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Astronomy 101 The Solar System Tuesday, Thursday Tom Burbine tomburbine@astro.umass

Explore key concepts like orbits, laws of motion, and gravitation, plus historical figures like Galileo and Newton. Access course materials online.

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Astronomy 101 The Solar System Tuesday, Thursday Tom Burbine tomburbine@astro.umass

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  1. Astronomy 101The Solar SystemTuesday, ThursdayTom Burbinetomburbine@astro.umass.edu

  2. Course • Course Website: • http://blogs.umass.edu/astron101-tburbine/ • Textbook: • Pathways to Astronomy (2nd Edition) by Stephen Schneider and Thomas Arny. • You also will need a calculator.

  3. HWs #1, 2, 3, 4, and 5 • HWs on Spark: • If you can’t get on Spark, the HWs are also on the website: • http://blogs.umass.edu/astron101-tburbine/ • Due Date: February 2, 2010 1:00 PM

  4. Exam #1 • Next Thursday • Covers all material from January 19-28

  5. A hypothesis is an educated guess, based on observation. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven, but not proven to be true. • A scientific theory summarizes a hypothesis or group of hypotheses that have been supported with repeated testing. A theory is valid as long as there is no evidence to dispute it. Therefore, theories can be disproven. • A law generalizes a body of observations. At the time it is made, no exceptions have been found to a law.

  6. Kepler’s Three Laws • http://brunelleschi.imss.fi.it/museum/esim.asp?c=500106

  7. Orbits • all the planets orbit the Sun in a counterclockwise direction (but they do not orbit it at the same rate). • The Earth rotates counterclockwise • The Sun, the Moon, the planets, and the stars all rise in the east and set in the west

  8. Arguments against the Sun being the center of the solar system • 1) If the Earth was moving, objects such as birds and clouds would be left behind as the Earth moved • 2) The heavens must be perfect and unchanging. Noncircular orbits do not fit this model • 3) Stellar parallax would be observable

  9. 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

  10. 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

  11. Galileo also found that Venus orbited the Sun

  12. Acceleration • Acceleration is when your velocity is changing • Velocity not changing, no acceleration

  13. 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

  14. 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

  15. Isaac Newton (1642-1727) • 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

  16. Force • Force – anything that can cause a body to change velocity

  17. Gravity • Gravity is a natural phenomenon by which objects with mass attract one another.

  18. 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

  19. Why do things on Earth not remain in motion?

  20. Why do things on Earth not remain in motion? • Friction

  21. Newton’s 2nd Law • Force = mass x acceleration • Units of Force kgm/s2 = newton

  22. 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

  23. 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

  24. 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

  25. http://www.vshiksha.com/system/files/u1/pslvc6-rocket.jpg

  26. 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

  27. Formula • Newton came up with this formula Force is proportional to M1 M2 r2 M1, M2 are the masses of the two objects r is the distance between the objects

  28. If you want to calculate actual forces F = G M1 M2 r2 M1, M2 are the masses of the two objects r is the distance between the objects G = constant = 6.67 x 10-11 m3/(kgs2)

  29. So what should you know about this formula F = G M1 M2 r2 • 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

  30. r assume all mass is concentrated in the center of a body r

  31. What is the attraction of two people in this room? F = G M1 M2 r2 • Say their masses are both 100 kg • Their distances are 10 meters apart • F = 6.67 x 10-11 m3/(kgs2) * 100*100 kg2/(10*10 m2) • F = 6.67 x 10-9 N = 0.0000000067 N • Remember the person weighs 980 N

  32. F = G M1 M2 r2 • The value of G was determined by Henry Cavendish between 1797-1798 • G = 6.67 x 10-11 m3/(kgs2) • 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

  33. F = G M1 M2 r2 • How would the force between the two people change if they were only 5 meters apart instead of 10 meters? • A) Stay the same • B) Double (Increase by a Factor of 2) • C) Quadrupul (Increase by a Factor of 4) • D) halve (decrease by a factor of 2)

  34. F = G M1 M2 =G M1 M2=4 G M1 M2 (r/2)2 r2/4 r2 • How would the force between the two people change if they were only 5 meters apart instead of 10 meters? • A) Stay the same • B) Double (Increase by a Factor of 2) • C) Quadrupul (Increase by a Factor of 4) • D) halve (decrease by a factor of 2)

  35. Acceleration of gravity (g) Mis the Earth’s mass F = ma = G Mmr is the Earth’s radius r2 m is the mass of an object F is the force a is the acceleration a = G M r2 g = a = G M r2

  36. Acceleration of gravity (g) Mis the Earth’s mass g = G Mr is the Earth’s radius r2 g = 6.67 x 10-11 m3/(kgs2) * (6.0 x 1024 kg) (6.4 x 106 m) * (6.4 x 106 m) g = 9.8 m/s2

  37. Gravitational acceleration • Gravitational acceleration is different on different planets because they have different sizes and masses • Gravitational acceleration (on Moon) = 1.6 m/s² (0.165 g) • Gravitational acceleration (on Jupiter) = 24.8 m/s² (2.53 g)

  38. Experiment on the Moon • http://www.youtube.com/watch?v=5C5_dOEyAfk

  39. How things fall • Heavy and light objects fall at the same rate • The heavy object does not fall faster (as long as there is no air resistance) g = G M (does not depend on mass of object) r2

  40. How does gravity work? • Gravity distort space-time • http://www.hulu.com/watch/19766/spacerip-einsteins-messengers

  41. Escape velocity • Velocity above this will allow an object to escape a planet’s gravity For Earth: v = square root[(2 x 6.67 x 10-11 m3/(kgs2) x (6.0 x 1024 kg)] (6.4 x 106 m) v = square root [1.25 x 108 m2/s2] v = 11.2 x 103 m/s = 11.2 km/s v

  42. Escape velocity • Escape velocity is different on different planets because they have different sizes and masses • Escape velocity (on Moon) = 2.4 km/s • Escape velocity (on Jupiter) = 59.5 km/s

  43. What causes tides on earth? • Moon pulls on different parts of the Earth with different strengths • http://www.youtube.com/watch?v=Rn_ycVcyxlY • http://www.youtube.com/watch?v=aN2RM5wa1ek

  44. Forces on Water • Average Force on 1 kg water on Earth from Moon F = G Mm= 6.67 x 10-11 m3/(kgs2) * (7.35 x 1022 kg) * (1 kg) r2 (3.84 x 108 m) 2 • F = 3.33 x 10-5 N • Force of 1 kg on water on near-side of Earth from Sun F = G M m = 6.67 x 10-11 m3/(kgs2) * (7.35 x 1022 kg) * (1 kg) r2 (3.84 x 108 m -6.37 x 106 m) 2 • F = 3.44 x 10-5 N • Difference in forces is 1.1 x 10-6 N • Called Tidal Force

  45. Tidal force arises because the gravitational force exerted on one body by a second body is not constant across its diameter • Water flows so this tidal force causes the tides that are seen on Earth

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