slide1
Download
Skip this Video
Download Presentation
Chapter 13 Gravitation

Loading in 2 Seconds...

play fullscreen
1 / 29

Chapter 13 Gravitation - PowerPoint PPT Presentation


  • 151 Views
  • Uploaded on

Chapter 13 Gravitation. Newton’s law of gravitation Any two (or more) massive bodies attract each other Gravitational force (Newton\'s law of gravitation) Gravitational constant G = 6.67*10 –11 N*m 2 /kg 2 = 6.67*10 –11 m 3 /(kg*s 2 ) – universal constant.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Chapter 13 Gravitation' - carrie


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Chapter 13

Gravitation

slide2

Newton’s law of gravitation

  • Any two (or more) massive bodies attract each other
  • Gravitational force (Newton\'s law of gravitation)
  • Gravitational constantG= 6.67*10 –11 N*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant
slide3

Gravitation and the superposition principle

  • For a group of interacting particles, the net gravitational force on one of the particles is
  • For a particle interacting with a continuous arrangement of masses (a massive finite object) the sum is replaced with an integral
slide4

Chapter 13

Problem 9

slide5

Shell theorem

  • For a particle interacting with a uniform spherical shell of matter
  • Result of integration: a uniform spherical shell of matter attracts a particle that is outside the shell as if all the shell\'s mass were concentrated at its center
slide6

Gravity force near the surface of Earth

  • Earth can be though of as a nest of shells, one within another and each attracting a particle outside the Earth’s surface
  • Thus Earth behaves like a particle located at the center of Earth with a mass equal to that of Earth
  • g = 9.8 m/s2
  • This formula is derived for stationary Earth of ideal spherical shape and uniform density
slide7

Gravity force near the surface of Earth

In reality gis not a constant because:

Earth is rotating,

Earth is approximately an ellipsoid

with a non-uniform density

slide8

Gravity force near the surface of Earth

Weight of a crate measured at the equator:

slide9

Gravitation inside Earth

  • For a particle inside a uniform spherical shell of matter
  • Result of integration: a uniform spherical shell of matter exerts no net gravitational force on a particle located inside it
slide10

Gravitation inside Earth

  • Earth can be though of as a nest of shells, one within another and each attracting a particle only outside its surface
  • The density of Earth is non-uniform and increasing towards the center
  • Result of integration: the force reaches a maximum at a certain depth and then decreases to zero as the particle reaches the center
slide11

Chapter 13

Problem 20

slide12

Gravitational potential energy

  • Gravitation is a conservative force (work done by it is path-independent)
  • For conservative forces (Ch. 8):
slide13

Gravitational potential energy

  • To remove a particle from initial position to infinity
  • Assuming U∞ = 0
slide14

Escape speed

  • Accounting for the shape of Earth, projectile motion (Ch. 4) has to be modified:
slide15

Escape speed

  • Escape speed: speed required for a particle to escape from the planet into infinity (and stop there)
slide16

Escape speed

  • If for some astronomical object
  • Nothing (even light) can escape from the surface of this object – a black hole
slide17

Chapter 13

Problem 33

slide18

Johannes Kepler

(1571-1630)

Tycho Brahe/

Tyge Ottesen

Brahe de Knudstrup

(1546-1601)

  • Kepler’s laws
  • Three Kepler’s laws
  • 1. The law of orbits: All planets move in elliptical orbits, with the Sun at one focus
  • 2. The law of areas: A line that connects the planet to the Sun sweeps out equal areas in the plane of the planet’s orbit in equal time intervals
  • 3. The law of periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit
slide19

First Kepler’s law

  • Elliptical orbits of planets are described by a semimajor axisa and an eccentricitye
  • For most planets, the eccentricities are very small (Earth\'s e is 0.00167)
slide20

Second Kepler’s law

  • For a star-planet system, the total angular momentum is constant (no external torques)
  • For the elementary area swept by vector
slide21

Third Kepler’s law

  • For a circular orbit and the Newton’s Second law
  • From the definition of a period
  • For elliptic orbits
slide22

Satellites

  • For a circular orbit and the Newton’s Second law
  • Kinetic energy of a satellite
  • Total mechanical energy of a satellite
slide23

Satellites

  • For an elliptic orbit it can be shown
  • Orbits with different ebut the same a have the same total mechanical energy
slide24

Chapter 13

Problem 50

slide25

Answers to the even-numbered problems

Chapter 13:

Problem 2

2.16

slide26

Answers to the even-numbered problems

  • Chapter 13:
  • Problem 4
  • 2.13 × 10−8 N;
  • (b) 60.6º
slide27

Answers to the even-numbered problems

  • Chapter 13:
  • Problem 20
  • G(M1 +M2)m/a2;
  • (b) GM1m/b2;
  • (c) 0
slide28

Answers to the even-numbered problems

  • Chapter 13:
  • Problem 32
  • 2.2 × 107 J;
  • (b) 6.9 × 107 J
slide29

Answers to the even-numbered problems

Chapter 13:

Problem 54

(a) 8.0 × 108 J;

(b) 36 N

ad