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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.): Earth at the center of the universe originated with Aristotle and persisted for 2000 years!
Ptolemy (150 A. D.): The “epicycle” model was developed to explain retrograde motion.
Copernicus: Mathematics indicated the Sun was at the center of the solar system. (mid-1500’s)
heliocentric model
PracticeWrite a compare and contrast sentence
which relates these models.
Aristotle Ptolemaic CopernicanStationary Earth Stationary Earth Rotating EarthEarth at Center Earth at Center Sun at CenterCircular Motion Circular motion Circular motionOrbital speeds
same for allOrbital speeds
same for allOrbital speeds
depend on distanceBased on
Observation ofApparent Motion
Based onObservation of
Apparent Motion
Based onMathematics
The Early 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 semi-major axis of it’s orbit.
Orbital Period Squared = Semi-major Axis Cubed
Practice1) 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 amount of distance traveled in some amount of time. (65 mph)
Velocity is speed in a particular direction. (65 mph South)
s = d t
Star
RadialVelocity
Motion of StarRelative to Sun(Space Velocity)
TangentialVelocity
Radius Vector(Sun to Star)
Acceleration is the change of velocity in some amount of time.
Change in speed or direction (Corners)
All objects on Earth have the same acceleration, downward.
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.
more mass more inertia
harder to change motion
Average Person 73 kg
Earth 5.972 x 1024 kg
Sun 1.989 x 1030 kg
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.
http://www.exploratorium.edu/ronh/weight/index.html
W = mg
Person on Earth 73 kg 716 Newtons 161 lbs
Person on Mars 73 kg 270 Newtons 61 lbs
Newton’s 3rd Law of Motion: Action-Reaction
When two objects interact, they create equal and opposite forces on each other.
Same PullOpposite directions
Practice
1) Does the Moon have weight?
2) Apply each of Newton's laws to our solar system.
What is Gravity?
Newton’s Universal Law of Gravitation:
Every object with mass attracts every other object with mass with a force.
F = GMm d2
Gravity is a property of mass
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 EinsteinEvery object with
mass creates a curvature of space-time.
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
• Atmospheres
• Galaxies
• Star Formation
• Shapes of Objects (spheres)
• Orbital Perturbations
• Synchronous Motion (moon)
• Weight
• Tides
OrbitalPerturbations
Gravity can cause slight deviations in orbital paths.
NeptuneExoplanets
Gravity may cause rotation to slow.
Moon & Venus
SynchronousMotion
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/sEarth’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 EnergyElliptical orbits are maintained by conservation of
mechanical energy. (KE + GPE)
KEMax
GPEMax