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Galileo, Newton and the Birth of Astrophysics

Galileo Galilei• scientist and

outspoken supporter of Copernicus’ heliocentric model

• lived and worked at the time of Brahe and Kepler

Galileo Galilei (1564-1642)

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Galileo’s Physics Experiments

• Performed many experiments on the motion of falling bodies

• Showed that objects of different mass dropped from the same height will fall to Earth at the same time (neglecting air resistance).

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Galileo’s Telescope• He was among the first to use

a telescope to observe the sky and publish his observations.

• Observed:– Mountains and valley on the

Moon (like Earth).

– Spots on the Sun and Solar rotation (imperfect Sun).

– Phases of Venus

– Moons of Jupiter

Galileo’s drawings of the Moon as seen through his telescope.

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The Moons of Jupiter• The discovery of

these moons proved that at least some things did not go around the Earth.

• These 4 moons were later named the Galilean satellites in honor of Galileo.

A copy of Galileo’s original notes showing Jupiter and four of its moons.

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Phases of Venus• We only can see

Venus due to reflected sunlight

• We should only see crescent phases of Venus if Venus went around the Earth.

• Instead we see almost all of the phases. Venus can’t orbit Earth.

Ptolemy’sEarth-centeredmodel. Venusmoving along itsepicycle.

Copernicus’Sun-centeredmodel. Venusin orbit aroundthe Sun.

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Photos of Venus’ Phases

What Galileo probably saw may have looked something like this.

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Galileo and the end of Ptolemy’s model

• By the end of Galileo’s life Copernicus’ Sun-centered model of the Solar System and Kepler’s Laws had gained wider acceptance.

• Galileo died almost 100 years after Copernicus published his model

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Isaac Newton (1642 - 1727)• Newton was born the year

Galileo died.

• It had been believed that there was one set of laws that applied to Earth and another set to the stars, Moon and planets.

• Newton recognized that there is one set of physical laws that apply everywhere.

• The same force that causes an apple to fall also keeps the Moon moving around the Earth.

Newton’s example showing how an object with enough initial velocity could be placed in orbit around Earth

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Newton’s Achievements• Considered the greatest physicist of

all time.

• Made significant contributions to astronomy, physics and optics

• Invented the reflecting telescope

• Developed the branch of mathematics called calculus

• His most famous contributions are to the study of motion and gravity.

• He recognized that gravity was the only force involved in keeping the planets moving around the Sun

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The Universal Law of Gravitation

• Every particle in the Universe attracts every other particle.

• The force is proportional to the product of their masses and inversely proportional to the square of the distance between them

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Newton’s Laws• 1st Law (Law of Inertia)

– A body at rest remains at rest unless made to change by a force

– A body in uniform motion (in a straight line) remains that way unless made to change by forces acting on it.

• Uniform motion means both speed and direction are unchanged

• A body not moving in a straight line or not moving at a constant speed must be experiencing a force.

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Acceleration

• Acceleration can be a change in speed (faster or slower) or a change in direction

• You can experience an acceleration due to a force.

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Mass and Weight are not the same

• Mass - the amount of matter a body contains.

• Weight - a measure of the gravitational force on an object

• On the Moon we would weigh less but have the same amount of mass

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Newton’s Laws• 2nd Law

– The amount of acceleration (a) that a force (F) can produce depends on the mass (m) of the object being accelerated

a=F/m

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Newton’s Laws• 3rd law

– When two bodies interact, they create equal and opposite forces on each other

– The force of gravity the Earth experiences due to the Sun is the same as the force the Sun experiences due to the Earth.

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Newton’s Version of Kepler’s 3rd Law

• Newton generalized Kepler’s 3rd Law so that it can be applied anywhere in the Universe not just to planets going around the Sun. (Remember P2(years) = a3(AU) ?)

• Newton’s version includes the mass of the two objects. So if you know the period of the orbit and distance you can determine the mass.

• By knowing the period of the orbit of one of Jupiter’s moons and its distance from Jupiter you can “weigh” Jupiter.

• We can use this formula to weigh anything (stars, galaxies, black holes, etc.)

Surface Gravity

• Surface gravity is the acceleration a mass undergoes at the surface of a celestial object (e.g., an asteroid, planet, or star)

• Surface gravity:– Determines the weight of a mass at a celestial object’s

surface• i.e., explains why you would weigh less on the Moon than on the

Earth.

– Influences the shape of celestial objects– Influences whether or not a celestial object has an

atmosphere

Surface Gravity Calculations• The surface gravity, denoted by g, is:

g = GM/R2

– Where G is the gravitational constant– M is the mass of the object (planet, star, black hole)– R is the radius of the object– Massive, compact objects have greater surface gravity than

low-mass, large objects

• gEarth = 9.8 m/s2 • gEarth/gMoon = 5.6 and gJupiter/gEarth = 3

– On the Moon you would weigh 5.6 times less than you do on Earth

– At Jupiter you would weigh three times more than you do on Earth

Escape Velocity

• To overcome a celestial object’s gravitational force and escape into space, a mass must obtain a critical speed called the escape velocity

• Escape velocity:– Determines if a spacecraft can move from one planet to

another

– Influences whether or not a celestial object has an atmosphere

– Relates to the nature of black holes

Escape Velocity

Escape Velocity Calculation

• The escape velocity, Vesc, is determined from Newton’s laws of motion and the Law of Gravity and is given by:

Vesc = (2GM/R)1/2

where M and R are the mass and radius of the celestial object from which the mass wishes to escape

• Notice dependence of Vesc on M and R, but not m

• Vesc,Earth = 11 km/s, Vesc,Moon = 2.4 km/s

Escape Velocity