Sir Isaac Newton (1642-1727) Perhaps the greatest genius of all time Invented the reflecting telescope Invented calculus Connected gravity and planetary forces Philosophiae naturalis principia mathematica

Example problem: Halley’s comet has an orbital period of 76 years and its furthest distance from the Sun is 35.3 AU. How close does Halley’s comet come to the Sun? How does this compare to the Earths distance from the Sun? What is its eccentricity? .

Forces acceleration Forces change the motion of objects. As long as the object’s mass does not change, the force causes a change in velocity, or an… acceleration

Newton’s Laws of Motion # 1 A body at rest or in motion at a constant speed along a straight line remains in that state of rest or motion unless acted upon by an outside force.

Newton’s Laws of Motion # 2 The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it. The proportionality constant is mass: F a a F = m a

Gravity: F = mg g is the gravitational acceleration (9.8 m/s2)

Gravitational Potential Energy E = F n h = mg n h m g h

Newton’s Laws of Motion # 3 For every applied force, a force of equal size but opposite direction arises.

Newton’s Laws of Motion

Is Mass the Same Thing as Weight? mass – the amount of matter in an object weight – a measurement of the force which acts upon an object When in “free-fall,” you are weightless!!

momentum – the (mass x velocity) of an object Forces Forces change the motion of objects – cause accelleration. momentum – the (mass x velocity) of an object p = mv [kg m/s] force – anything that can cause a change in an object’s momentum F = D(mv) = mDv = ma [kg m/s2 =N]

Escape velocity ! Can an object escape the gravitational attraction of the Earth? Does it have enough kinetic energy to overcome the gravitational potential energy of the Earth? mgh I ½ mv2 ????

Depending on its initial velocity, the cannonball will either fall to Earth, continually free-fall (orbit), or escape the force of Earth’s gravity.

Newton’s Laws of Motion A body at rest or in motion at a constant speed along a straight line remains in that state of rest or motion unless acted upon by an outside force. # 1 # 2 The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it. # 3 For every applied force, a force of equal size but opposite direction arises.

y Dx Dy b x y= mx+b where m=Dy/Dx

s= mt+constant where m=Ds/Dt i.e., speed Now consider plotting distance (s) versus time (t). Then the slope is simply the speed. s Dt Ds t s= mt+constant where m=Ds/Dt i.e., speed