**Modern Astronomy (1500 – 1800 A.D.)**

*Nicolaus Copernicus (1473-1543)*

The Polish astronomer Nicolaus Copernicus advocated the heliocentric view, calculated distances to planets and period of planets, and explained the retrograde motion. Before his death in 1543, Copernicus revolutionized astronomy by publishing his work, De revolutionibus orbium coelestium (*On the Revolutions of the Celestial Spheres*).

*Tycho Brahe (1546-1601)*

The Danish astronomer Tycho Brahe made accurate measurements of planetary positions by using a “quadrant.”

*Johannes Kepler (1571-1630)*

As Tycho Brahe’s student, Johannes Kepler received his teacher’s measurements when Brahe died in 1601. In 1610, Kepler then derived the three laws of planetary motion using Brahe’s measurements and empirical rules. Instead of the circular orbits that Copernicus advocated, Kepler discovered that the planets and stars traveled in elliptical orbits.

**Kepler’s 1st Law (1609)**: ** **The planets move around the Sun in ellipses, having the Sun at one of its foci.

Ellipse: 1) each orbit has a shape and a size; 2) the eccentricity (e = 1- B/A) describes how elongated the ellipse is; 3) the size is described by the semi-major axis (2A); 4) when B=A, the orbit is circular and e=0 (eccentricity ranges from 0 to 1, with 1 as the most eccentric)

**Kepler’s 2nd Law (1609)/ Law of Equal Areas**: Each planet revolves in such a way that the line joining it to the Sun sweeps over equal areas in equal time intervals

**Kepler’s 3rd Law (1618)/ Harmonic Law**: The square of the period of revolution is proportional to the cube of the average distance of the planet to the Sun (P²=A³, where P = the period in years and A = the semi-major axis of an orbit in AU)

*Consequence*: Distant planets take longer to orbit the Sun and travel at slower speeds

*Galileo Galilei * (1564-1642)

Italian astronomer Galileo Galilei, the “father of modern science,” was the first to use the telescope to observe the Moon, Jupiter and its moons (Io, Europa, Ganymede, and Callisto), Saturn, and phases of Venus. His observations supported the heliocentric view. After making the telescope in 1609, Galileo observed mountains on the Moon and discovered the Galilean moons of Jupiter. While Ptolemy thought Venus will always appear as a “crescent” and never as a full circle, Galileo discovered that Venus appears in phases. However, Galileo, deemed a heretic by the Roman Catholic Church Inquisition in 1615, was placed under house arrest for the rest of his life.

*Isaac Newton* (1642-1727)

LIFE & ACHIEVEMENTS: English physicist Isaac Newton, often known as the greatest and most influential scientist who ever lived, revolutionized astronomy and physics with his three laws of motion and law of universal gravitation. Born in 1642 (Galileo’s death) and into a world of mysticism, Newton was the last philosopher/ scientist. Newton derived Kepler’s three laws of planetary motion, invented calculus, and answered fundamental questions about the nature of light, motion, and time. Still, with all his achievements, Newton invented a new kind of telescope, studied theology, alchemy, and chemistry.

THE WORLD AROUND NEWTON: At the time, “gravity” meant solemn and was a mood, not a force. People believed that the world was not “solvable.” Light and heavy things separated themselves “naturally.” Time was hard to separate and the concept of motion was not well-defined. Philosophers/ scientists constrained motion to: pushing, pulling, carrying, twirling, combining, separating, waxing, and waning. Aristotle had defined things “in motion” as: an apple ripening, a dog running, a child growing up, and a spinning top.

EARLY LIFE: At Cambridge University, Aristotle was the sole authority on logic, ethics, rhetoric, cosmology, and mechanics. Because his tutor was a linguist, Newton mostly studied on his own. Born poor, Newton conserved paper costs by writing in a tiny font.

ROAD TO DISCOVERY: While Galileo had discovered uniform acceleration (all bodies fall at the same rate), Newton asked: How and why does something’s velocity change? In 1664, the plague in England caused Cambridge to close down, but Newton continued to discover fundamental ideas in astronomy and physics. By first reading works such as Euclid’s “Elements” and that of Descartes, Newton explored the concept of infinity, curvature, and the rate of the bending of lines, trajectories. “To resolve problems of motions,” Newton then invented calculus. To explore the nature of light, Newton used a prism to “isolate” blue light and passed the blue light through a second prism; the light stayed blue. Newton discovered that prisms only separate color and white light was “made up of” different colors. Furthermore, light comes from the Sun in eight minutes, the Moon tugs at the Earth to create waves, and the same Universal Laws exist throughout the Universe.

IMPACT: Newton defined these concepts: “mass,” “action,” “reaction,” “momentum,” “inertia,” “to feel the force of gravity.” He quantified the world with calculus and made people Newtonians (think that the world is solvable). Starting from the Newtonian Age, scientists linked mathematics and science to prove facts and claims.

**Law of Universal Gravitation**: Every particle in the Universe attracts every other particle with a force proportional to the product of their mass and inversely proportional to the square of the distance between them.

Gravity = the force between two objects that depends on the objects’ masses and on the distance between them

- Gravity is a mutual force acting on both bodies
- The force on each body is t he same size, but in opposite directions

**Newton’s 1st Law/ Law of Inertia**: Every material object continues in its state of rest, or of motion in a straight line, unless it is compelled to change that state by external forces. In other words, a stationary object will stay at rest, while a moving object will stay in constant motion unless an unbalanced force acts on it. “Constant” motion = at a constant speed and a constant direction.

Inertia = the resistance of any physical object to its state of motion or at rest

Balanced Forces = Forces cancel one another and no change in motion results (e.g. sitting in a chair)

Unbalanced Forces = One force is greater than another, causing a change in motion (e.g. jumping off a diving board)

Speed and Velocity = Velocity combines the speed of an object and the direction of motion and is equal to the change in distance over change in time (V = d/t) (e.g. speed = driving 60 miles/ hr; velocity = driving 60 miles/hr **east**)

**Newton’s 2nd Law**: The acceleration of an object is directly proportional to the net force acting on it

Acceleration = a change in velocity; objects of different masses on earth fall at the same rate

**Newton’s 3rd Law**: For every action there is an equal and opposite reaction.

Forces and Orbits: For objects in uniform circular motion, the force of gravity is perpendicular to the motion, the object orbits at constant speed, gravity changes the direction only of the motion, and there is still an acceleration.

Elliptical Orbits: For planets in elongated orbits, gravity changes both the direction and the speed of the planet, the planet slows down as it moves away from the Sun, and the planet speeds up as it approaches the Sun

Gravity Depends on Mass: **F gravity = G x (m1m2)/r²**, where m1 and m2 are the masses of the two objects, r is the distance between the two masses, G is Newton’s gravitational constant (6.7 x 10-¹¹ m³kg s²)

Newton’s Derivation of Kepler’s Laws Using His Law of Gravity: **a1 = F gravity/ m1 = G x m2/r²**;** **accelerations are smaller for objects far from the Sun (when r is large)

Newton’s Derivation of Kepler’s 3rd Law: **P² = [( 4∏ )/ G (m1 + M2)] (R³)**