Orbital Mechanics

 

When the satellite is placed in orbit around Neptune, it will release three probes, each at 45° intervals of its rotation. The image below illustrates the probe’s entrance into Neptune’s atmosphere. This image has been taken from NASA’s homepage from Cassini’s mission to Saturn. Cassini also dropped a probe (Huygens) on Saturn’s natural satellite Titan. Contrary to Saturn, Neptune is a gassy planet. The probes will likely to be destroyed as they go deeper and deeper into the atmosphere, facing more physical constraints like enormous pressure (up to 1000 bars, 1000 times the pressure on Earth) and high temperatures (up to 500°K). This brings a critical aspect to the mission, because as much data as possible is needed to be collected before the probes are destroyed or connection is lost.

        

                       

The probes will take 25 hours to reach 500 bars, starting from Neptune’s surface. The most important question arises: in what orbit must we place the satellite in order for it to be in the line of sight of the probes as much time as possible? It turns out that the best orbit for the satellite would be a low period orbit, in the order of a few hours. Thus, the probes will not be in the line of sight of the satellite all the time, but this problem could easily be solved by using on board RAM to store the data and transmit it as soon as an acceptable signal to noise ratio is detected. The satellite would then use a beacon that will be detected by the probes. When the power level of the signal is strong enough, the probes will transmit their data buffered in the RAM. A period of about 2.8 hours is achievable by placing the satellite on a circular orbit with an altitude of 770 km from the surface of Neptune.

 

Figure 1. Orbit of the satellite around Neptune

 

In 25 hours, the satellite will evolve 9 times around Neptune, each time collecting the data from the probes. However, the drawback of having a very Low orbit satellite is Doppler Effect considerations. The velocity of the satellite on this orbit is 16,000 km/s. Let us calculate the Doppler shift incurred from the satellite and the probe’s relative velocities:

 

         Assuming the probe takes 25 hours to descend 420 km into Neptune’s atmosphere, its average velocity is then 16.8 km/h, or 61 m/s. Note that as the probe descends into the atmosphere, its velocity decreases due to higher friction. I haven’t been able to find Neptune’s viscosity in order to calculate the probe’s terminal velocity; we will simply use the average velocity to get an estimate of the Doppler shift. The Doppler shift is at maximum when the satellite and the probe are moving in opposite directions:

 

 

The Doppler shift is then:

 

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Since the probes transmit in UHF at 410 MHz, the Doppler shift is calculated to be 23 kHz. This shift must be taken into account when allocating frequency bands in the FDMA scheme by adding a guard band of at least twice the Doppler shift. To be safe against higher instantaneous velocities when the probe is still close to the surface, a guard band of 200 kHz has been implemented.

 

                Conclusions on Orbital mechanics

 

Again, we had better discuss the issue with an aerospace specialist. It might be difficult to place the satellite at 770km from Neptune’s surface, but a good comparison is the mission to Mars where the orbiter was at about 200 km from Mars surface. Moreover, Neptune’s atmosphere is colder than Mars’, which makes closer approach to the planet more possible.

 

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