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

Practice Practice Write a compare and contrast sentence which relates these models. 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 1 st Law: Ellipses Planets move in elliptical orbits with the Sun at one focus.

 Kepler’s 2 nd Law: Equal Areas Planets sweep out equal areas of space in equal time intervals.

 Kepler’s 3 rd Law: P 2 = a 3 The orbital period of a planet is related to the semi- major 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?

 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 Radial Velocity Motion of Star Relative to Sun (Space Velocity) Tangential Velocity 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 m/s 2

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 1 st 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

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 2 nd 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 Earth73 kg716 Newtons161 lbs Person on Mars73 kg270 Newtons61 lbs

 Newton’s 3 rd 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?  Newton’s Universal Law of Gravitation: Every object with mass attracts every other object with mass with a force. F = GMm d 2 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 Einstein  Every 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

Orbital Perturbations  Gravity can cause slight deviations in orbital paths. Neptune Exoplanets  Gravity may cause rotation to slow. Moon & Venus Synchronous Motion

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 ( 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) CommonCenter Of Gravity

Conservation of Energy  Elliptical orbits are maintained by conservation of mechanical energy. (KE + GPE) KE Max GPE Max