Doppler Plots of Galileo's Perijove Raise Maneuver
This plot shows the measured spacecraft carrier frequency versus time during the Perijove Raise maneuver on March 14, 1996. The X axis is Earth Received time (ERT) in UTC (Pacific Standard Time + 8 hours). The Y axis (which runs from 2295199000 to 2295203000 Hz) is the spacecraft carrier frequency received at the Canberra 70-meter diameter Deep Space Network (DSN) antenna. This carrier frequency would be steady if the spacecraft and antenna were stationary. But the carrier frequency changes because of the Doppler shift effect. We use this effect to measure the change in the spacecraft's velocity (or delta-V) from the engine burn.
There are several major contributions to the Doppler shift: the station motion due to the Earth's rotation and the earth's motion about the Sun, and the spacecraft's motion relative to the Earth. We can see each of these components.
The curved section of the plot from 15:30 to 20:00 hours comes from the station motion. This part of the Doppler shift is always in the received Doppler and shows up as a sine wave with a 24-hour period (the rate of the Earth's rotation).
From 20:01 to 20:25 we see the effect of Galileo's engine burn. The engine gives a total planned delta-V of 377.1 m/s (about 840 miles per hour) in 24 minutes. This is an average acceleration of 0.262 m/s?2 or about 2.7% of one Earth gravity.
With a little math, the plot provided a check that the burn proceeded correctly. The spacecraft is pointed 46.6 degrees away from the Earth, so the line-of-sight component of the burn acceleration was 0.262 * cos 46.6 = 0.18 m/s?2. This line- of-sight acceleration converts (roughly) to a frequency slope using this formula:
frequency slope (or Df/Dt) = baseline freq. * (acceleration / speed of light)
This gives a slope = 2295000000 * (0.18 m/s?2 / 3 x 10?8 m/s) = 1.37 Hz/sec, approximately the slope shown by the realtime data in the plot! This was the first-level confirmation that the burn was going correctly.
The next level of checking out the spacecraft manuever is to compare the measured carrier frequency to a prediction based on the spacecraft trajectory and a model for the spacecraft engine burn. The difference between the measured and predicted carrier frequency is called the Doppler residual and is shown in the above plot.
If there is no difference between the predicts and the data, the plot would just be a horizontal straight line at Y = 0. Because actual engine performance varies slightly from predictions, this is never the case.
The X axis is Earth Received time in UTC. The Y axis is the Doppler residual frequency in Hz. The engine thrust varies from the predicted model so that it produces the behavior shown on the plot between 20:01 and 20:25. Based on the residuals shown on the plot, the navigation team can monitor how closely the engine is following the expected behavior and if the thrust is high or low. The thrust at the start of the burn was slightly higher than expected, but for the remainder of the burn the thrust was low. The departures from the predicts are quite small. The net effect of the approximately 4 Hz residual is a 0.22% underburn.