home observation science solar system stars our galaxy cosmology astrobiology exoplanets astrophotography
icon Introduction
icon Astronomy Tools
1. Electromagnetic Spectrum
2. Atmosphere Limitations
3. Space Observations
1. Telescopes
2. Radio
3. Space Tools
4. Photography
5. Spectroscopy
6. Computers
7. Advanced Methods
8. Radio Astronomy
icon Basic Mathematics
Scientific Notation
Log Scales
icon Physics
- Basic Units of Measure
- Mass & Density
- Temperature
- Velocity & Acceleration
- Force, Pressure & Energy
- Atoms
- Quantum Physics
- Nature of Light
- Brightness
- Cepheid Rulers
- Distance
- Doppler Shift
- Frequency & Wavelength
- Hubble's Law
- Inverse Square Law
- Kinetic Energy
- Luminosity
- Magnitudes
- Convert Mass to Energy
- Kepler & Newton - Orbits
- Parallax
- Planck's Law
- Relativistic Redshift
- Relativity
- Schwarzschild Radius 
- Synodic & Sidereal Periods
- Sidereal Time
- Small Angle Formula
- Stellar Properties 
- Stephan-Boltzmann Law
- Telescope Related
- Temperature
- Tidal Forces
- Wien's Law
icon Computer Models
icon Additional Resources
1. Advanced Topics
2. Guest Contributions
Physics - Formulas - Kepler and Newton - Orbits

In 1609, Johannes Kepler (assistant to Tycho Brahe) published his three laws of orbital motion:
  1. The orbit of a planet about the Sun is an ellipse with the Sun at one Focus.
  2. A line joining a planet and the Sun sweeps out equal areas in equal time.
  3. The square of the sidereal period of a planet is directly proportional to the cube of the semi-major axis of the orbit.

While laws 1 and 2 are statements, law 3 is presented as an equation:

A semi-major axis is the full width of an ellipse. Law 3 states that if a planet has a sidereal orbit of 11.87 years (like Jupiter in the previous page), the diameter of the orbit is:

Kepler was not the only one interested in orbits. Sir Isaac Newton, using his fundamental work of gravity and forces modified the Kepler equation to take into account the gravity effects of the orbiting bodies:

This equation actually gives us a bit more power. By applying Newton's Law of Gravitation, we can determine how mass influences rotation, as well as determine mass if we know the orbital diameter. To understand this a bit better, think about the standard forces and centripetal motions when dealing with an orbit that is circular (not elliptical like a planets orbit):

Unfortunately I am not a mathematics wizard so I cannot explain the concepts behind these (and other) equations, but my understanding of these problems came about by just looking at the equations (without their corresponding values) and imaging how each variable interacts with each other. Either way, hopefully this section (and the other sections) are helpful.

Back to Top


Search | Site Map | Buy Stuff - Store | Appendix
©2004 - 2013 Astronomy Online. All rights reserved. Contact Us. Legal. Creative Commons License
The works within is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.