Developing the Science of Astronomy
(Chapter 4)
Student Learning Objectives
• Compare ancient and modern theories of the
solar system
• Apply Kepler’s Laws & Newton’s Laws to
our solar system
• Describe gravity
• Analyze orbital motion
How did early Greek philosophers describe motions in the sky?
The Greeks had 3 basic
theories for the sky
1. All heavenly bodies
spheres that move in
circles
2. Heavens unchangeable
3. Earth stationary at center
of universe
 Most Greeks in B.C. times
believed in the geocentric
model.
Aristotle (300 B. C.):
Ptolemy (150 A. D.):
Earth at the center of the
The “epicycle” model
universe originated with
was developed to
Aristotle and persisted
explain retrograde
for 2000 years!
motion.
 Copernicus:
Mathematics
indicated the Sun
was at the center of
the solar system.
(mid-1500’s)
heliocentric model
The Early Models
Aristotle
Stationary Earth
Earth at Center
Circular Motion
Orbital speeds
same for all
Based on
Observation of
Apparent Motion
Ptolemaic
Stationary Earth
Earth at Center
Circular motion
Orbital speeds
same for all
Based on
Observation of
Apparent Motion
Copernican
Rotating Earth
Sun at Center
Circular motion
Orbital speeds
depend on distance
Based on
Mathematics
Practice
Write a compare and contrast sentence
which relates these models.
Tycho Brahe: Designed and utilized new instruments
for measuring precise angles in the sky. (late 1500’s)
Although Tycho Brahe
believed in a geocentric
system, his
measurements were later
used to provide proof for
the heliocentric system.
What are Kepler’s Laws?
 Kepler: Used Tycho Brahe’s observations and
measurements of planetary positions to develop three
laws of planetary motion. (early 1600’s)
Kepler’s 1st Law: Ellipses
Planets move in elliptical
orbits with the Sun at one
focus.
Kepler’s 2nd Law: Equal Areas
Planets sweep out equal areas of space in
equal time intervals.
Kepler’s 3rd Law: P2 = a3
The orbital period of a planet is related to the semimajor axis of it’s orbit.
Orbital Period Squared = Semi-major Axis Cubed
Practice
1) Which planet has the longer orbital period?
Saturn: a = 9.54 AU
Jupiter: a = 5.2 AU
2) How do we measure birthdays?
http://www.exploratorium.edu/ronh/age/index.html
The planets in our solar system actually follow
orbits that are nearly circular.
Eccentricity indicates the elongation of the
ellipse. (e = 0 to 1)
Galileo Galilei
Galileo (early 1600’s):
Observations provided
visual proof of
Copernicus’s Sun
centered system.
 First to use telescope to
view sky
 Planet positions
confirmed
 Moon & Sun not perfect
spheres
 Objects orbiting Jupiter
(not Sun or Earth)
How are the motions of objects described?
Average speed is the
Velocity is speed in a
amount of distance
particular direction.
traveled in some amount
(65 mph South)
of time. (65 mph)
s=d
t
Star
Radial
Velocity
Radius Vector
(Sun to Star)
Tangential
Velocity
Motion of Star
Relative to Sun
(Space Velocity)
Acceleration is the
change of velocity in
some amount of time.
All objects on Earth
have the same
acceleration, downward.
 Change in speed or
direction (Corners)
9.81 m/s2
Practice
1) Is the acceleration due to gravity greater on a
book or a feather?
2) If the Moon maintains an average orbital
speed of 1,023 m/s, does the moon experience
acceleration?
What are Newton’s Laws of Motion?
Newton’s 1st Law: Inertia
An object will remain at rest or maintain a constant
velocity unless an unbalanced force causes the object’s
motion to change.
 Inertia is the tendency of an object to maintain its motion.
Mass is the amount of material contained
in an object.
Average Person
73 kg
Earth
5.972 x 1024 kg
Sun
1.989 x 1030 kg
more mass
 more inertia
 harder to change motion
Practice
1) Mass is often defined in elementary school as
“the amount of space an object takes up”.
Why is this not correct?
2) Would your mass be different if you were on
the moon right now?
Newton’s 2nd Law of Motion: F = ma
An unbalanced force acting on a mass gives the
mass an acceleration in the same direction as the
unbalanced force.
Weight
Weight is a force; it is the gravitational force
acting on a mass.
W = mg
Person on Earth
Person on Mars
73 kg
73 kg
716 Newtons 161 lbs
270 Newtons 61 lbs
http://www.exploratorium.edu/ronh/weight/index.html
 Newton’s 3rd Law of Motion: Action-Reaction
When two objects interact, they create equal and
opposite forces on each other.
Same Pull
Opposite directions
Practice
1) Does the Moon have weight?
2) Apply each of Newton's laws to our solar
system.
What is Gravity?
Gravity is a property of mass
Newton’s Universal Law of Gravitation:
Every object with mass attracts every other object with
mass with a force.
F = GMm
d2
Mutual Force of Attraction
Both masses pull the same on each other!
Inverse Square Law
Force decreases with the square of the distance.
Practice
1) Is the gravitational force zero in space?
2) If Earth had twice as much mass, would this change
your weight? Would it change your mass?
3) If the distance changes between two objects, does the
acceleration due to gravity change?
According to Einstein
Every object with
mass creates a
curvature of spacetime.
 According to Einstein, mass
does not create a force, but
rather a warping of space
which other objects follow.
 Objects (heavy and light)
will follow the same path in
curved space-time.
A black hole is an object that creates an extreme
curvature of space.
More Mass = More Curvature
What are some effects of gravity?
• Orbits
• Orbital Perturbations
• Atmospheres
• Galaxies
• Synchronous Motion
(moon)
• Star Formation
• Weight
• Shapes of Objects
(spheres)
• Tides
Orbital
Perturbations
Gravity can cause slight
deviations in orbital
paths.
Neptune
Exoplanets
Synchronous
Motion
Gravity may cause
rotation to slow.
Moon & Venus
Weightlessness
The feeling of weightlessness occurs when an
object and its reference frame accelerate at the
same rate.
Objects fall together.
Gravity is changing our Earth-Moon system.
Earth’s rotation is slowing
(0.0015 seconds/century)
Our Moon is drifting away
(3.8 cm/year)
Gravity causes tides.
Practice
1) Do the astronauts on the space station have
weight? Explain.
2) The Sun's tidal affects are weak compared to
the Moon. Why?
What is the physics of orbital motion?
Centripetal force
(“center-seeking” force)
causes a constant change
in motion, a constant
change in direction.
Objects in orbit around the Earth, are falling
around the Earth.
Earth’s escape velocity = 11.2 km/s
Earth’s circular velocity = 8 km/s
Practice
1) If the force keeping an object in a circular
orbit is removed, what will be the path of the
orbiting object?
2) What is a geosynchronous orbit?
3) What would be the path of an open orbit?
Center of Mass
Astronomical objects actually orbit about the center
of mass of the system. (Elliptical Orbits)
Common
Center
Of Gravity
Conservation of Energy
Elliptical orbits are maintained by conservation of
mechanical energy. (KE + GPE)
GPEMax
KEMax