Lesson 14: Conservation Laws in Astronomy
In this lesson,
we will learn about angular momentum and how it applies to
the rotation and orbits of planets. We will then study energy in its different
forms and talk about how energy is measured.
Angular momentum is the circling momentum that the Earth and
every other planet in
the solar system has as it turns through an angle of 360 degrees.
The law of conservation of angular momentum states that total angular momentum
does not change. It can only change for an object if that object transfers or
receives angular momentum from another object. Angular momentum explains why
the Earth manages to keep rotating and going around the Sun day after day and
year after year.
Angular momentum equals 'm' times 'v' times 'r'. So to
calculate the Earth's angular momentum as it goes around the Sun, you would
multiply the Earth's mass times its orbital velocity times the radius of its
orbit.
Earth does not need any fuel to keep orbiting the Sun and
will keep doing so unless angular momentum is taken away.
Earth's orbital speed is faster closer to the Sun and
slower further away. That is because based on the angular momentum formula,
when the radius, or the distance from the Sun changes, velocity has to change
accordingly for angular momentum to remain the same.
Note that
this is exactly what we learned with Kepler's second law of planetary motion.
The law of conservation of angular momentum simply explains why Kepler's second
law is true.
Also,
angular momentum applies to the Earth's rotation. The Earth's *rotational*
angular momentum will also remain unchanged and the Earth will keep rotating as
long as it does not transfer any of that momentum to another object.
Just like momentum and
angular momentum, total energy does not change. Energy can be transferred from
one object to another, or transformed, but the amount of energy stays the same.
This is known as the law of conservation of energy. Based on this law, it is
understood that the energy of any object can be traced back to the origin of
the universe in the Big Bang.
The laws of conservation of angular momentum and
conservation of energy allow us to understand almost every major process that
occurs in the universe.
What is energy?
Energy is what makes matter move. There are
three main categories of energy - kinetic, radiative and potential energy.
Kinetic energy is the energy of motion. If an object is falling, spinning, or
moving in any way, it has kinetic energy.
Radiative energy is the energy carried by light. All light carries energy,
which is why the Sun's light can warm the surface of our planet.
Potential energy is stored energy,
which can be later converted into kinetic or radiative energy.
Joule is the standard unit of energy. One food calorie is roughly 4,184 joules.
One of the most important forms of kinetic energy in Astronomy is thermal energy,
which represents the kinetic energy of the atoms and molecules moving randomly
within a rock or gas or air or other substance.
Thermal energy and temperature are
related, but different. While thermal energy represents the *total* kinetic
energy of the atoms and molecules in a substance, temperature is the *average*
kinetic energy of those particles. So for example, if you compare an oven and a
big pot of boiling water, the air in the oven will be hotter than the water in
the pot, but the water is a lot denser - it has a lot more molecules than the
air. This means that the 212 degree boiling water will have a lot more thermal
energy than the 400 degree oven air - in other words, the total kinetic energy
of all of the molecules in the water is greater than the total kinetic energy
in all of the molecules in the oven air.
That also explains why the boiling water would burn you much faster than the
hot air - there is a lot more thermal energy to be transferred.
While we normally use Celsius and
Fahrenheit to talk about temperature,
scientists use the Kelvin scale for measuring temperature.
There are no negative temperatures on the Kelvin scale;
it starts at what is known as absolute zero,
which is the coldest possible temperature. Absolute zero is equivalent to
-273 degrees Celsius or -459 degrees Fahrenheit.
There are many types of potential energy in
astronomy but two are
very important - gravitational potential energy and mass energy.
An object's gravitational potential energy depends on its mass and
how far it can fall as a result of gravity.
Gravitational potential energy increases when an object moves higher and
decreases when it moves lower. For example, if you drop a ball from a building,
at the top of its fall, it has the greatest potential energy and the least
kinetic energy. As it drops, due to the law of conservation of energy, the
ball's kinetic energy increases and it moves faster as its potential energy
decreases.
Mass itself is a form of potential energy. Mass energy is described by
Einstein's equation E = mc² where E is the amount of potential energy, m is
the mass of the object and c is the speed of light.
This equation shows that
a small amount of mass can contain a large amount of energy. For example, the
huge amount of energy released by a 1-megaton hydrogen bomb comes from
converting 0.05 kg of mass into energy.
Einstein's formula not only tells us that mass can be converted into energy;
it also tells us that
energy can be transformed into mass. That is the idea behind the Big Bang - a
massive amount of energy was transformed into the mass which makes up all
objects in the universe.