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How to Determine Planetary Orbits

Scientists describe a planet̵7;s orbit using two main parameters: semi-major axis and period. The semi-major axis is half the diameter of the orbit̵7;s elliptical shape, while the period is the amount of time needed for the planet to return to the same position in space. You can find both of these parameters from observations of a planet over time or from previously-calculated values listed in tables. Minor parameters, such as the planet̵7;s inclination (tilt from the plane of the solar system) and eccentricity (the orbit̵7;s deviance from a perfect circle), complete the description of an orbit.

Things You'll Need

Planetary information table
Calculator
Ruler
Protractor
2 pins
String tied in a loop
Pencil

Instructions

Steps to Determine Planetary Orbits
- 1
  Find the period, inclination and eccentricity of the planet from reference material. Many astronomical resources list these parameters in different units. The period is the time taken for the object to complete one revolution on its orbit; for example, the period of the Earth is 1 year.
- 2
  Convert the period to units of years. If the orbital periods are listed in days, use the equation P = D/365.25, where P is the period in years and D is the period in days.
- 3
  Calculate the semi-major axis of the orbit using Kepler̵7;s 3rd Law. The equation is period squared = semi-major axis cubed (P^2 = a^3), where the period is in years and the semi-major axis is in astronomical units (equal to the length of the Earth̵7;s semi-major axis).
- 4
  Convert the semi-major axis to more familiar units, such as kilometers or miles. There are 93,000,000 miles or 150,000,000 kilometers in 1 astronomical unit.
- 5
  Convert the period to the most appropriate units. For inferior planets like Mercury and Venus, periods should be in units of days. For the superior planets (Mars, Jupiter, Saturn, Uranus and Neptune), you should use units of years.
- 6
  Determine the distance between the foci of your ellipse. Use the eccentricity to find the foci̵7;s separation (f = e * a, where f is the distance between the foci, e is the eccentricity and a is the semi-major axis). Locate the two foci at the center of the line of the semi-major axis.
- 7
  Model your orbit. Measure inclination with a protractor, scale down the length of the semi-major axis to an appropriate size for your model, and draw the actual orbit with a looped string hooked around pins inserted at the foci. Make sure the ellipse you draw is the same width as the semi-major axis.

Astronomy