Units 17, 18, 19, 20

1
Units 17, 18, 19, 20
Homework 3 is on the website of the
course http//www.astro.wisc.edu/lazarian/ast103_
2014/
2

• Acceleration of a body is its rate of change of
• Mass
• Weight
• Velocity
• Positions

3
An object orbiting the sun in a circle can be
said to be

1. Weightless
2. Always accelerating
3. Moving at a constant velocity
4. Moving under equal and opposite forces

4

• An accelerating body must at all times
• Have a changing direction of motion
• Have an increasing velocity
• Be moving
• Have a changing velocity

5
Which of the following statements about an
asteroid moving in a circular orbit around the
Sun is untrue?

1. It is moving on a flat plane
2. It is moving with constant velocity
3. It is accelerating
4. It is moving with constant speed

6
Orbits

• As we saw in Unit 17, we can find the mass of a
  large object by measuring the velocity of a
  smaller object orbiting it, and the distance
  between the two bodies.
• We can re-arrange this expression to get
  something very useful

We can use this expression to determine the
orbital velocity (V) of a small mass orbiting a
distance d from the center of a much larger mass
(M)
7
Calculating Escape Velocity

• From Newtons laws of motion and gravity, we can
  calculate the velocity necessary for an object to
  have in order to escape from a planet, called the
  escape velocity

8
What Escape Velocity Means

• If an object, say a rocket, is launched with a
  velocity less than the escape velocity, it will
  eventually return to Earth
• If the rocket achieves a speed higher than the
  escape velocity, it will leave the Earth, and
  will not return!

9
Escape Velocity is for more than just Rockets!

• The concept of escape velocity is useful for more
  than just rockets!
• It helps determine which planets have an
  atmosphere, and which dont
• Object with a smaller mass (such as the Moon, or
  Mercury) have a low escape velocity. Gas
  particles near the planet can escape easily, so
  these bodies dont have much of an atmosphere.
• Planets with a high mass, such as Jupiter, have
  very high escape velocities, so gas particles
  have a difficult time escaping. Massive planets
  tend to have thick atmospheres.

10
Konstantin Tsiolkovsky, pioneer of space
exploration
11
Werner Von Braun --Dark Genius of Rocket Science
12
Centripetal Force

• If we tie a mass to a string and swing the mass
  around in a circle, some force is required to
  keep the mass from flying off in a straight line
• This is a centripetal force, a force directed
  towards the center of the system
• The tension in the string provides this force.
• Newton determined that this force can be
  described by the following equation

13
Masses from Orbital Speeds

• We know that for planets, the centripetal force
  that keeps the planets moving on an elliptical
  path is the gravitational force.
• We can set FG and FC equal to each other, and
  solve for M!
• Now, if we know the orbital speed of a small
  object orbiting a much larger one, and we know
  the distance between the two objects, we can
  calculate the larger objects mass!

14
Newtons Modification of Keplers 3rd Law

• Newton applied his ideas to Keplers 3rd Law, and
  developed a version that works for any two
  massive bodies, not just the Sun and its planets!
• Here, MA and MB are the two objects masses
  expressed in units of the Suns mass.
• This expression is useful for calculating the
  mass of binary star systems, and other
  astronomical phenomena

15
The Origin of Tides

• The Moon exerts a gravitational force on the
  Earth, stretching it!
• Water responds to this pull by flowing towards
  the source of the force, creating tidal bulges
  both beneath the Moon and on the opposite side of
  the Earth

16
High and Low Tides
As the Earth rotates beneath the Moon, the
surface of the Earth experiences high and low
tides
17
The Sun creates tides, too!

• The Sun is much more massive than the Moon, so
  one might think it would create far larger tides!
• The Sun is much farther away, so its tidal forces
  are smaller, but still noticeable!

• When the Sun and the Moon line up, higher tides,
  call spring tides are formed
• When the Sun and the Moon are at right angles to
  each other, their tidal forces work against each
  other, and smaller neap tides result.

18
The Conservation of Energy

• The energy in a closed system may change form,
  but the total amount of energy does not change as
  a result of any process

19
Kinetic Energy

• Kinetic Energy is simply the energy of motion
• Both mass (m) and velocity (V) contribute to
  kinetic energy
• Imagine catching a thrown ball.
• If the ball is thrown gently, it hits your hand
  with very little pain
• If the ball is thrown very hard, it hurts to
  catch!

20
Thermal Energy

• Thermal energy is the energy associated with heat
• It is the energy of the random motion of
  individual atoms within an object.
• What you perceive as heat on a stovetop is the
  energy of the individual atoms in the heating
  element striking your finger

21
Potential Energy

• You can think of potential energy as stored
  energy, energy ready to be converted into another
  form
• Gravitational potential energy is the energy
  stored as a result of an object being lifted
  upwards against the pull of gravity
• Potential energy is released when the object is
  put into motion, or allowed to fall.

22
Definition of Angular Momentum

• Angular momentum is the rotational equivalent of
  inertia
• Can be expressed mathematically as the product of
  the objects mass, rotational velocity, and radius
• If no external forces are acting on an object,
  then its angular momentum is conserved, or a
  constant

23
Conservation of Angular Momentum

• Since angular momentum is conserved, if either
  the mass, size or speed of a spinning object
  changes, the other values must change to maintain
  the same value of momentum
• As a spinning figure skater pulls her arms
  inward, she changes her value of r in angular
  momentum.
• Mass cannot increase, so her rotational speed
  must increase to maintain a constant angular
  momentum
• Works for stars, planets orbiting the Sun, and
  satellites orbiting the Earth, too!