# Why are ICESAT-2 and CRYOSAT 2 both at inclinations of almost exactly 92 degrees?

Authorisation was given on Tuesday for Europe's Cryosat-2 spacecraft to raise its orbit by just under one kilometre.

This will hugely increase the number of coincident observations it can make with the Americans' Icesat-2 mission.

and

Nasa's Icesat-2, which orbits the globe at about 500km in altitude, uses a laser to measure the distance to the Earth's surface - and hence the height of objects. This light beam reflects directly off the top of the snow.

Esa's Cryosat-2, on the other hand, at around 720km in altitude, uses radar as its height tool, and this penetrates much more deeply into the snow cover before bouncing back.

and

On Tuesday, managers at Esa gave final approval for the joint campaign known as Cryo2Ice.

Cryosat will fire its thrusters on 16 July to climb a few hundred metres higher into the sky. The manoeuvre, which will take a couple of weeks to complete, will not compromise the longevity of the mission as the spacecraft has ample fuel on board.

Esa's Cryosat's mission manager, Dr Tommaso Parrinello, told BBC News: "Icesat is quite a bit below us so we can't go down to meet them, but by going up we find this incredible resonant orbit in which for every 19 orbits for us and 20 orbits for them - we will meet at the poles within a certain time lag. Basically, every 1.5 days, we meet over the poles within a few hours of each other and that means we can observe the same ice almost simultaneously.

But this only works along an extended path of ground track if they have the same inclinations, and lo and behold they do!

The current TLEs for these from https://celestrak.com/satcat/search.php are:

ICESAT-2
1 43613U 18070A   20189.92212711  .00000701  00000-0  25259-4 0  9993
2 43613  92.0063  66.8810 0002210  90.4354 269.7149 15.28271517101018

CRYOSAT 2
1 36508U 10013A   20189.86496501  .00000000  00000-0 -64194-6 0  9997
2 36508  92.0333 112.6828 0008788 129.2185 230.9804 14.52174175543231


CRYOSAT 2's mean motion of 15.2827 orbits per day times $$\frac{19}{20}$$ is 14.518565, just slightly faster than ICESAT-2's 14.5217 orbits per day, so it's easy to see how a small orbit raising of ICESAT-2 will bring the two orbits in to a 19:20 mean motion coincidence state. (Though intuitive-sounding, "resonance" is not the right word here).

Question: Why are ICESAT-2 and CRYOSAT 2 both at inclinations of almost exactly 92 degrees? At these altitudes a Sun-synchronous orbit would be at around 98°, so it's not that. And while the ground tracks of orbits at 86.4° or 93.6° cross the equator perpendicularly, that seems irrelevant here. So what's so special about 92.0° degrees and why were both spacecraft at this inclination?

• – uhoh
Jul 8 '20 at 3:11
• I don't have enough time to write a complete answer, so a comment. Both ICESAT-2 and CRYOSAT 2 have repeat ground track orbits. In the case of Sun-synchronous orbits, the inclination is chosen so that the orbit precesses by 360° every year. In the case of repeat ground track orbits, the inclination is chosen so that the ground track repeats after an integer number of orbits. Jul 8 '20 at 4:22
• @DavidHammen The question has two parts I guess; 1) why the same, and 2) why about 92.0°? For short periods of time a repeat ground track just needs the right period, so the inclination is chosen for its rate of precession in order to maintain the repeat condition over an extended period of time? A slightly different altitude could not compensate for the rate of precession of a different inclination?
– uhoh
Jul 8 '20 at 5:00
• When you do the math, you'll find that there are near repeats on possible inclinations for repeat ground orbits with different altitudes and with different number of orbits after which the ground track repeats. I do not want to post that math. Doing so would take hours. Jul 8 '20 at 6:25
• @DavidHammen but I don't see why a specific inclination like 92.0° would be special. It seems to me that one can have repeat ground track orbits for any inclination.
– uhoh
Jul 8 '20 at 13:31

ICESAT-2

The POD team developed the ICESat-2 orbit with the initial requirements of: (1) a 92°inclination orbit for coverage of polar ice and sea ice while still producing orbit-crossings for altimeter cross-over observations, (2) a frozen orbit to limit altitude variation at any given latitude in order to maintain beam pattern geometry on the surface, (3) a ~91-day repeat to sample seasonal variation with a ~30-day near repeat for temporal sampling of sea ice, (4) low earth orbit for altimeter instrument radiometry considerations.

ICE, CLOUD, and Land Elevation Satellite (ICESat-2) Project Algorithm Theoretical Basis Document(ATBD) for Precise Orbit Determination, Orbit Design, and Geolocation Parameter Calibration

CRYOSAT-2

The Cryosat orbit control is different from the other ESA Earth Observation satellites described above because:

• The propulsion system does not allow the execution of significant out of plane manoeuvres.
• There is no requirement on the LTAN evolution. No Sun-synchronism is required.
• The intended repeat cycle is very long compared to those of ERS-2 and Envisat.

...

A reference orbit generated in the classical way for Cryosat would not show a homogeneous distribution of longitudes at the node crossings, since there would be a non-constant drift of the right ascension of the ascending node induced by the inclination drift. Such a reference orbit does not meet the science requirements of the Cryosat mission because a homogeneous distribution of longitudes at the node crossings is required in order to have the right density of ground-track crossovers. This effect is compensated by designing a reference orbit with a non-constant orbital period. This strategy means, in other words, to advance or delay the Equator crossings times in such a way that a homogeneous distribution of nodes is achieved.

CRYOSAT-2: FROM LEOP TO ACQUISITION OF THE REFERENCE ORBIT

• This is excellent, exactly what I needed! Apparently more than "a little bit like "frozen orbits" While CRYOSAT-2's orbit is not really a classical frozen orbit, it gets the job done in a similar fashion.
– uhoh
Jul 8 '20 at 23:36
• @uhoh I thought you would enjoy the linked references. They were a bit over my head. Jul 9 '20 at 0:04