**2. Geometry and coordinate definition for dynamic link analysis**

#### **2.1 Antenna coordinate system space vectors of interest**

**Figure 1** illustrates the antenna coordinate system space vectors of interest [5].

**3. Dynamic link calculation**

*Antenna coordinate definition.*

**Figure 2.**

*<sup>φ</sup>* <sup>¼</sup> <sup>1800</sup>

stage tracking is explained below:

**165**

**3.1 Dynamic link formulas of interest**

Cone Angle <sup>¼</sup> <sup>1800</sup>

EL <sup>¼</sup> <sup>90</sup><sup>0</sup> � <sup>1800</sup>

*<sup>π</sup>* tan 2�<sup>1</sup> UVXBD � �ð Þ SR

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle*

*DOI: http://dx.doi.org/10.5772/intechopen.92462*

**3.2 Tracking signals and link analyses along the trajectory**

<sup>1</sup> The authors would like to thank Dr. James Yoh for his derivation of these formulas.

This section provides a summary of the dynamic link model of interest [6]. More detailed derivation of other variables, especially UVZBD, UVYBD, and UVXBD, can be found in [5]. For station elevation angle, either LV or SV elevation or cone angle (EL or theta or ϴ), and LV or SV clock or azimuth angle (AZ or Phi or Ф), we have1

*<sup>π</sup>* cos �<sup>1</sup> UVZBD � �ð Þ SR

*<sup>π</sup>* cos �<sup>1</sup> GS � SR

j j SR ,

Clock Angle ¼ Ф � Offset

As mentioned in the introduction, there are three separate tracking signals along the flight trajectory that we need to analyze ensuring that they have adequate link margins of three dB or more. Most of the present DLA covers only two stages of launch coverage and neglecting the third stage coverage. The requirement for third

j j SR in Deg (1)

j j GS <sup>∗</sup> j j SR in Deg (2)

UVYBD � �ð Þ SR j j SR in Deg (3)

#### **2.2 Antenna coordinate system definition**

**Figure 2** defines the antenna coordinate system used in this chapter. The azimuth (AZ or Ф) or clock angle is used in the antenna cut configuration. The elevation angle (EL or ϴ) also called as cone angle is also used in the antenna gain data file. The antenna gain is a changing variable as a function of mission elapsed time (MET). The antenna gains are used in the following dynamic links.

**Figure 1.** *Space vehicle and ground station vector definition.*

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle DOI: http://dx.doi.org/10.5772/intechopen.92462*

**Figure 2.** *Antenna coordinate definition.*

payload (PL) separation from LV, using LV, to Tracking and Data Relay Satellite System (TDRSS) [1] satellite link, which is also called beyond line of sight (BLOS) link. A third SV tracking, after SV payload separation from LV, is a tracking link between SV and a ground station (GS). This third SV tracking is now added in this

*Satellite Systems - Design, Modeling, Simulation and Analysis*

The tracking link used from liftoff to the end of LOS uses a UHF noncoherent FSK signal for command and a digital FM or BPSK for tracking telemetry link as described in detail in [2]. From the end of LOS to BLOS, the tracking telemetry link is usually a BPSK or QPSK signal, using a NASA Tracking Data Relay Satellite System to relay tracking data from the LV to White Sands or Goddard ground station (WSGT/GRGT) and finally routing it to other user ground stations. After SV payload separation and orbital insertion, the SV tracking link to an Air Force Satellite Control Network (AFSCN) ground station [3] will use Space-to-Ground Link Subsystem (SGLS) or a non-SGLS (NSGLS) waveform described in [3, 4] and

in Section 3 for tracking signals along the trajectory. In the following pages, supporting link analyses for the two LV and one SV tracking stages will be

**2. Geometry and coordinate definition for dynamic link analysis**

**Figure 1** illustrates the antenna coordinate system space vectors of

**Figure 2** defines the antenna coordinate system used in this chapter. The azimuth (AZ or Ф) or clock angle is used in the antenna cut configuration. The elevation angle (EL or ϴ) also called as cone angle is also used in the antenna gain data file. The antenna gain is a changing variable as a function of mission elapsed time (MET). The antenna gains are used in the following

**2.1 Antenna coordinate system space vectors of interest**

**2.2 Antenna coordinate system definition**

chapter.

presented.

interest [5].

dynamic links.

**Figure 1.**

**164**

*Space vehicle and ground station vector definition.*
