Nicholas Copernicus ( ) Accounted for problems with calendar by introducing (re-introducing) the heliocentric model of the universe. The “New” Astronomy TheNewAstronomy.ppt

The “New” Astronomy Sidereal Day – Time it takes for the stars to return to directly overhead at a given time. Because the starts are so far away, this time corresponds to one rotation of the earth on it’s axis. Fixed Star Background

The “New” Astronomy Sidereal Day – Time it takes for the stars to return to directly overhead at a given time. Because the starts are so far away, this time corresponds to one rotation of the earth on it’s axis. Solar Day – Time it takes for the sun to return to directly overhead. Because the sun is not so far away as compared to the stars, the earth must rotate a bit farther to get the sun directly overhead. Fixed Star Background

Tycho Brahe ( ): Constructed an observatory, and made detailed measurements of the stars and planets. Introduced a modified heliocentric universe with the earth’s sphere centered on the sun, and all other celestial spheres centered on the earth. The “New” Astronomy

Johannes Kepler ( ) Believed in geocentric universe. Problem with celestial spheres – what holds them up? Kepler attempted to construct the universe, including the spacing between the spheres (which was known) by using the 5 platonic solids as “scaffolding.” The “New” Astronomy

Kepler’s Laws 1. The orbits of the planets are ellipses, with the sun at one focus of the ellipse. 2. The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse. 3. The ratio of the squares of the revolutionary periods (P) of two planets is equal to the ratio of the cubes of their semimajor axes (a) P 2 1 / P 2 2 = a 3 1 / a 3 2

Kepler’s Laws 1. The orbits of the planets are ellipses, with the sun at one focus of the ellipse.

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Focus

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Major Axis

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Semimajor Axis

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Minor Axis

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Semiminor Axis

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. XX Eccentricity (e) is the ratio of the distance between the foci to the length of the major axis e = d f /d ma dfdf d ma

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse. Note on geometry (a is the length of the semimajor axis): XX Eccentricity (e) is the ratio of the distance between the foci to the length of the major axis e = d f /d ma a(1-e) a(1+e)

Kepler’s Laws 1.The orbits of the planets are ellipses, with the sun at one focus of the ellipse.

Terminology The point of closest approach to the sun is called the Perihelion The point of furthest distance from the sun is called the Aphelion Perihelion Aphelion a(1-e) a(1+e)

Kepler’s Laws 1. The orbits of the planets are ellipses, with the sun at one focus of the ellipse. 2. The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse. 3. The ratio of the squares of the revolutionary periods (P) of two planets is equal to the ratio of the cubes of their semimajor axes (a) P 2 1 / P 2 2 = a 3 1 / a 3 2

Kepler’s Laws 2.The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse.

Kepler’s Laws 2. The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse. Equal time intervals

Kepler’s Laws 2. The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse. Implications – Planets move faster and slower in their orbits

Kepler’s Laws 1. The orbits of the planets are ellipses, with the sun at one focus of the ellipse. 2. The line joining the planet to the sun sweeps out equal areas in equal times as the plates travels around the ellipse. 3. The ratio of the squares of the revolutionary periods (P) of two planets is equal to the ratio of the cubes of their semimajor axes (a) P 2 1 / P 2 2 = a 3 1 / a 3 2

Kepler’s Laws 3. The ratio of the squares of the revolutionary periods (P) of two planets is equal to the ratio of the cubes of their semimajor axes (a) P 2 1 / P 2 2 = a 3 1 / a 3 2 Note: If P is measured in fraction of earth years, and a is measured in a.u., then P 2 = a 3 (See Table 2.1) Period is the amount of time it takes for the planet to complete one orbit

The “New” Astronomy Definition – Astronomical Unit (A.U.) – One A.U. is defined to be equal to the length of the semimajor axis of the orbit of the earth.

Galileo Galilei (1564 – 1642) Basics of modern Mechanics (the study of motion). The “New” Astronomy

Fundamental Quantities and Units The “New” Astronomy Some Physics Background QuantityMKS Unit MassKilogram DistanceMeter TimeSecond TemperatureKelvin Amount of SubstanceMoles Electric CurrentAmperes Luminous IntensityCandela

Adopted the position of Renee’ Descartes that objects tended to maintain their motion (a property later called inertia by Newton). Mass (kilograms) is the amount of material in an object. The “New” Astronomy Some Physics Background

Galileo Galilei (1564 – 1642) Basics of modern Mechanics (the study of motion). x – position (meters) d - distance (meters) d= Δ x v – speed, velocity (meters/second) v = Δ x/ Δ t Velocity includes direction, speed does not a – acceleration (meters/second 2 ) a = Δ v/ Δ t An object accelerates if the magnitude and/or direction of the velocity changes Δ In mathematics means “change in” The “New” Astronomy

Other Quantities The “New” Astronomy Some Physics Background QuantityExpressionMKS Unit ForcemaNewtons Kinetic Energy½ m v 2 Joules Charge-Coulombs Electric Field-N/C Magnetic Field-Tesla

Galileo Galilei (1564 – 1642) All objects in free fall near the surface of the earth accelerate at 9.8 m/sec 2 Symbol: g = 9.8 m/sec 2 The “New” Astronomy

Galileo Galilei (1564 – 1642) Made a telescope, observed the moons on Jupiter. First (?) observation of something that did not orbit the earth – ruled out geocentric universe in favor of heliocentric universe. The “New” Astronomy

Isaac Newton (1643 – 1727)) 1. Everybody continues in it’s state of rest or uniform motion unless it is acted upon by a net external force (Law of Inertia) 2. The acceleration of an object is equal to the net force on the object divided by the mass of the object 3. If one object exerts a force on a second object, the second object will exert an equal and opposite force on the first (Law of Action-reaction) The “New” Astronomy

Isaac Newton (1643 – 1727)) 1. Everybody continues in it’s state of rest or uniform motion unless it is acted upon by a net external force (Law of Inertia) Inertia is the property by which objects maintain their motion Mass is the measure of inertia. A large mass corresponds to large inertia. The larger the mass, the harder it is to change the objects motion. Explains why objects in orbit continue to move. The “New” Astronomy

Isaac Newton (1643 – 1727)) 1. Everybody continues in it’s state of rest or uniform motion unless it is acted upon by a net external force (Law of Inertia) 2. The acceleration of an object is equal to the net force on the object divided by the mass of the object 3. If one object exerts a force on a second object, the second object will exert an equal and opposite force on the first (Law of Action-reaction) The “New” Astronomy

Isaac Newton (1643 – 1727)) 2. The acceleration of an object is equal to the net force on the object divided by the mass of the object F NET = m a The “New” Astronomy

Isaac Newton (1643 – 1727)) 1. Everybody continues in it’s state of rest or uniform motion unless it is acted upon by a net external force (Law of Inertia) 2. The acceleration of an object is equal to the net force on the object divided by the mass of the object 3. If one object exerts a force on a second object, the second object will exert an equal and opposite force on the first (Law of Action-reaction) The “New” Astronomy

Isaac Newton (1643 – 1727)) 3.If one object exerts a force on a second object, the second object will exert an equal and opposite force on the first (Law of Action-Reaction) Pushes and pulls in the universe occur as action-reaction pairs The “New” Astronomy

Isaac Newton Mass is the generator of gravity. The force of gravity exists between any objects that possess mass. The Universal Law of Gravity F = G {m 1 m 2 / r 2 } G = 6.67 x Nm 2 /Kg 2 The “New” Astronomy m1m1 m2m2 r r is measured center to center

The “New” Astronomy Calculation of gravitational forces on an object a distance h above the surface of a planets RpRp MpMp m h

The “New” Astronomy Calculation of gravitational forces on an object a distance h above the surface of a planets RpRp MpMp m r = R p + h

The “New” Astronomy Calculation of gravitational forces on an object a distance h above the surface of a planets RpRp MpMp m r F = G M p m / r 2 = G M p m / (R p + h) 2

The “New” Astronomy Acceleration due to gravity at distance h above the surface of a planets RpRp MpMp m r F = G M p m / r 2 = G M p m / (R p + h) 2 = m a

The “New” Astronomy Acceleration due to gravity at distance h above the surface of a planets RpRp MpMp m r Therefore: a = G M p / (R p + h) 2

The “New” Astronomy Acceleration due to gravity near the surface of a planet RpRp MpMp r Therefore: a = G M p / R p 2 h ≈ 0

The “New” Astronomy Acceleration due to gravity near the surface of the earth RERE MEME r Therefore: a = G M E / R E 2 = 9.8 m/sec 2 h ≈ 0 Symbol: g = 9.8 m/sec 2

The “New” Astronomy The force of gravity on an object is called the object’s weight. Since, near the surface of the Earth the acceleration due to gravity is g, the weight (W) of an object near the surface of the Earth is given by (using Newton’s Second Law): W = m a = m g Away from the surface of the earth, one calculates the acceleration due to gravity using g = G M p / (R p + h) 2 W = m g

The “New” Astronomy An object in orbit MUST be accelerating, since the direction of the velocity must be changing. For a circular orbit, a = v 2 / r Where v is the speed of the object and r is the distance from the center of the circle. For a circular orbit, a is called the centripital acceleration. It is directed toward the center of the circle. Direction of a Direction of v

The “New” Astronomy What is the force of gravity on a satellite that is one Earth radius above the surface of the Earth? The weight of the satellite on Earth is 10,000 N?

The “New” Astronomy What is the force of gravity on a satellite that is one Earth radius above the surface of the Earth? The weight of the satellite on Earth is 10,000 N? At one Earth radius above the surface of the Earth, h = R E. Therefore g = G M p / (R p + h) 2 g = G M p / (R p + R E ) 2 g = G M p / (2 R p ) 2 g = (¼) G M p / ( R p ) 2 = (¼) 9.8 m/sec 2 Therefore W = m (1/4) g = ¼ m g = ¼ (10,000 N) = 2,500 N

A closer look at elliptical orbits: The sun is not actually located at a focus of the elliptical orbit. The Center of Mass of the sun-planet system is located at the focus. Center of Mass: The “average” location of the material in a system. The “New” Astronomy

A closer look at elliptical orbits: The sun is not actually located at a focus of the elliptical orbit. The Center of Mass of the sun-planet system is located at the focus. Center of Mass: The “average” location of the material in a system. The “New” Astronomy

Center of Mass The “New” Astronomy

Center of Mass The “New” Astronomy In the figure below, the larger object is high mass and the smaller object is small mass

Center of Mass The “New” Astronomy X In the figure below, the larger object is high mass and the smaller object is small mass

Center of Mass The “New” Astronomy X In the figure below, the larger object is high mass and the smaller object is small mass

Center of Mass The “New” Astronomy X X In the figure below, the larger object is high mass and the smaller object is small mass

Center of Mass The “New” Astronomy X X In the figure below, the larger object is high mass and the smaller object is small mass

Center of Mass The “New” Astronomy X X X In the figure below, the larger object is high mass and the smaller object is small mass

The “New” Astronomy Center of Mass Implication: BOTH the sun and planet orbit the center of mass of the sun – planet system. This introduces a “wobble” in the location of the sun Another planet in the solar system? Exoplanets