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Lecture 10

ASTA01H3 Lecture Notes - Lecture 10: Orbital Period, Inverse-Square Law, Edmond Halley

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Kristen Menou

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For the last 10 years of his life, Galileo studied the nature of motion, especially the
accelerated motion of falling bodies.
Although Galileo made extraordinary progress in observations and formulated what is
now known as the first law of Neto’s dais, he as ot ale to elate his
discoveries about motion to the heavens.
That final step was taken by Isaac Newton. The publication of his work in his book
Principia Mathematica Philosophiae Naturalis in 1687 placed the fields of physics and
astronomy on a new firm base.
But it was only though prodding by the famous astronomer Edmund Halley and the
ok of Neto’s ah-enemy Hook, that Newton was persuaded to write Principia.
Edmund Halley, architect Christopher Wren, and physicist and the secretary of the Royal
Society Robert Hooke had meetings and discussions at coffeehouses of London.
They were interested in physical causes of elliptic orbits discovered by Kepler and
confirmed in comets by Halley.
Hooke had an exchange of letters 1679-1680 about it with Newton, which probably gave
Newton both a motivation (which he admitted later) and crucial ideas to study orbits,
like combining inertia and gravity to produce orbits, and the Universal Gravitation (all of
which Newton later denied)
Speed is the rate at which an object moves (changes position).
It is the total distance moved divided by the total time taken to move that distance.
For example, if it took you 2 hours to travel 100 km, then your speed was 50 km/hr.
Velocity specifies both the speed and direction of travel of an object.
For example, if car A moves 60 km east in 2 hours and car B moves 60 km south in 2
hours, they have the same speed of 30 km/hour, but their velocities are different
because they are travelling in different directions.
Thus, velocity can change if: (i) the speed changes, (ii) the direction changes, or (iii) both
speed and direction change.
Acceleration is the rate of change of velocity with time. It is thus the change in velocity
divided by the time taken for the change to occur. Since velocity changes if speed
changes, speeding up is an example of acceleration and slowing down is negative
acceleration (in a direction opposing the direction of travel), or deceleration. a = dv/dt
He was able to find three universal laws of motion that made it possible to predict
exactly how a body would move if the forces acting on it were known
Neto’s fist la of otio states that a ojet eais at est o at ostat eloit
unless a net force acts to change its speed or direction.
When a car is at rest or travelling at a constant speed and direction, the forces exerted
by the wheels to drive it forward are balanced by the air drag and other drag forces in
such a way that the net (total) force is zero.
Neto’s seod la If the mass m(amount of matter) of the object does not change,
then the acceleration is proportional to the force exerted.
Hence, if you want to double your acceleration the applied force must be doubled
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