ASTRONOMY 161 Introduction to Solar System Astronomy

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ASTRONOMY 161Introduction to Solar System
Astronomy
Class 7
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A161 1st Midterm Results (last year)
E D C B A
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Few midterm sample questions

• On the first day of winter the sun rises
• A) Due South
• B) South of East
• C) Due East
• D) North of East
• E) Due West

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Few midterm sample questions cont

• If you could observe Earth through a telescope
  from Mars, Earth would
• A) always be in gibbous or full phase
• B) always be in crescent phase
• C) go through all phases from crescent to full
• D) have largest apparent diameter when in full
  phase
• E) appear at full phase when seen at opposition

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Few midterm sample questions cont

• Where is the full moon just after sunset?
• (A) Near the Western horizon
• (B) Nearly overhead
• (C) Close to the North star
• (D) Close to the South star
• (E) Near the Eastern horizon

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Newtons LawsWednesday, October 7
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Few opening questions

• 1) While driving a car, you throw a baseball in a
  direction perpendicular to your motion. What
  happens?
• 2) Now you throw a baseball in the direction of
  your motion. What happens?
• 3) While driving a car, you press the gas pedal.
  What happens?
• 4) While driving a car, you press the brake. What
  happens?

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Newtons Laws Key Concepts

• Three Laws of Motion
• (1) An object remains at rest, or moves in a
  straight line at constant speed, unless acted on
  by an outside force.
• (2) The acceleration of an object is directly
  proportional to force, and inversely proportional
  to mass.
• (3) For every action, there is an equal and
  opposite reaction.
• Law of Gravity
• (4) The gravitational force between masses M and
  m, separated by distance r, is

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Isaac Newton (1643-1727) English

• Discovered
• three laws of motion,
• one law of universal gravitation.

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Newtons great book

• Newtons laws are universal in scope, and
  mathematical in form.

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(1) Newtons First Law of Motion

• An object remains at rest, or moves in a straight
  line at constant speed, unless acted on by an
  outside force.
• Precise mathematical laws require precise
  definitions of terms
• SPEED rate at which an object changes its
  position. Example 65 miles/hour.
• VELOCITY speed plus direction of travel.
  Example 65 miles/hour to the north.

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Acceleration

• rate at which an object changes its velocity.
• Acceleration can involve
• increase in speed
• (2) decrease in speed
• OR
• (3) change in direction.

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Force

• a push or pull acting on an object.
• Examples
• gravity pull
• electrostatic attraction pull
• electrostatic repulsion push

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(2) Newtons Second Law of Motion

• The acceleration of an object is directly
  proportional to the force acting on it, and
  inversely proportional to its mass.
• In mathematical form
• Or alternatively

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Example of Newtons Second Law

• A package of cookies has mass
  m 0.454 kilograms,
• And experiences gravitational acceleration
  g 9.8 meters/second2
• How large is the force acting on the cookies?

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(3) Newtons Third Law of Motion

• For every action, there is
  an equal and opposite reaction.
• Whenever A exerts a force on B, B exerts a force
  on A thats equal in size and opposite in
  direction.
• All forces come in pairs.

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Example of Newtons Third Law

• Cookies push on hand F 1 pound, downward.
• Hand pushes on cookies F 1 pound, upward.
• Remove hand!
• Earth pulls on cookies F 1 pound, downward.
• Cookies pull on earth F 1 pound, upward.

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• THIRD Law states
  force on Earth force on cookies
• SECOND Law states
  acceleration force divided by mass
• Mass of Earth 1025 x mass of cookies
• Therefore, acceleration of cookies
  1025 x acceleration of Earth.
• (Cookies reach a high speed while the Earth
  hardly budges.)

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• Butwhy do the cookies and the Earth exert a
  force on each other?
• Newtons Law of Gravity states that gravity is an
  attractive force acting between ALL pairs of
  massive objects.
• Gravity depends on
• (1) MASSES of the two objects,
• (2) DISTANCES between the objects.

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(4) Newtons Law of Gravity

• The gravitational force between two objects
• F gravitational force
• M mass of one object
• m mass of the second object
• r distance between centers of objects
• G universal constant of gravitation

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• Gravitational force varies
  directly with mass and
  inversely with square of distance.
• Double the distance between objects
  Force 1/4 as large.
• Triple the distance between objects
  Force 1/9 as large.

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Example What is gravitational force between
Earth and cookies?
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Example Encore What is acceleration of
cookies?
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• Newtons question can GRAVITY be the force
  keeping the Moon in its orbit?
• Newtons approximation Moon is on a circular
  orbit.
• Even if its orbit were perfectly circular, the
  Moon would still be accelerated.

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• The Moons orbital speed
• radius of orbit r 3.8 x 108 m
• circumference of orbit 2pr 2.4 x 109 m
• orbital period P 27.3 days 2.4 x 106 sec
• orbital speed
• v (2pr)/P 103 m/sec 1 km/sec!

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Acceleration required to
keep Moon on a circular orbit
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Acceleration provided by gravity
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Bottom Line

• If gravity goes as one over the square of the
  distance,
• Then it provides the right acceleration to keep
  the Moon on its orbit (to keep it falling).
• Triumph for Newton!!

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Few closing questions

• 1) Imagine we move Earth twice as far away from
  the Sun. How long would be the year on Earth?
• 2) How many times faster or slower would Earth
  move in its new orbit?
• 3) How long would be the day on such an Earth?
• 4) Imagine you decrease the mass of Earth by a
  factor of two. What would be a mass of a kilogram
  of cookies there?