Astro 103 - Lecture 2

Lectures Lecture page Astro103 page


1. The advance of knowledge

Essential ingredients:

  • Ability and willingness to question

  • New observations

    • methodology (methods of inquiry)
    • technology

  • Analytical tools

    • mathematics (analytic solutions)
    • computers (numerical solutions)

Ancient and modern debates:




(Earth centered)

(Sun centered)

... compare to:

Steady State


Big Bang

(Universe always existed)

(Creation event)

Simplistic Chronology
Conceptual Developments in Western Cosmology
400 BC  
  Aristotle 384-322
300 BC  
  Aristarchus 310-230
  Eratosthenes 276-194
200 BC  
  Hipparchus 146-127
100 BCConquest
100 AD
  Ptolemy 140
200 AD
300 AD
400 AD
Middle Ages
500 AD Dark Ages
600 AD
700 AD
800 AD
900 AD 
1000 AD
1100 AD
1200 AD
1300 AD
1400 AD Renaissance
  Copernicus 1473-1543
1500 AD
  Tycho Brahe 1546-1601
  Galileo Galilei 1564-1642
1600 AD
  Kepler 1571-1630
  Isaac Newton 1642-1727
1700 AD
  Industrial & Scientific
1800 AD
  Albert Einstein 1879-1955
1900 AD
  Edwin Hubble 1889-1953
2000 AD ?
2100 AD
2200 AD

2. Kepler's Laws of Planetary Motion

A precise mathematical description of Tycho Brahe's accurate planetary observations.

(i) The orbital paths of the planets are elliptical, with the Sun at one foci;      

(ii) Equals areas of the ellipse are swept out in equal intervals of time during a planet's orbit;      

(iii) The square of the orbital period (P) is proportional to the cube of the orbital semi-major axis (a).      

Period (P):

the time it takes for the planet to orbit once (360 degrees) around the ellipse

Semi-major axis (a):

half (semi) of the longest (major) line that can be drawn through an ellipse.

One limit of an ellipse is a circle; then a is the same as the radius.

Where's the physics ?

3. Newton's Laws of Motion and Gravitation

A physical theory for how matter interacts

(i) Every body continues in a state of rest or in uniform motion unless acted on by a force      

(ii) When a force acts on a body of mass M, it produces an acceleration A equal to the force F divided by the mass M.

F = M A

(iii) To very action there is an equal and opposite reaction


Force - F

Mass - M

Acceleration - A

4. Gravity

Masses attract!

Gravity is one of 4 forces known in nature:

FORCE CARRIER Relative Strength Examples where force is dominant
gravitational gravitational waves, or gravitons 10-39binds planets, stars, galaxies, the universe
electro-magnetic light waves, or photons 1/137 binds atoms and molecules
weak W and Z particles 10-13radioactive decay of particles
strong gluons 1 binds nuclei

Gravitational force (the law of gravity):

Imagine two objects of different mass:

Object #1 has mass M1

Object #2 has mass M2

The two objects are separated by distance R

What's the gravitational force that they each exert on the other?

FGRAVITY = G M1 M2 / R 2


G is a universal constant, but there is currently no theory for why it has the particular value we observe.

But the rest is just Newton's 2nd law:

FGRAVITY = M1   G M2 / R 2

... or ...

FGRAVITY = M2   G M1 / R 2

and simple geometry!      


5. Orbital Motion

Competition between inertia (Newton's 1st law) and the force of gravity      

suborbital velocity

orbital velocity

escape velocity

A grand analogy:

The expansion of the Universe!

Will it collapse, or expand forever?

a ton of bricks a ton of feathers

Which is more massive?

Which would weigh more on the Moon?

Would the mass of the feathers change if taken to the Moon?

Would the mass of the bricks change if taken to the Moon?

Would their weight change?

Q2.1 Which is more massive: A ton of bricks on the Earth or a ton of feathers on the Moon?

(a) the same

(b) it depends on the phase of the Moon

(c) it depends on the kind of feathers

(d) the feathers

(e) the bricks

Q2.2 How is the observable universe like a time machine?

(a) the universe expands as it ages

(b) there was a beginning of time, and time moves in only one direction

(c) the speed of light is finite, the hence light from more distant objects takes longer to reach us

(d) bigger objects are older

(e) the speed of light increased in the past

Lectures Lecture page Astro103 page

Last updated: Aig 23, 2011 Matthew A. Bershady