ASTR 1P01 - Lecture 6: Newtonian Physics Summary

Some basic concepts in physics

• Mass: Measure of how much matter is in an object, measured in kilograms (kg).
• Weight:
  • Proportional to mass but not the same.
  • Mass is constant; weight is gravitational force attracting the object to a planet's surface.
  • Weight varies depending on gravity (e.g., less on the Moon, none in space).
• Density: Mass per unit volume, measured in kg/m3.
  • Example: Bricks vs. Feathers (same mass, different densities).
  • If a material has a density of 1 kg/m3:
    • 1 m3 of this material will have a mass of 1 kg.
    • 2 m3 of this material will have a mass of 2 kg. And so on.
• Momentum: Product of mass and velocity.
  • Mass is analogous to the number of atoms.
  • Momentum = mass × velocity = adding up the velocities of all the atoms.
  • Units are kg ⋅ m/s.
• Rate of change:
  • Velocity: Rate of change of position (meters per second, m/s).
  • Acceleration: Rate of change of velocity (meters per second squared, m/s2).

Newton's first law of motion

• Isaac Newton (1642-1727) was an English mathematician, physicist, and astronomer.
• Established classical mechanics.
• In 1687, published "Mathematical Principles of Natural Philosophy," introducing three laws of motion and universal gravitation.
• An object moving at a constant velocity will not change its speed unless acted on by a force.
• Constant velocity includes being at rest.
• Applies to objects on Earth and in space, indicating planets are made of the same matter as Earth.
• Speed vs. Velocity:
  • Speed is how fast you're moving (e.g., 100 km/h).
  • Velocity includes speed and direction (e.g., 100 km/h due north).
  • Mathematically:
    • speed is a number
    • velocity is a vector (arrow with length and direction).
• Force:
  • Mathematically, force is a vector (length and direction).
  • Physically, force is an interaction that pushes or pulls an object.
  • Measured in newtons (N).
• Friction, air resistance, and gravity are types of forces that affect motion on Earth.
• In space, objects can move at constant speed without slowing down due to the vacuum.

Newton's second law of motion

• Force is equal to the rate of change of momentum.
• If there's no force, there's no change in momentum and if there's a force, the momentum changes.
• If mass is constant, force equals mass times acceleration: F = ma
  • F is the force,
  • m is the mass (assumed to be constant),
  • a is the acceleration.
• 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s2.
• Newton's First Law defines inertial frames of reference.
  • Inertial frame: observer is at rest, and Newton’s first law holds.
  • Accelerating frame: Non-inertial frame.
• We can only feel acceleration not constant speed, so in an inertial frame, if you're moving at a constant speed, then there's no force acting on you, and therefore nothing to feel.

Newton’s third law of motion

• If two objects exert forces on each other, these forces are equal in magnitude and opposite in direction.
• Every action has an equal and opposite reaction.
• Examples: walking (feet push ground), rockets (exhaust gas).
• Conservation of momentum:
  • The total momentum of two interacting objects never changes.
  • Mass and velocity are not conserved but momentum is conserved.
• Angular momentum:
  • “Total rotation” of an object around a point.
  • Defined as mass × velocity × distance from the point.
  • Also conserved.

Newton’s universal law of gravitation

• There must be a force bending the paths of the planets, since they do not move in straight lines.
• Every object in the universe has gravity.
• Consistent with Newton’s 3rd law: forces come in equal and opposite pairs.
• All objects with mass attract each other.
• Newtonian gravity is precise but general relativity provides a more precise definition of gravity.
• To define a theory precisely, we must use mathematics.
• Newton had to invent calculus, which deals with change, to formulate and test this theory.
• Scientific hypothesis can only be accepted as a theory if its predictions match experimental and observational data.
  • This happened before, with Ptolemy’s model. When it no longer matched the data, it had to be replaced with the heliocentric model, Kepler’s laws, and eventually Newtonian gravity.
• Newtonian gravity can be precisely described by the equation: F = G \frac{m1 m2}{r^2}
  • m_1 is the mass of the first object.
  • m_2 is the mass of the second object.
  • F is the force of gravity between the objects.
  • r is the distance between the objects.
  • G is a constant of proportionality called the gravitational constant. Its value doesn’t matter, it’s just used to convert units.
• Force is larger if masses are larger and smaller if distance is larger.
• Gravity fades with distance but never disappears completely which is why the Sun’s gravity attracts objects in
  • The Kuiper belt, at 30-50 AU.
  • The Oort cloud, at 2,000 to 200,000 AU.
• The Sun’s gravity also affects nearby stars such as Alpha Centauri.
• Outside the Milky Way galaxy, the gravity of our Sun alone is so small that it has no effect on its own.
• This means that other smaller galaxies orbit the Milky Way, just like planets orbit the Sun.
• These galaxies are called satellite galaxies and includes the Large Magellanic Cloud and the Small Magellanic Cloud.
• The mass of your body participates in the gravitational pull that acts on entire galaxy superclusters!

Free fall

• Astronauts in space feel no gravity and can float in the air, even though they are only a few hundred km above the surface.
• Astronauts in orbit are in free fall, falling around the Earth.
• Astronauts and space station fall at the same rate, so they appear to float.
• Weight is the gravitational force on the body, which is why the astronauts feel “weightless”.
• The astronauts don’t feel a normal force because they are falling at the same rate as everything around them.
• Weightlessness can also be achieved using a plane inside Earth’s atmosphere which passengers will experience weightlessness for a short time.