Source Material for this week

1
Source Material for this week

• Wednesday Friday (Lecs 18 19)
• Keplers Laws from CP 3.3 (pp. 73-74 you skipped
  them before)
• CP 4.4 4.5 (Gravity Orbits)
• SKIP the section on Tides (Begin again at Why do
  all objects fall at the same rate?)

2
Source Material for next week

• Monday Wednesday (Lecs 20 21) Applications
  of Energy, Motion, Gravity, Orbits
• CP 7.3 Spacecraft Exploration of the Solar
  System
• CP 24.5 Just section on How difficult is
  interstellar travel? (including Starship Design)

3
4. Gravity All about Orbits
Our goals for learning

• How does gravity cause orbits?
• Weight vs. mass
• What is the universal law of gravitation?
• What is orbital energy?
• Will a spacecraft passing by a planet be sucked
  in?
• Keplers Laws of planetary motion
• gravity explains them
• Measuring masses using gravity

4
Weightlessness

• Why do objects in the Space Shuttle float?
• A No gravity in space
• B Falling with Space Shuttle
• C They have no mass
• D Air pressure

5

• Compared to your mass here on Earth, your mass
  out in space between the stars is
• A zero
• B negligibly small
• C much much greater
• D the same
• E cant tell from the info given

6
Mass vs. Weight

• mass amount of matter in an object
• weight the force which acts upon an object

weightless really means falling! When in
free-fall, you are weightless!! Click Here
7
Universal Gravitation Everything Sucks

• Gravity explains orbits, but what is gravity?
• Every object in the universe attracts every other
  with a force
• Depends on masses and distance between them
  (FGm1m2/d2)
• Double Mass ? Double force
• Double distance ? ¼ force

8
Clicker Question

• You are currently experiencing an attraction
  towards your neighbor by the force of gravity
  (although other forces are much stronger than
  this one).
• True
• False

9
Why gravity pulls towards the Earths center
10
Weight on Different Planets

• The Moon is ¼ the radius of the Earth, and its
  mass is 81 times smaller. On the Moons surface,
  the force of gravity is 1/6th that of the Earths
  surface. On the Moon you would weigh
• The same as on Earth
• 6 times as much as on Earth
• 1/6th as much as on Earth
• Cant tell without trying it!

11
Falling Causes Orbits

• Depending on initial velocity, the cannonball
  either
• falls
• orbits
• escapes

12
Gravity Question

• If one could magically turn off gravity the Earth
  would
• A leave the solar system along a straight line
  connecting the Earth and Sun
• B spiral out of control and leave the solar
  system in a chaotic path
• C travel in a nearly straight line along its
  present velocity perpendicular to a line
  connecting Earth and Sun
• D move outwards to collide with the Moon

13
Orbit Basics

• Circular velocity needed to maintain a circular
  orbit.
• Orbits with other velocities are ellipses
• Escape velocity needed to escape entirely
• Stronger acceleration due to gravity, then object
  must move faster to maintain orbit
• Implies closer together and/or larger masses

14
Clicker Question

• A man-made satellite orbits because
• A) it is constantly firing rockets to keep it
  from falling to Earth
• B) it is falling around the Earth
• C) it has enough energy to escape Earths
  gravity entirely

15
Gravity Question

• If the Sun were suddenly replaced by a black hole
  with the same mass as the Sun, the Earth would
• A move off the current orbit in a straight line
• B remain in the same orbit
• C move into a smaller orbit
• D be pulled into the black hole

16
Conservation of EnergyOrbits

• Orbital energy Kinetic Energy Potential
  Energy
• conservation of energy implies
• orbits cant change spontaneously
• Need some sort of acceleration (thrusters, air
  friction.)

17
Applying this to Planets!

• Recall
• Copernicus Sun-centered model didnt precisely
  match Tycho Brahes careful observations
• Johannes Kepler figured out why
• Planet orbits not circles, but ellipses (nearly
  circular)
• Planet motion not uniform

• Kepler found 3 laws of planetary motion
• but didnt know why they worked
• Newton figured it out!

18
Keplers First Law

• Each planets orbit around the Sun is an ellipse,
  with the Sun at one focus (NOT circular motion!)

NOTE Orbits of planets are almost circular
19
Orbits are ellipses

• But nearly circular!

From Nick Strobels Astronomy Notes
http//www.astronomynotes.com.
20
Keplers Second Law

• A planet moves along its orbit with a speed such
  that a line from the planet to the Sun sweeps out
  equal areas in equal intervals of time. (NOT
  uniform motion) (moves fastest when nearest Sun)

21
Newtons Explanation of Keplers 1st Two Laws

• Newtons Law of gravity predicts
• Orbits are ellipses (Keplers 1st Law)
• Angular momentum should be conserved
• Objects move faster when they are closer to the
  Sun (think figure skater)
• Translates to law of equal areas

22
Keplers Third Law

• The ratio of the cube of a planets average
  distance from the Sun to the square of its
  orbital period is the same for each planet.

R3 / P2 1
R3 P2
Inner planets orbit more quickly
23
Newtons Explanation of Keplers Third Law

• Newtons law of gravity predicts Keplers 3rd
  Law
• Close to Sun
• acceleration due to gravity stronger
• planet must move faster to stay in orbit
• moving faster and along shorter path means
  orbital period is smaller

24
Concept Question

• Two satellites orbit the Earth. One is in a very
  large elliptical orbit, and the other is in a
  small circular orbit.
• The satellite in an elliptical orbit
• A) moves at the same speed at all points in its
  orbit
• B) must eventually spiral into the Earth
• C) takes longer to orbit the Earth than the
  satellite in a circular orbit
• D) will eventually have a circular orbit

25
Newtons Version of Keplers 3rd Law Measuring
Masses
General form (P in years, R in AU, m in Solar
Masses)
(m1 m2) R3 / P2

• Measure
• orbital period of two objects (P)
• distance between them (R)
• Calculate
• sum of both masses (m1 m2)
• If m2 ltltm1 only the larger mass matters (e.g.
  moons around Jupiter, planets around Sun)
• In the case of the Sun, this becomes Keplers 3rd
  Law
• Can use measured orbit of something small to
  determine the mass of whatever it is orbiting!

26
Thats the Math Now Why Does it Work?

• Gravity!
• Speed required to keep object in orbit depends on
  gravity
• Acceleration due to gravity depends on distance
  and mass involved (stronger if closer and/or more
  mass)
• How measure?
• Distance between objects size of orbit
• Measure angular size distance TO objects
• Period how long it takes to go around
• Combine
• Orbit size orbit period ? orbit speed!
• Figure out mass that corresponds to that orbit
  speed

27
Question

• If the Earth were in the same size orbit about a
  star that had 2 the mass of the Sun, then
• A) a year would be the same length
• B) a year would be longer
• C) a year would be shorter

28
Question

• Planet Bee is 0.5 AU from its star Daffodil. Bee
  takes 2 years to go around Daffodil. Then
• A Daffodil is more massive than the Sun
• B Daffodil is less massive than the Sun
• C Daffodil is the same mass as the Sun
• D You dont have enough information to compare
  the mass of Daffodil to that of the Sun

29
Astronomical Masses
ONLY

• Newtons Law of Gravity is the
  tool we have for measuring astronomical masses!
• THIS is how we measure masses in the solar system
  (and therefore densities!)
• We use the same concept to measure all masses in
  astronomy!
• e.g. Two stars can also orbit one another
• Mizar (central star in handle of Big Dipper)