# Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite
## 3 Simulation Results
### Results
#### 3.2.1 Effects of Geometric Configuration  
Since the geometric configuration consisting of the Ajisai satellite and the two ground stations has more complicated effects on the TLTT link budget than those of ordinary SLR observation, we investigated the effect of the geometric configuration in terms of slant range, zenith angle and phase angle to analyze the capability of time synchronization via TLTT technique.  
The energy of electromagnetic waves is inversely proportional to the square of the distance between source and target (i.e., slant range) in free space; it also decreases proportionally to the atmospheric propagation angle between the satellite and SLR station (i.e., zenith angle). The peak value of the geometric term due to these two effects is obtained when the slant range and zenith angle to the Ajisai satellite from the two stations are at their minimum, and the ratios of these minimum values are 5.5%, 7.5%, and 7.7%, respectively, of the peak value of each combination case during the simulation period, as shown in Figure 3.  
In order to validate the impacts of these effects on the link budget compared to ordinary SLR observation, the ratios of geometric terms were analyzed; these are defined as the relative size of Equation (4) for the TLTT link (i.e., Sejong-Ajisai-three stations) with respect to Equation (1) for the SLR link (i.e., Sejong-Ajisai-Sejong), neglecting other terms in the link budget. Figure 4 shows that the ratio is in a range of 0.05% to 17.5% for the three combination cases, depending on the position of the Ajisai satellite and ground stations; the largest value of each case increases with the distance of the receiving station from the transmitting station. This means that the TLTT link budget is significantly affected (by two orders of magnitude) by the free space loss and atmospheric transmission.  
Figure 3: Ratio of geometric term to peak value including free space loss, atmospheric attenuation and cirrus cloud transmission in TLTT link budget. (**a**) Sejong\(-\)Geochang, (**b**) Sejong\(-\)Beijing and (**c**) Sejong\(-\)Koganei.  
Another term affected by the geometric configuration in the TLTT link budget is the effective cross section of target, which is the function of the phase angle between the target satellite and the two ground stations, as in Equation (7). The maximum cross section of the target satellite is achievable when the transmitting and receiving paths are exactly the same (i.e., \(\theta_{ph}\)= 0). This case is usually applied to calculate the laser link budget for tracking space objects not equipped with CCRs [22; 23].  
The effective cross section of the Ajisai satellite varies from 771.1 to 725.1 m\({}^{2}\) during the simulation period, with phase angle of 0.83-40.02 degrees for the three geometric combination cases. In the simulation, the minimum value of the effective cross section is in the range of 93.9% to 99.9% when compared to the peak value in each configuration. The cross section has less influence on the laser link budget than does the geometric effect resulting from the free space loss and atmospheric transmission.  
In conclusion, the geometric effects coming from the variation of slant range, zenith angle and phase angle for the TLTT link using the Ajisai satellite reduce the link budget by three orders of magnitude, as shown in Figure 5, when compared to the peak value of TLTT link budget during the simulation period.  
Figure 4: Ratio of geometric effects including free space loss and atmospheric transmission in TLTT link budget with respect to ordinary SLR observation. (**a**) Sejong\(-\)Geochang, (**b**) Sejong\(-\)Beijing and (**c**) Sejong\(-\)Koganei.  
Figure 5: Ratio of geometric term in TLTT link budget to peak value including free loss, atmospheric transmission and effective cross section in time domain. (**a**) Sejong\(-\)Geochang and (**b**) Sejong\(-\)Koganei.