Survey of the Universe Tom Burbine [e-mail]

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Survey of the UniverseTom Burbinetburbine_at_mtho
lyoke.edu
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Galileo Galilei (1564-1642)

• He was able to figure out answers to these
  arguments
• 1) Things in motion tend to remain in motion.
• 2) He used a telescope to see sunspots on the Sun
  and features on the Moon.
• 3) Galileo found that stars were more numerous
  and more distant than imagined

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He also

• He discovered the moons of Jupiter and saw that
  they were orbiting Jupiter
• Io
• Europa
• Ganymede
• Callisto
• Proving that bodies could orbit other bodies
  besides the Earth

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Galileo also found that Venus orbited the Sun
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Difference between mass and weight

• Mass is the amount of matter in your body
• Weight is the amount of force acting on your body
• So on the Moon, you would have the same mass as
  on Earth but weigh less on the Moon since the
  Moon is less massive than Earth
• Mass in metric system is usually measured in
  kilograms

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Isaac Newton (1642-1727)

• Supposedly saw an apple fall to the ground
• He then understood that gravity was universal,
  meaning it affected both the planets and us on
  Earth
• Came up with 3 Laws of Motion
• Also came up with calculus

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Force

• Force anything that can cause a body to change
  velocity
• Velocity a speed in a particular direction

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Gravity

• Gravity is a natural phenomenon by which objects
  with mass attract one another.

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Newton

• http//www.youtube.com/watch?v_q6CXni6yTE

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Newtons 1st Law

• In the absence of a net (overall) force acting
  upon it, an object moves with a constant velocity
• An object at rest remains at rest
• An object in motion tends to remain in motion
  unless a force is acting upon it

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Why do things on Earth not remain in motion?
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Why do things on Earth not remain in motion?

• Friction

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Objects in orbit

• Because the planets are moving in elliptical
  orbits around the Sun and not straight lines,
  there must be a force acting on the planets
• This force is gravity

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Acceleration

• Acceleration is when your velocity is changing
• Velocity not changing, no acceleration

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Acceleration

• a ?v/?t
• Car is travelling at 10 m/s
• Increases its speed to 30 m/s over 5 seconds
• a (30 m/s 10 m/s)/5 seconds
• a 4 m/s2

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Acceleration due to Earths gravity

• g 9.8 m/s2
• If something is dropped, it will gain 9.8 m/s in
  velocity for every second it falls

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Newtons 2nd Law

• Force mass x acceleration
• Units of Force kg?m/s2 newton

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Newton

• A Newton is equal to the amount of force required
  to accelerate a mass of one kilogram at a rate of
  one meter per second per second

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How much do you weigh?

• So much do you weigh
• Say your mass is 100 kg
• F 100 kg x 9.8 m/s2
• F 980 Newtons
• 9.8 m/s2 is the acceleration of gravity on Earth
• This is the acceleration due to the Earths
  gravitational field

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Newtons 3rd Law

• For any force, there is an equal and opposite
  reaction force
• Gravity is holding you on the ground
• The ground is also pushing back up on you with
  the same amount of force

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http//www.vshiksha.com/system/files/u1/pslvc6-roc
ket.jpg
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Newtons Universal Law of Gravitation

• Every mass attracts every other mass through the
  force called gravity
• Every point mass attracts every single other
  point mass by a force pointing along the line
  intersecting both points.
• The force is directly proportional to the product
  of the two masses and inversely proportional to
  the square of the distance between the point
  masses

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Formula

• Newton came up with this formula
• Force is proportional to M1 M2
• 
  d2
• M1, M2 are the masses of the two objects
• d is the distance between the objects

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• If you want to calculate actual forces
• F G M1 M2
• d2
• M1, M2 are the masses of the two objects
• d is the distance between the objects
• G constant 6.67 x 10-11 m3/(kg?s2)

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So what should you know about this formula

• F G M1 M2
• d2
• The force of attraction between any two objects
  is directly proportional to the product of their
  masses
• The force of attraction between two objects
  decreases with the square of the distance between
  their centers
• G is a very small number

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assume all mass is concentrated in the center of
a body
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What is the attraction of two 100 kg people in
the same room?

• F G M1 M2
• d2
• Say their masses are both 100 kg
• Their distances are 10 meters apart
• F 6.67 x 10-11 m3/(kg?s2) 100100 kg2/(1010
  m2)
• F 6.67 x 10-9 N 0.0000000067 N
• Remember the person weighs 980 N

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• F G M1 M2
• d2
• The value of G was determined by
• Henry Cavendish between
• 1797-1798
• G 6.67 x 10-11 m3/(kg?s2)
• http//blogs.howstuffworks.com/2009/04/13/diy-calc
  ulate-the-gravitational-constant-like-cavendish-di
  d/

http//www.makingthemodernworld.org.uk/learning_mo
dules/maths/06.TU.02/illustrations/06.IL.09.gif
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Any Questions?