1. Lecture 5: Gravity and Motion

2. Describing Motion and Forces
speed, velocity and acceleration
momentum and force
mass and weight
Newton’s Laws of Motion
conservation of momentum
analogs for rotational motion

3. Torque and Angular Momentum
A torque is a twisting force
Torque = force x length of lever arm
Angular momentum is torque times velocity
For circular motion, L = m x v x r

4. Laws for Rotational Motion
Analogs of all of Newton’s Laws exist for rotational motion
For example, in the absence of a net torque, the total angular momentum of a system remains constant
There is also a Law of Conservation of Angular Momentum

6. Conservation of Angular Momentum during star formation

7. Newton’s Universal Law of Gravitation
Every mass attracts every other mass through a force called gravity
The force is proportional to the product of the two objects’ masses
The force is inversely proportional to the square of the distance between the objects’ centers

8. Universal Law of Gravitation

9. The Gravitational Constant G
The value of the constant G in Newton’s formula has been measured to be G = 6.67 x 10 –11 m3/(kg s2)
This constant is believed to have the same value everywhere in the Universe

10. Remember Kepler’s Laws?
Orbits of planets are ellipses, with the Sun at one focus
Planets sweep out equal areas in equal amounts of time
Period-distance relation:
(orbital period)2 = (average distance)3

11. Kepler’s Laws are just a special case of Newton’s Laws!
Newton explained Kepler’s Laws by solving the law of Universal Gravitation and the law of Motion
Ellipses are one possible solution, but there are others (parabolas and hyperbolas)

12. Conic Sections

13. Bound and Unbound Orbits
Unbound (comet)
Unbound (galaxy-galaxy)
Bound
(planets,
binary stars)

14. Understanding Kepler’s Laws: conservation of angular momentum
L = mv x r = constant
smaller distance
smaller r
bigger v
planet moves faster r
larger distance
smaller v
planet moves slower

15. Understanding Kepler’s Third Law
Newton’s generalization of Kepler’s Third Law is given by:
4p2 a3
p2 =
G(M1 + M2)
4p2 a3
p2 =
GMsun
Mplanet << Msun, so 

16. This has two amazing implications:
The orbital period of a planet depends only on its distance from the sun, and this is true whenever M1 << M2

17. An Astronaut and the Space Shuttle have the same orbit!

18. Second Amazing Implication:
If we know the period p and the average distance of the orbit a, we can calculate the mass of the sun!

19. Example: How can we use this information to find the mass of the Sun?
Io is one of the large Galilean moons orbiting Jupiter.
It orbits at a distance of 421,600 km from the center of
Jupiter and has an orbital period of 1.77 days.
How can we use this information
to find the mass of the Sun?

20. Tides

21. The Moon’s Tidal Forces on the Earth

27. Tidal Friction

28. Synchronous Rotation

29. Galactic Tidal Forces