M

Although we have determined the orbit's size (a) and orientation (i, W) with respect to the Earth's equatorial plane, we still need one more vital orbit element if we are to predict where the satellite will be in the future. If we do not know where the satellite was at some time in the past, then we will have no way of knowing where the satellite will be in the future.

The Mean Anomaly (M) indicates where the satellite was in its orbit at some epoch time (t). This value is normally measured from the orbit's perigee (closest distance), however since we are assuming a circular orbit, we can use the orbit's RAAN as the reference point where M=0°.

The Mean Anomaly is determined by using the following equation:

M = cos^-1 [ cosd₁cos(a₁ - a_W) ]

M = 128°.06 (from the ascending node)

The time of the first endpoint was 23:39:55.537 UTC on October 3, 2013. This means that the satellite had completed 128°.06 of its orbit since ascending node at this exact time.

Some might have noticed that the Mean Anomaly and the Argument of Latitude are the same in this example. This is correct. Since we have assumed that the orbit is perfectly circular, the orbit has no perigee or apogee points, therefore the orbit has no proper Mean Anomaly or argument of perigee. However, we can define a Mean Anomaly using the ascending node as a reference point.

Now that we have a satellite location in its orbit at a specific time, we can use the determined orbit elements to predict where the satellite will be in the future.

PROCEED TO STEP #8