# Astro 103 - Lecture 2 # FROM HERESY TO GRAVITY

## 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:

### (Creation event)

Simplistic Chronology
of
Conceptual Developments in Western Cosmology
 Antiquity 400 BC Aristotle 384-322 300 BC Aristarchus 310-230 Eratosthenes 276-194 200 BC Hipparchus 146-127 100 BC Conquest & Empire 0 100 AD Ptolemy 140 Empire & Decay 200 AD 300 AD 400 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

Concepts:

Force - F

Mass - M

Acceleration - A

## 4. Gravity

Masses attract!

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

Why?

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! FGRAVITY 1 / R 2

## 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

Last updated: Aig 23, 2011 Matthew A. Bershady