survey of the universe tom burbine [email protected]
TRANSCRIPT
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
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
Galileo also found that Venus orbited the Sun
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
• 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
Isaac Newton (1642-1727)
Force
• Force – anything that can cause a body to change velocity
• Velocity – a speed in a particular direction
Gravity
• Gravity is a natural phenomenon by which objects with mass attract one another.
Newton’s 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
Why do things on Earth not remain in motion?
Why do things on Earth not remain in motion?
• Friction
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
Acceleration
• Acceleration is when your velocity is changing
• Velocity not changing, no acceleration
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
Acceleration due to Earth’s gravity
• g = 9.8 m/s2
• If something is dropped, it will gain 9.8 m/s in velocity for every second it falls
Newton’s 2nd Law
• Force = mass x acceleration
• Units of Force kgm/s2 = newton
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
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 Earth’s gravitational field
Newton’s 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
http://www.vshiksha.com/system/files/u1/pslvc6-rocket.jpg
Newton’s 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
Formula
• Newton came up with this formulaForce is proportional to M1 M2
d2
M1, M2 are the masses of the two objectsd is the distance between the objects
• If you want to calculate actual forcesF = G M1 M2
d2
M1, M2 are the masses of the two objectsd is the distance between the objectsG = constant = 6.67 x 10-11 m3/(kgs2)
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
assume all mass is concentrated in the center of a body
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/(kgs2) * 100*100 kg2/(10*10 m2)
• F = 6.67 x 10-9 N = 0.0000000067 N
• Remember the person weighs 980 N
F = G M1 M2
d2
• The value of G was determined by
Henry Cavendish between
1797-1798
• G = 6.67 x 10-11 m3/(kgs2)
• http://blogs.howstuffworks.com/2009/04/13/diy-calculate-the-gravitational-constant-like-cavendish-did/
http://www.makingthemodernworld.org.uk/learning_modules/maths/06.TU.02/illustrations/06.IL.09.gif
Any Questions?