AST 101: EXAM 2 STUDY GUIDE
THE COPERNICAN REVOLUTION:
How did Copernicus, Tycho, and Kepler challenge the Earthcentered model? Modern science began with the Copernican revolution.
∙ Believed that tables of planetary motion based on the Ptolemaic model were becoming
∙ He began to look for new ways to predict planetary positions
∙ Believed in heliocentric ideas discovered geometric relationships that strengthened this believe, because they allowed him to calculate each planet’s orbital period and relative
distance from the Sun
∙ His model was complex, because it was based on the believe of perfectly circular
heavenly motions; Copernicus kept adding more and circles
∙ Wasn’t as accurate
∙ Observed an alignment of Jupiter and Saturn
∙ Observed a nova (new star) and proved that it was farther away
∙ He also saw a supernova – explosion of a distant star
∙ Proved that comets lay in the realm of the heavens We also discuss several other topics like What is the purpose of heuristics?
∙ Improved the Copernican system; more accurate, but didn’t come up with an explanation for planetary motion If you want to learn more check out Why was the american revolution considered a process instead of an event?
Don't forget about the age old question of What is the inverse function of the exponential function?
We also discuss several other topics like Where were oldowan artifacts excavated?
∙ He was convinced that planets must orbit the Sun, but because he couldn’t detect stellar
parallax, he thought that the Earth was stationary
∙ His model: the Sun orbits Earth and planets orbit the Sun
∙ Worked to match circular motions to Tycho’s data; which still was off by about 8
arcminutes, which is why he had to abandon the idea of circular orbits
∙ Found that orbits are not circles, but are special ovals – ellipses
∙ Each ellipse has two foci
∙ The long axis of the ellipse is called major axis, each half of which is called semimajor
∙ The short axis is minor axis, half of which is semiminor axis
∙ Eccentricity – describes how stretched out an ellipse is compared to a circle ∙ A circle is an ellipse with zero eccentricity We also discuss several other topics like The origins of rome are explained using what?
By using elliptical orbits, Kepler created a Suncentered model that predicted planetary positions with outstanding accuracy. We also discuss several other topics like How are reliability and validity related?
Kepler’s three laws of planetary motion:
KEPLER’S FIRST LAW:
The orbit of each planet about the Sun is an ellipse with the Sun at one focus. The planet is closest to the Sun at the perihelion and farthest from the Sun at the aphelion.
KEPLER’S SECOND LAW:
A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times
KEPLER’S THIRD LAW:
More distant planets orbit the Sun at slower average speeds, obeying the relationship p2 = a3 P is planet’s orbital period and a is its average distance from the Sun
The fact that the more distant planets move more slowly led Kepler to suggest that the planetary motion might be the result of a force from the Sun
∙ Demonstrated that a moving object remains in motion unless a force acts to stop it ∙ He built a telescope and saw sunspots on the Sun and proved that the Moon has
mountains and valleys
∙ Observed the Milky Way and concluded that stars were far more distant ∙ Observed four Moons orbiting Jupiter
∙ Observed that Venus goes through phases in a way that proved that it must orbit the Sun and not Earth
An object is accelerating if either its speed or its direction is changing
The acceleration of a falling object is called the acceleration of gravity
An object’s momentum is the product of its mass and velocity
The only way to change the object’s momentum is to apply force to it
The net force acting on the object represents the combined effect of all the individual forces put together
An object must accelerate whenever a net force is applied to it
NEWTON’S LAWS OF MOTION:
Newton showed that the same physical laws that operate on Earth also operate in the heavens.
NEWTON’S FIRST LAW:
An object moves at constant velocity if there is no net force acting upon it
In space, there is friction of air:
That is why a spacecraft doesn’t need fuel to keep going after its launched into space and why astronomical objects don’t need fuel to travel through the universe
NEWTON’S SECOND LAW:
Force = mass x acceleration
F = ma
This law explains why large planets such as Jupiter have a greater effect on asteroids and comets than smaller planets such as Earth
Because Jupiter is much more massive than Earth, it exerts a stronger gravitational force on passing asteroids and comets, and sends them scattering with greater acceleration
NEWTON’S THIRD LAW:
For any force, there is always an equal and opposite reaction force
What keeps the planet rotating and orbiting the Sun?
Conservation of angular momentum: an object’s angular momentum cannot change unless it transfers angular momentum to or from another object
The law of conservation of energy tells us that energy cannot appear out of nowhere or disappear into nothing
Objects can gain or lose energy by exchanging it with other objects
Conservation of energy: energy can be transferred from one object to another or transformed from one type to another, but the total amount of energy is always conserved
Types of energy:
Kinetic energy – energy of motion
Potential energy – stored energy
In astronomy the most important subcategory of kinetic energy is thermal energy – the total kinetic energy of many individual particles
Gravitational potential energy: depends on the object’s mass and how far it can fall as a result of gravity; it increases when it moves higher and decreases when it moves lower
THE LAWS OF GRAVITY:
Isaac Newton discovered that the basic law that describes how gravity works. Newton expressed the force of gravity mathematically with his universal law of gravitation:
∙ Every mass attracts every other mass through the force called gravity ∙ The strength of the gravitational force attracting any two objects is directly proportional
to the product of their masses
∙ The strength of gravity between two objects decreases with the square of the distance between their centers. Gravitational force follows an inverse square law
Fg = G M 1M 2
Newton’s version of Kepler’s third law allows us to calculate the masses of distant objects