Gravity

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Chapter 9 10

• Gravity

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Pythagoras (550 BC)

• Claimed that natural phenomena could be described
  by mathematics

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Aristotle (350 BC)

• Asserted that the universe is governed by
  physical laws

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• The ancient Greeks believed that the earth was at
  the center of a revolving sphere with stars on it.

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• The Geocentric Model implies Earth-Centered
  Universe.

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Copernicus (1500's)

• Developed a mathematical model for a Sun-centered
  solar system

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Tycho Brahe (1500's)

• Made precise measurements of the positions of the
  planets

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Kepler (1600's)

• Described the shape of planetary orbits as well
  as their orbital speeds

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Keplers First Law

• The orbit of a planet about the Sun is an ellipse
  with the Sun at one focus.

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Keplers Second Law

• A line joining a planet and the Sun sweeps out
  equal areas in equal intervals of time.

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Keplers Third Law

• The square of a planet's orbital period is
  proportional to the cube of the length of its
  orbit's semimajor axis.
• Or simply T2 R3 if T is measured in years
  and R is measured in astronomical units.

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An Astronomical Unit...

• is the average distance of the Earth from the
  Sun.
• 1 AU 93,000,000 miles 8.3 lightminutes

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Keplers Laws

• These are three laws of physics that relate to
  planetary orbits.
• These were empirical laws.
• Kepler could not explain them.

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Keplers Laws...Simply(See page 192.)

• Law 1 Elliptical orbits
• Law 2 Equal areas in equal times
• Law 3 T2 R3

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Newtons Law of Universal Gravitation

• From Kepler's 3rd Law, Newton deduced inverse
  square law of attraction.

• G6.67 10-11 N m2/kg2

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Gravity Questions

• Did the Moon exert a gravitational force on the
  Apollo astronauts?
• What kind of objects can exert a gravitational
  force on other objects?
• The constant G is a rather small number. What
  kind of objects can exert strong gravitational
  forces?

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Gravity Questions

• If the distance between two objects in space is
  doubled, then what happens to the gravitational
  force between them?
• What is the distance is tripled?
• is quadrupled?
• What if the mass of one of the object is doubled?
• tripled?
• quadrupled?

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Weight and Weightlessness

• Weight
• the force due to gravity on an object
• Weight Mass ? Acceleration of Gravity
• W m g
• Weightlessness - a conditions wherein
  gravitational pull appears to be lacking
• Examples
• Astronauts
• Falling in an Elevator
• Skydiving
• Underwater

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Ocean Tides

• The Moon is primarily responsible for ocean tides
  on Earth.
• The Sun contributes to tides also.
• What are spring tides and neap tides?

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Spring Tides
Sun
Earth
New Moon
Full Moon

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Neap Tides
First Quarter
Sun
Earth
Last Quarter

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End of Section
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Einsteins Theory of Gravitation

• Einstein perceived a gravitational field as a
  geometrical warping of 4-D space and time.

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BLACK HOLES

• Lets observe a star that is shrinking but whose
  mass is remaining the same.
• What happens to the force acting on an
  indestructible mass at the surface of the star?

SFA
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Remember that the force between the two masses
is given by
R
R
R
R

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BLACK HOLES

• If a massive star shrinks enough so that the
  escape velocity is equal to or greater than the
  speed of light, then it has become a black hole.
• Light cannot escape from a black hole.

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Near a Black Hole