PES 106        Spring 2003
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General Astronomy II
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Lecture Notes:

Gravity and the Laws of Motion

text: Chapter 1 Sections 1.4 and 1.5, Overview 2, Chapter 2 Sections 2.1 - 2.9

History: Newton and Gravity

  • 1670 ................... England
    • Isaac Newton
      • Recognized that motion of a ball thrown on Earth and motion of planets are governed by SAME laws of physics.

 

Definitions:

Mass - amount of matter in object

weight - force of gravity on object

volume - amount of space object occupies

density - amount of mass in a volume

acceleration - change in speed or direction, includes speeding up or slowing down or turning

See figure 2.5 for the definition of acceleration. Here is a link to the figure.

Here is a more detailed discussion of acceleration (and velocity and force).

weight vs. mass

gravity of moon is less than Earth

=> astronauts on moon have same mass, but weigh less

Newton's Laws of Motion

1. An object remains at rest, or continues moving in a straight line with constant speed, unless acted on by a force.

This link has a more detailed description of the first law with pictures and animations.

2. The ability of a force to change the motion of an object depends on the object's mass.

Apply the same force to a piano or chair ....... harder to change the motion of a piano.

Which would you rather stand in front of: ..... a 60 mph train or a 60 mph ping pong ball ??

See Figure 2.6 for a picture of this concept. Here is a link to the figure.

Here is a more detailed description of Newton's 2nd law.

3. For every force, there is an equal and opposite force.

Force is an interaction.

In a rocket: rocket pushes hot gas down AND hot gas pushes rocket up.

Here is a more detailed discussion of Newton's 3rd law.

Apply these to orbits:

Planets would move in straight lines unless some force acts on them to pull them into orbits.

That force is the force of GRAVITY from the Sun.

Here is a link to an English translation of Newton's "Principia" - for the history of science fans.

Newton's Law of Gravitation

All pairs of objects have attractive gravitational forces acting between them.

Gravitational force depends on:

  • mass of both objects
    • more mass => more force
  • distance between centers of objects
    • more distance => less force

Mathematical form:

F = G M1 M2 / r2

where F is the force, G is a constant number, M1 is the mass of one object, M2 is the mass of the other object, and r is the distance between the centers of the two objects.

In general: when you see A = B / C

A gets bigger as B gets bigger.

A gets smaller as C gets bigger.

How would your weight change if you went up to the top of Pike's Peak?

How would your mass change if you went up to the top of Pike's Peak?

Orbits are stable:

The force of gravity is just enough to change the direction of the planet, but not enough to pull it in.

Gravity holds stars together !

Kepler's Laws can be derived from Newton' Laws.

We find that Kepler's 3rd Law also depends on masses.

This gives up a way to measure mass:

Observe the orbital period and distance.

Use these to determine mass of planets and moons and stars which orbit other stars.

Here is a good link describing the relationship of Kepler's Laws to Newton's laws.

CD: You may want to look at the force of gravity animation. under animations in Gravity and Motion (Astronomy Basics)

Here is a more detailed description of Newton's Law of Gravitation.

Surface gravity

We often want to know the force of gravity on the surface of a star or planet.

Surface gravity (acceleration) depends on

  • mass of the star or planet
    • more mass => stronger surface gravity
  • size of the star or planet
    • larger radius => weaker surface gravity

mathematical form:

g = G M / R2

where g = surface gravity (acceleration), G = a constant number, M = mass of the star or planet, and R = radius of the star or planet.

We can compare "g" on the Earth and Moon:

Mass of Earth is greater than moon ......... expect that g of Earth is greater

Radius of Earth is greater than moon ....... expect that g of Earth is smaller

=> We can not actually know the answer without doing the math !!!

We find: g of moon is about 1/6 g of Earth

Since weight is the force of gravity on an object. Your weight will change if you are on the suface of different planets. This on-line calculator will allow you to find your weight if you were on the surface of other planets: http://kids.msfc.nasa.gov/Puzzles/Weight.asp Remember, your mass does not change.

Escape Velocity

escape velocity is the speed needed for an object to escape from the force of gravity

escape velocity depends on:

  • mass of the star or planet (or moon)
    • more mass => need higher speed to escape
  • size of star or planet (or moon)
    • larger radius => need less speed to escape

Failures of Newton's Model

Newton's laws do not work for

  • very large masses
  • very high speeds

=> we need a better model

(although Newton's laws work well enough for almost everything we need in this semester)

General Theory of Relativity

  • 1915 ................. Switzerland
    • Albert Einstein
      • developed General Theory of Relativity
        • mass changes space and time around the object
        • space becomes curved
        • time slows down
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