Newton's Laws of Motion

• I, Inertia: An object moves at constant velocity, unless it feels a net force.
• 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. When two objects feel each other's (equal!) forces, the lighter one's motion is more strongly affected. You can't push without being pushed.
• Examples: Does a satellite necessarily need some force to keep it up in orbit? When a rocket lifts off, does it push against the ground?
• Mass and Weight: They are not the same thing; Mass is the "amount of substance" of an object and does not change; Weight is the effect of gravity on mass, and can be zero or appear to be zero; You can be weightless, but not massless.

Newton's Law of Gravity

• The law: There is a (weak) force of gravity between any two objects, including celestial objects (there is gravity in space), and this force can be calculated using the inverse-square law F = G M m / r².
• 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.
• New twist #1: Planets actually orbit around the center of mass of the planet + Sun system (and the Sun does too!).
• New twist #2: There can be new types of orbits, unbound ones [hyperbolas or parabolas], in addition to ellipses.
• New twist #3: What relates orbit size and period of an orbit in Kepler's third law is the sum of the two masses involved.
• New twist #4: Planets feel each other's gravity, and that of everything else.
• Question: So, in the real world, are the orbits of planets really ellipses?

  Other Situations and Related Concepts

• Acceleration of gravity: Because mass affects both the force of 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, gravity explains the fact that small moons and asteroids are not round, while larger objects are.
• Satellites around the Earth: Larger orbits have longer periods; e.g., geosynchronous ones [42,000 km], or 90 minutes for the Space Shuttle.
• Our Moon: Its orbit is elliptical too [and the period that enters into Kepler's laws is the sidereal month, rather than the lunar one].
• New concept: The escape velocity from a center of attraction; depends on its mass and size [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: One can 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.