Chapter 3: Inertia and Newton's Law of Motion

Inertia

  • Galileo developed the idea of inertia.
  • Newton used it as his 1st law of motion.
  • Net force = The sum of all forces pulling in various directions.
  • If the net force = 0, inertia is constant.
  • A body that is not moving will remain motionless = constant velocity.
  • A moving body’s motion will remain constant at the same speed and in the same direction = constant velocity.

Speed and Velocity

  • Speed is a change of position in some amount of time, such as m/s or km/h.
  • Velocity is a speed in a particular direction.
  • NOTE: The units, m/s, are still the same, which can cause confusion.
  • If the speed remains constant, but the direction changes, the velocity changes.

Orbital Motion and Gravity

  • Newton understood that orbiting objects, such as the Moon and Earth, have constantly changing velocity because of the changing direction.
  • Newton realized that a force causes this changing velocity.

Acceleration

  • When an object accelerates, its velocity changes.
  • Its speed may increase in some length of time.
  • Its speed may decrease in some time = a deceleration or a negative acceleration.
  • If an object’s direction of motion changes its velocity changes even though its speed may remain constant = acceleration.
  • Units are m/sΛ2m/s^{\Lambda }2

Mass

  • Mass - amount of matter in a body.
  • Impossible to count the number of atoms and molecules in a body.
  • Express the mass in kilograms (kg).
  • Mass is NOT the same as weight.
  • Weight is the force of gravity on a mass.
  • Confusion is caused when people use the kg for both mass and weight - wrong.
  • The unit of weight is the Newton.

Newton's Laws

Newton’s 2nd Law of Motion

  • With the quantities we have defined, we can state Newton’s 2nd law of motion.
  • A net force causes of body with a mass to accelerate and the relationship is acceleration = net force/mass (a=F/m)
  • It is a simple equation, but it explains the motions of all objects on Earth, in the solar system, and throughout the Universe.

Newton’s 3rd Law of Motion

  • When two objects interact with each other the force of object 1 on object 2 is equal to the force of object 2 on object 1.
  • Action = Reaction

Newton’s Law of Gravitational Force

  • Newton needed to develop a law for the force of gravity for his laws of motion.
  • Force of gravity depends on all masses: for two objects these are M for the larger mass and m for the smaller mass.
  • Force of gravity depends on the separation.
  • Greater separation \rightarrow weaker force.
  • Weakens as (1/separation) = “inverse square law”
  • Force of gravity never goes to zero, no matter how far away.
  • Newton’s equation:
  • F(G)=G(Mm/(dΛ2))F(G) = G*(Mm/(d^{\Lambda }2))
  • G = universal gravitational force constant.
  • M = the mass (kg) of the larger object.
  • m = the mass (kg) of the smaller object.
  • d = the separation (m) between the two objects.

Gravity is important for Astronomy

  • Astronomical objects have:
  • Huge masses \rightarrow huge force of gravity.
  • Huge separations \rightarrow weak force of gravity.
  • Small separations \rightarrow huge force of gravity.
  • Mass is only a positive quantity.
  • Gravity cannot cancel out.
  • Gravity never stops, even at the largest distances.

Earth and Moon

  • The force of Earth’s gravity on the Moon is FG=G(MEarchmmoon/dΛ2)F_{G}=G(M_{Earch}\cdot m_{moon}/d^{\Lambda }2)
  • However, the Earth and Moon respond differently to the same force because they have different masses.
  • For the Moon amoon = FG/mmoon
  • For the Earth aEarth = FG/MEarth
  • NOTE: The force of gravity causes both the Moon and Earth to accelerate.

Measuring Masses

  • Measuring orbits is the fundamental way of measuring masses in astronomy.
  • To make things simple, assume M>>m.
  • Combine Newton’s 2nd law of motion and his law of gravity to get M = dV^2/G.
  • The mass equation can be rewritten as a modified version of Kepler’s 3rd law (PΛ2=aΛ3).(P^{\Lambda }2 = a^{\Lambda }3).
  • Newton’s version: M=(4piΛ2dΛ3)/(GPΛ2)M = (4\cdot pi^{\Lambda }2\cdot d^{\Lambda }3)/(GP^{\Lambda }2)
  • This can be used for any planet.

The Sun, Surface Gravity, Escape Velocity and Planets

The Mass of the Sun

  • To measure the Sun’s mass we can use Earth’s orbit.
  • d = 1 AU
  • P = 1 year
  • G = 6.6710Λ116.67 \cdot 10^{\Lambda }-11
  • This results in about 300,000 MEarth

Surface Gravity

  • We experience “surface gravity” here on Earth every day, and that would also be true on the Moon or another planet.
  • Surface gravity is the acceleration caused by a planet’s (such as Earth) gravity.

Escape Velocity

  • The surface gravity determines how fast an object must travel to escape into space.
  • The equation can be found from Newton’s laws of motion and gravity.
  • Earth’s escape velocity is found using its mass and radius.
  • The moon’s escape velocity is much less because its mass and radius are less

Atmospheres of Planets

  • A planet’s ability to have an atmosphere depends on two things:
  • Distance from the Sun, which determines the temperature of the atmospheric gas: closer to the Sun the gas is hotter and moves faster (molecules in hot temperature are more active).
  • The escape velocity of the planet.
  • If the gas speed > escape speed, the planet cannot hold an atmosphere.


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