© 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. 11

Realized physical laws that operate on Earth also operate in the heavens  one universe Discovered laws of motion and gravity Experiments with light; first reflecting telescope (using mirrors rather than lenses) Invented calculus. Isaac Newton Sir Isaac Newton ( )

1. What determines the strength of gravity? The Universal Law of Gravitation 1.Every mass attracts every other mass. 2.Attraction is directly proportional to the product of their masses. 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 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, Velocity, and Acceleration speed: rate at which object moves velocity is a “vector”: speed and direction Example: 10 m/s, due east acceleration: rate of change of velocity. units of speed/time (m/s per s) Note: Acceleration occurs if a) speed changes b) direction of motion changes c)or both change Example: speed of 10 m/s or 100 km/hr

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

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

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

The Acceleration of Gravity On Earth, all falling objects accelerate at the same rate (ignoring air resistance). On Earth, g = 9.8 m/s 2  Speed increases 9.8 m/s each second of falling. 9.8 m/s 19.6 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

The Acceleration of Gravity (g) Galileo showed that g is the same for all falling objects, regardless of their mass. 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

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

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

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

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:

Question: Is there a net force? (A) YES (B) NO 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.

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

What have we learned? How do we describe motion? Speed = distance/time Speed + direction => velocity (v) Change in velocity => acceleration (a) Force causes a change in momentum, which means acceleration.

What have we learned? How did Newton change our view of the universe? He discovered laws of motion & gravitation. He realized these same laws of physics were identical in the universe and on Earth. What are Newton’s Three Laws of Motion? 1)Object moves at constant velocity if no net force is acting. 2)Force = mass  acceleration 3)For every force there is an equal and opposite reaction force.

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