1. Gravity

2. Mom was healer that was accused of being a witch
Dad left to become a mercenary
Crippled by small pox as a child
Wanted to be a minister
Thrown out of Lutheran church

3. Johannes Kepler Lived around the time of Galileo
Mathematician, Astronomer, Astrologer
Biggest job: provide update astrological charts of the Emperor Rudolph II
Copernican vs. Ptolemaic Model

4. Mars’ orbit not a circle
Eyes are source of depth perception
Sun rotates on an axis
Moon is the cause of tides

5. Keplers Law’s

6. Keplers First Law: planet paths are not circles but an ellipses with the sun at one focus of the ellipse

7. Keplers First Law
Elliptical Motion of Planets

8. Keplers Second Law: A line drawn from the sun to a planet sweeps out an equal area in an equal time period.

9. Kepler’s Second Law
Equal area in equal time interval

11. Keplers Third Law: The square of the ratio of the period of two planetary orbits is equal to the cube of the ratio of their average distance to the sun.
(T1/T2)2 = (R1/R2)3

12.                                                             
(T1/T2)2 = (R1/R2)3

13. Example: Earth and Mars both orbit the sun
Example: Earth and Mars both orbit the sun. If the Earth has an orbital period of 365 days and an orbital radius of 1.50 x 1011m and Mars has an orbital radius of 2.28 x 1011m . How long is a Martian year?

14. TEarth = 365 days
REarth = 1.5 x m
RMars = 2.28 x 1011 m
TMars = ? T

15. Law of Universal Gravitation

16. Son of a farmer who hated farming
No money for college
Did work-study at Cambridge
School taught Aristotle
Preferred to read Copernicus, Galileo and Keplier

17. Introduce Infinitesimal Calculus
Spectral Colors of White Light
Laws of Motion
Universal Law of Gravitation
Philosophiae Naturalis Principia Mathematica

18. “Objects attract other objects with a force…”
Philosophiae Naturalis Principia Mathematica

19. “Objects attract other objects with a force that is proportional to the product of their masses…”
Philosophiae Naturalis Principia Mathematica

20. “Objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.”
Philosophiae Naturalis Principia Mathematica

22. Newton’s Law of Universal Gravitation:
Every body in the universe attracts every other body
with a force
that is directly proportional to the product of their masses
and is inversely proportional to the square of the distance
between their centers.
Where: G
Universal
Gravitational
Constant
Equation:

23. m1 m2 F
2m1 m2 2F
2m2
2m1 4F 6F
2m2
3m1

24. same force, but different accelerations.
Even though the masses may be different sizes, they exert the same amount of force on each other – this is because of Newton’s third law.
F = ma
F = ma
same force, but different accelerations.

25. m1 m2 r F
Inverse Square Law m1 m2 2r
1/4 F m1 m2
the greater the distance between the masses, the less the force between them 3r
1/9 F m1 m2 4F
1/2r

26. Example: Find the force of gravitational attraction between two students separated by 1.2 m. The masses of the students are 60 kg and 70 kg.

27. Weighing the Earth:
Purpose: Use the Law of Universal Gravitation to determine
the mass of the Earth.
Let m1 = mass of object = mo
m2 = mass of Earth = ME
r = radius of Earth = RE
= km
= x 106 m

28. Since Fg is the weight of the object,
&

29. Also can find g at any height above a planet’s surface.
Note: developed the equation:
Or in general
P : any planet
Given the mass of any planet and its radius,
the acceleration due to gravity on that planet can be found.
Also can find g at any height above a planet’s surface.
R= height + radius of the planet

30. Example:
Find the value of g on Mars, using the information
on pg 173.

31. What is g 1000 km above the surface of mars?

32. 1 AU: (Astronomical Unit) average distance from
earth to the sun 149,597,870.7 km
92,955,807.27 miles
Mercury 0.387
Venus 0.723
Earth 1 (of course)
Mars 1.52
Jupiter 5.20
Saturn 9.54
Uranus 19.2
Neptune 30.1
Pluto 39.4

33. 1 parsec: One parsec is approximately
3.262 light-years
The nearest known star to the Earth, other than
the Sun, is Proxima Centauri 1.29 parsecs away.
The center of the Milky Way is about 8 kpc from the Earth, and the Milky Way is about 30 kpc across.
The Andromeda Galaxy (M31) is slightly less than 800 kpc away from the Earth.