Outline

1. Kepler's Laws of planetary orbits
2. Newton's Laws of motion

Terms to Know

1. Kepler's Laws of planetary orbits

1. Orbits of planets are ellipses with the Sun at one focus
2. The area swept out by a planet in its orbit around the Sun is always the same in a given time interval (i.e., planets move faster when closer to the Sun)
3. P² = a³, where P=Orbital Period (years) and a = Distance from Sun (A.U.)

2. Newton's Laws of Motion

1. Law of Inertia: A body remains at rest or moving in a straight line unless acted upon by some external force
2. F = ma : A force F applied to a body with mass m will cause it to accelerate (change speed and/or direction) at rate a.
3. Action and Reaction: Every force (or action) applied by one body on a second body results in an equal but opposite force (or action) by that second body back on the first body.

• Since the Moon travels in an orbit around the Earth (and thus not in a straight line), Newton's First Law requires that some force must act upon the Moon.
• Newton's insight: This force is the same one that pulls objects to the ground on the Earth.
• Newton determined a quantitative relationship for the gravitational force between two masses (m_a and m_b) separated by a distance r_ab.

  

  • G is just a number -- the gravitational constant. If you measure mass in kilograms, separation in meters, and force in newtons(!), then G=6.67 x 10^-11.
• Any two masses attract one another gravitationally, each one -- according to the Third Law -- exerting an equal attractive force on the other.
  • The greater the masses, the greater the force.
  • The smaller the separation, the greater the force.
• This law provides the physical explanation for Kepler's observations.