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