 times the KE; 10 times the velocity, 100 times the KE!
Radiation is often used as a synonym for light. The most valuable source
of radiative energy for life on Earth is the Sun. The Sun annually
produces enough energy to power about 1031, 100-watt
bulbs for a year. It produces about 100,000,000,000,000 more energy a
year than the United State consumes: a huge, basically untapped source
for our future needs.
Science provides ways to quantify energy in terms of its three basic types
(kinetic, potential, and radiative). Thermal energy, or the energy of heat,
is actually a form of kinetic energy since all the individual particles in
a warm substance are moving. The temperature measures the average kinetic
energy of the moving particles, while the total thermal energy content depends
on both the temperature and the density of particles.
Potential energy takes many different forms. Gravitational potential energy
is the potential energy of objects that, if released, will fall toward a
center because of gravity. Chemical potential energy is stored in chemical
bonds; examples include the energy stored in food and gasoline. Mass
itself is a form of potential energy, often called mass-energy, which
is quantified by Einstein's famous formula E = mc˛. (We visit Einstein's
formula when
we discuss how the Sun generates its energy via nuclear fusion.)
One of the most important laws of nature is the law of conservation
of energy, which states that energy can neither be created nor destroyed.
It can only be converted form one form to another.
Terms you should know:
| Remember conservation of energy well. You will find out that it explains why asteroids make huge craters when they hit the Earth or other solid body, why Jupiter is still warm, the source of Saturn's internal heat, even why the Earth is getting warmer. |
Although matter seems like an "obvious" concept in everyday life, it
is really quite subtle. Matter generally consists of atoms, which consist
of a nucleus made from protons and neutrons and a "smeared out" cloud of
electrons. The nucleus is very tiny compared to the cloud of electrons.
Each chemical element has a different atomic number, which is the number
of its protons. The atomic weight (or atomic mass) of an atom is the
combined number of its protons and neutrons. Atoms with different atomic
weights but the same atomic number are called isotopes of one another.
An electrically neutral atom must have a number of electrons that is
equal to its atomic number, since protons are positively charged and
electrons are negatively charged.
Matter can exist in the different phases. Most matter is solid at
very low temperatures. At higher temperatures it may become a liquid
or a gas. The process of solid matter losing some atoms (or molecules)
to the gas phase is called sublimation; the process of a liquid losing
atoms (or molecules) to the gas phase is called evaporation. If the
matter consists of molecules made from two or more atoms, at relatively
high temperatures the molecules will dissociate into individual atoms,
a process called molecular dissociation. At very high temperatures,
electrons may be stripped from atoms in what we call ionization. A
gas that consists of ions (the leftover atoms that are missing one
or more of their electrons) and free electrons is called a plasma.
Hydrogen has just one electron, and so when it is ionized, only a proton
is left. If we consider heavier atoms, such as oxygen, we can identify
how many electrons it has by a simple code: OI, is neutral oxygen; OII
is singly ionized oxygen (minus 1 electron); OIII is doubly ionized; etc.
Iron has 26 electrons, and in extremely hot plasma, can have numerous
electrons missing. For example, we have identified highly ionized iron
atoms in the 1,000,000 degree corona of the Sun.
Terms you should know:
Atoms contain electrical potential energy by virtue of the distribution of their electrons. However, atoms can have only very specific amounts of this potential energy, and not other amounts in between. An atom is said to be in its ground state when it has its lowest possible amount of electrical potential energy. If one or more of its electrons gains energy, the atom is then said to be in an excited state. If enough energy is added to the atom, one or more of the electrons may leave entirely, which is what we call ionization. The energy levels are different and unique for each different type of atom and ion, which means these energy levels essentially represent a "fingerprint" from which we can identify the type of atom or ion.
For more information on the atom, in easier-to-understand language,
visit NASA's Imagine the Universe page on
Atoms and Light Energy.
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