Issue 112

Jack’s Astro Corner Revisit: The Molniya Orbit

Friend of the Flash, Jack Anthony, wrote about the Molniya orbit in a couple of his “Jack's Astro Corner” articles. For those who might need a refresher I give you the following excerpts from the 3 July and 17 July 2022 Final Frontier Flashes. Let's take a closer look at the HEO orbit like this and introduce Kepler's…

Friend of the Flash, Jack Anthony, wrote about the Molniya orbit in a couple of his “Jack’s Astro Corner” articles. For those who might need a refresher I give you the following excerpts from the 3 July and 17 July 2022 Final Frontier Flashes.

Let’s take a closer look at the HEO orbit like this and introduce Kepler’s Second law of orbital motion. OK, see the tick marks with elapsed time in hours. These show position in the orbit every 1 hours. Notice that this HEO satellite whizzes by perigee area in less than 2-hrs. From perigee to reach apogee for this orbit takes 6 hrs. What Kepler’s Second Laws says is if you made a triangle type figure it sweeps out “equal area in equal time.” Thus, you are slowest at apogee and fastest at perigee. I call the HEO orbit the “hang time” orbit. Do you see that the “hang time” above the northern hemisphere is more than 10 hours.

Â

The central gravitational force of the Earth is what makes satellites orbit the Earth. We assume a spherical Earth and that’s pretty good for starters. But in reality, it’s not a spherical point source of gravity. The Earth has oblateness, that is it’s squished a little and football shaped, wider at equator and shorter to the poles. Can’t really see it, but this is true. This causes some additional forces to be put on an orbiting satellite. The biggy Earth oblateness effect is called the J2 effect. It has an effect mostly the right ascension of the ascending node (RAAN) (twist) and the Argument of Perigee (defines where the closest approach to Earth is). You can get a constant change over time in those orbit elements; it’s called a secular perturbation. The equation that determines the motion of perigee due to J2 can be solved to find the inclination where perigee will not drift. There are two specific inclinations where the rate of change of perigee movement due to J2 is zero. Holy cow, now that can be helpful. The answer is 63.4 and 116.6 degrees and it’s called the critical inclination. Remember the HEO orbit? Well, if you launched into 63.4-degree inclined orbit and had perigee positioned in the southernmost part of your orbit, then it would not drift away from there and rotate away from this southernmost point. That’s helpful for keeping the “hang time” part of the orbit (apogee) over the northern hemisphere.