Experiment 11:Orbital Inclination

Objective :

To extract the orbital inclination of a planet with respect to orbital plane of earth.

Introduction :

All Planets are inclined to the orbital plane of earth at an angle which is very small. All Planets are roughly on the Ecliptic plane. Up to now we have assumed that the planetary orbits all lie in the plane of the ecliptic. However, we know that all planets other than Earth have orbits inclined to the ecliptic. Therefore inclination of Mars to ecliptic is same as inclination to Earth's orbital plane. The orbit of Mars is inclined at an angle of ~1°51' (approximately) to the orbital plane of Earth, when it is at a maximum distance from Sun.The value may vary due to precession and other perturbations in motion.

All superior planets are most easily visible at their oppositions because they are near their closest approach to Earth . Two planets are considered in opposition to each other if solar elongation (the measurement of the angle between a planet and the Sun) of 180° is present, which is considered maximum elongation. In simplest terms, Opposition is when a planet is opposite the Sun in the Earth’s sky, or occurs when the Earth is situated between the planet and the Sun. This enables an astronomer to chart the position of a planet with respect to a fixed reference point → the Sun. Therefore We will consider the dates when the planet is at opposition to Earth and at a maximum distance from Sun.


Fig: Screenshot showing Planets on ecliptic plane.

To find the orbital inclination using Stellarium, follow the procedure given below:

Procedure :

  • Step 1: Start Stellarium

  • Step 2: We need to configure Angle Measure tool if it is not visible in toolbar, to do so (press F2), Go to configuration window→ go to plugins →select Angle Measure → check the "Load at startup" box → Restart Stellarium.This feature is available in most versions of stellarium.

  • Step 3: If they are on, turn off Ground, Atmosphere and Fog (press G, A and F).

  • Step 4: If the projection is not Stereographic (press F4 ) go to 'Sky and viewing option window', go to markings section and select 'Stereographic' projection, It preserves the angles at which curves cross each other.

  • Step 5: Open Sky and Viewing Option window in the Stars section, un-check the Dynamic Eye Adaptation box (Use F4).

  • Step 6: To display the Planets and their orbits, open the View window (press F4), in the Planets and Satellites section, check the three boxes next to 'Show Planets', 'Show Planet Markers' and 'Show Planet Orbits'.Also, in the Labels and Markers section, put a check next to Planets and drag the slider next to Planets all the way to the right

  • Step 7: To View the solar system,open the Search window and search for "Solar System Observer" (Press Enter).

  • Step 8: Locate Sun and press [space] to center on selected object, (Press 'Ctrl+G' ) this will change your location to 'Sun'.

  • Step 9: Zoom Out (press \). Locate Earth and Mars orbiting Sun, (Press /) to zoom in.

  • Step 10: Open Date/Time window, (press F5) change the date according to the date of opposition provided in the table, (press k) to pause the time rate.

    • Date Of Opposition Distance from Sun Time
    26 Feb 1980 101.32MKm 05:43
    12 Feb 1995 101.08MKm 02:32
    29 Jan 2010 99.33MKm 19:37


    The Dates can be taken from following link, consider the dates when the distance from sun is maximum.-

    For Data- Mars Opposition Dates

    For Website link* - Mars Opposition Dates-http://spider.seds.org/spider/Mars/marsopps.html

  • Step 11: Zoom in, till orbit of Earth and Mars are visible seperately, Zoom in as much as possible (Use Page up/down).

  • Step 12: Enable the Angle Measure tool by clicking the tool-bar button, (pressing 'ctrl+A'), message will appear at the bottom of the screen means the tool is active. Drag a line from the first point that is from Mars to the second point Earth using the left mouse button . Note the angle value or take a screen shot.

  • Step 13: To clear the measurement, click the right mouse button To deactivate the angle measure tool, press the tool-bar button again, or (press control-A) on the keyboard.

  • Step 14: Take a screen shot. (Use Ctrl + S) .


    Fig-Screenshot showing angle measured.

    •  

    Project:

  • Repeat the experiment for other dates of opposition provided in Catalog.

  • Observe the inclination of other Planets using similar procedure.

Planet Inclination to ecliptic
Jupiter 1.31°
Saturn 2.49°

*Acknowledgement Data taken from link -http://spider.seds.org/spider/Mars/marsopps.html