Newton's Laws of Motion

• I, Inertia: An object moves at constant velocity, unless a net force acts on it.
• II, Force: If a net force acts the acceleration is inversely proportional to the mass.
• III, Action and Reaction: The force of B on A is equal and opposite to that of A on B.
• What is he saying? The easiest things for us to see are position and speed, but forces do not cause motion, they cause acceleration ("What keeps a satellite up?"). When two objects feel each other's (equal!) forces, the lighter one's motion is more strongly affected.
• Mass and Weight: They are not the same thing; You can be weightless, but not massless.
• For example: When a rocket lifts off, does it push against the ground?

Newton's Law of Gravity

• The law: There is a force of gravity between any two objects, including celestial objects (there is gravity in space), and this force can be calculated as F = G M m / r² (inverse-square law).
• And planetary motion: Celestial objects like planets obey the same laws as earthly ones! We now understand Kepler's laws, they can be explained using the force of gravity that the Sun pulls with.
• 1st new twist: Planets actually orbit around the center of mass of the planet + Sun system (and the Sun does too!).
• 2nd new twist: There can be new types of orbits, unbound ones [hyperbolas or parabolas], in addition to ellipses.
• 3rd new twist: What relates orbit size and period of an orbit in Kepler's third law is the sum of the two masses involved.
• Question: In the real world, are the orbits of planets really ellipses?

  Other Situations and Related Concepts

• Acceleration of gravity: Because mass affects both gravity and the resistance to accelerate, all objects end up falling at the same rate.
• Gravity on Earth: At our distance from the Earth's center, using the mass of the Earth, we get an acceleration of 9.8 m/s².
• Around other objects: The laws of motion and gravity hold for any body around any gravitational center of attraction, even asteroids, binary stars and galaxies... By the way, how is gravity related to the fact that small moons and asteroids are not round, while larger ones are?
• Satellites around the Earth: Larger orbits have longer periods; e.g., geosynchronous ones [42,000 km], or 90 minutes for the Shuttle.
• Our Moon: Should we use a sidereal or a lunar month as the orbital period?
• New concept: The escape velocity from a center of attraction [11 km/s from the Earth's surface].

Other Consequences

• Tides on Earth: Every 12 hours, due to the Moon (and the Sun, so we get enhanced spring tides at full and new moon, and reduced neap tides), affecting mostly the water.
• Consequences: The Earth's rotation rate is slowing down (by 1 day every 50,000 years!), and the distance to the Moon increasing.
• Other tides: Our Moon's rotation (and that of other moons in the Solar System) became locked to its revolution; Comets can break into pieces when approaching planets; Extreme cases near black holes; Pairs of galaxies in which tides seem to enhance star formation...
• Effects of gravitational encounters: Capture or slingshot effect by energy transfer [but gravity-even black holes-does not "suck in" anything!].
• Use of the third law: Calculate masses from sizes of orbits and periods; e.g., Jupiter and its moons, Sirius A and B; asteroid Ida and its satellite.
• Motion around the center of mass: If both objects move, we can notice the presence of one even if we only see the other one...

Other Comments on Newton

• Ideas in common with Aristotle: Time is uniform and ever-flowing.
• Telescopes: He invented the reflecting telescope.