© 2005 Pearson Education Inc., publishing as Addison- Wesley The Planets Prof. Geoff Marcy The Law of Gravity Velocity and Acceleration Newton’s Laws: Force = mass acceleration (F=ma) Kepler’s 3 rd Law: Newtonian Form Mass vs Weight Lecture Sept. 17

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Realized behavior of nature that operates on Earth also operates outside the Earth.  Laws of chemistry, math, and physics apply everywhere. Discovered laws of motion and gravity. Properties of light: first reflecting telescope (using mirrors not lenses). Invented calculus. Isaac Newton Sir Isaac Newton ( )

1. Law of Gravity The Universal Law of Gravitation 1.Every mass attracts every other mass. 2.Attraction is directly proportional to M 1 x M 2 3.Attraction is inversely proportional to the square of the distance between their centers.

Question: You grab the moon, pulling it to 1/3 of its current distance from Earth. (d  d/3) The grav. force by the moon on the Earth is: Question: You grab the moon, pulling it to 1/3 of its current distance from Earth. (d  d/3) The grav. force by the moon on the Earth is: A.9x greater force than before B.3x greater C.1/3 of the force before. D.1/9 of the force before.

Question: You grab the moon, pulling it to 1/3 of its current distance from Earth. (d  d/3) The grav. force by the moon on the Earth is: Question: You grab the moon, pulling it to 1/3 of its current distance from Earth. (d  d/3) The grav. force by the moon on the Earth is: A.9x greater force than before B.3x C.1/3 of the force before. D.1/9 of the force before.

Speed and Velocity speed: rate at which object moves velocity is a “vector”: speed and direction Example: 10 m/s, due east distance = velocity * time Example: speed of 10 m/s or 100 km/hr d = v t Solve for t: t = d / v

Question: An asteroid orbits the Sun at a = 4 AU. How fast does it travel around Sun? Question: An asteroid orbits the Sun at a = 4 AU. How fast does it travel around Sun? A.25% as fast as Earth B.Half as fast as Earth C.Twice as fast as Earth D.4x Faster than Earth Hint: Use Kepler’s 3 rd Law

Question: An asteroid orbits the Sun at an average distance a = 4 AU. How fast does it travel around Sun? Question: An asteroid orbits the Sun at an average distance a = 4 AU. How fast does it travel around Sun? To get Period, use Kepler’s 3 rd Law: P 2 = a 3  P = Square Root( a 3 ) = 8 years a

Question: An asteroid orbits the Sun at an average distance a = 4 AU. How fast does it travel around Sun? Question: An asteroid orbits the Sun at an average distance a = 4 AU. How fast does it travel around Sun? A.25% as fast as Earth B.Half as fast as Earth C.Same speed as our Earth D.Twice as fast as Earth

Acceleration Acceleration Acceleration occurs if a) speed changes b) direction of motion changes c)or both change Acceleration: rate of change of velocity. units of speed/time (m/s per s)

The Acceleration of Gravity On Earth, all falling objects accelerate at the same rate (ignoring air resistance). On Earth, g = 9.8 m/s per sec  Speed increases 9.8 m/s each second of falling. v = 9.8 m/s v = 19.6 m/s t=3 s velocity = ??? a)29.4 m/s b)39.2 m/s c)64.8 m/s d)86.4 m/s

© 2005 Pearson Education Inc., publishing as Addison-Wesley Using Calculus to Describe Motion Position s Velocity v Acceleration a Integration Differentiation Example: Falling ball

Newtonian Physics: Planets and ordinary objects move by the same laws Isaac Newton

All objects fall with the same acceleration: g Dropping a Feather and Hammer. Apollo 15

Newton’s first law of motion An object moves at constant velocity unless a net force acts to change its speed or direction. Object moving at constant velocity in straight line: Won’t deflect or change velocity unless a force acts on it Object at rest: Won’t move unless a force acts on it

What is Force? Simple question, subtle answer. however: Pressure = force / area Hook’s law: force of a spring

Force = mass  acceleration Units: Newton = kg  m s -2 Newton’s second law of motion

1.A car coming to a stop? 2.A bus speeding up? 3.An elevator moving at constant speed? 4.A bicycle going around a curve? 5.A moon orbiting Jupiter? Question: Is there a net force? (A) YES (B) NO Y Y N Y Y

For every force, there is always an equal and opposite reaction force. Newton’s third law of motion Earth pulled upwards Apple pulled downwards

Newtons’s 2nd Law F = m a Universal law of Gravitation How does Newton explain Keplerian orbits?

Newtons’s 2nd Law F = m a Universal law of Gravitation How does Newton explain Keplerian orbits? Newton derived the relation from the two laws above. Found a correction to Kepler’s 3 rd law: Kepler had found empirically:

Interactive Quiz Where in the orbits does the largest force act on the planet? A B C D (A) Point A (B) Point B (C) Point C (D) Point D

Interactive Quiz Where in the orbit does the largest acceleration occur? A B C D (A) Point A (B) Point B (C) Point C (D) Point D

Interactive Quiz Where in the orbit does the planet move with lowest speed? A B C D (A) Point A (B) Point B (C) Point C (D) Point D

Quiz Where in the orbit does the Sun get jerked (accelerated) hardest? most by the planet. A B C (A) Point A (B) Point B (C) Point C (D) The same for all points D

How is mass different from weight? mass – the amount of matter in an object it relates force and acceleration (F=ma) weight – measures the gravitational force that acts upon an object (F=mg)

Question On the Moon: A.My weight is the same, my mass is less. B.My weight is less, my mass is the same. C.My weight is more, my mass is the same. D.My weight is more, my mass is less.

Question On the Moon: A.My weight is the same, my mass is less. B.My weight is less, my mass is the same. C.My weight is more, my mass is the same. D.My weight is more, my mass is less.

How is mass different from weight? mass – the amount of matter in an object weight – the force that acts upon an object You are weightless in free-fall!

Why are astronauts weightless in space? There IS gravity in space… weightlessness is due to a constant state of free-fall:

Next time... Conservation of energy Orbits Tides Conservation of laziness