# RE: North Korea satellite: NOTAMs inconsistent with claimed sun-synchronous orbit

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Mon Apr 02 2012 - 12:34:11 UTC

• Next message: Ted Molczan: "RE: North Korea satellite: NOTAMs inconsistent with claimed sun-synchronous orbit"

```David Tiller asked:

> It seems that there are two parameters that are used to compute the particulars of a sun-
> synchronous orbit - orbital altitude is used to derive the correct orbital inclination which
> then drives the launch azimuth based on latitude. Your analysis assumes that the stated
> launch altitude is correct and the launch azimuth is incorrect.
>
> What orbital altitude would be correct for a sun-synchronous orbit assuming that the launch
> azimuth will be as the DPRK stated?

The defining property of a sun-synchronous orbit is that its rate of planar precession exactly negates the -0.9856 deg/d
(westward) precession due to Earth's motion about the sun. That is accomplished by taking advantage of the perturbation
due to Earth's oblateness that causes an orbit's plane to precess, which is a function of its size, shape and
inclination. The rate of planar precession varies in direct proportion to the cosine of the inclination; therefore, to
achieve the required +0.9856 (eastward) precession requires a retrograde inclination, i.e. >90 deg.

North Korea's NOTAM's for of its upcoming launch correspond to a launch azimuth of about 181 deg, which corresponds to
an inclination of approximately 88.7 deg, which would not support a sun-synchronous orbit at any altitude, since it is

The lowest orbit that would survive for at least one revolution before decay, ~140 km, requires an inclination of 96.13
deg to be sun-synchronous, which requires a launch azimuth of about 190.6 deg for a direct ascent trajectory. The 500 km
orbit announced by North Korea requires a 97.42 deg inclination to be sun-synchronous, which requires an approximately
192.3 deg launch azimuth.

Ted Molczan

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