## Session

Swifty Session 1

## Location

Utah State University, Logan, UT

## Abstract

The first Delta launch vehicle to launch multiple secondary payloads was Δ-104. Carried, as the 2^{nd} piggyback payload on that mission was an amateur radio Smallsat, AMSAT-OSCAR-7 (AO-7). The launch, on 15 November 1974, was to a 1460 km SSO. This spacecraft, as its name suggests, was the 7^{th} in an on-going series of spacecraft operating in the Amateur Satellite Service. The amazing story associated with the mission of this small satellite is being reported elsewhere in these proceedings. While the particulars of this satellite's lifetime are exciting, we didn't particularly expect this "old bird's set of tricks to extend into our investigation of its orbit. We were particularly interested in determining when the spacecraft would be in 100% sun moving forward in time. To do this we investigated the orbit's history. We were surprised by the outcome. This paper describes our observations.

We utilized the information now available on Space-Track.com to look into this spacecraft's first 50 years of space flight history. This website "publishes" the, now famous, TLEs (two-line elements) dating back to 1958 when NORAD (now CSpOC) began its role of maintaining the catalog of all space objects. In order to discover if the satellite had progressed slowly forward in its sun-synchronous orbit as we had expected, we needed to track the sun angle (φ) over time. To simplify the procedure of following the mean sun time of the orbit, we describe a method for sampling the AO-7 orbit RAAN value at Vernal Equinox of each year.

Our search for the drift in our SSO led to the unexpected finding that both the elements RAAN (**Ω**) and inclination (**i**) exhibit a sinusoidal variation with a period of approximately 29 years. We further identified this to be caused by a solar gravity gradient torque, which perturbs LEO sun-synchronous orbits. We, here, provide in Appendix 2 the full analysis confirming that the solar gravity-gradient torque acting on the plane of the orbit is the cause of the observed oscillation. The differential equation we derived is essentially the same as that of the classical pendulum equation, which can be linearized to become a simple harmonic oscillator. While we initially believed we had discovered a new form of orbit perturbation, we've now uncovered an earlier finding of this phenomenon described in a NASA X-document by Ken Duck. Quite ironically, this discovery by K. Duck, a NASA/GSFC employee, used the ITOS series orbit to demonstrate his version of the solution to this differential equation. This is the same orbit into which AO-7 was injected. While we cannot, therefore, claim the discovery of this solar gravity-gradient perturbation along with the coupling of this effect with the Earth's J_{2} perturbation, we are able to use 50 years of NORAD data to demonstrate that K. Duck's discovery is valid over nearly two cycles of the perturbation. And, we've verified this not only using the data for the still functional AO-7 spacecraft, but we've also verified this using the TLEs for the NOAA-4 spacecraft, the primary Δ-104 passenger (now non-functional); this spacecraft also experienced the same solar gravity-gradient perturbation.

AMSAT-OSCAR-7: 50 Years in a Sun-Synchronous Orbit - And Still Counting - Confirmation of the Long-Term Solar Gravity-Gradient Perturbation

Utah State University, Logan, UT

The first Delta launch vehicle to launch multiple secondary payloads was Δ-104. Carried, as the 2^{nd} piggyback payload on that mission was an amateur radio Smallsat, AMSAT-OSCAR-7 (AO-7). The launch, on 15 November 1974, was to a 1460 km SSO. This spacecraft, as its name suggests, was the 7^{th} in an on-going series of spacecraft operating in the Amateur Satellite Service. The amazing story associated with the mission of this small satellite is being reported elsewhere in these proceedings. While the particulars of this satellite's lifetime are exciting, we didn't particularly expect this "old bird's set of tricks to extend into our investigation of its orbit. We were particularly interested in determining when the spacecraft would be in 100% sun moving forward in time. To do this we investigated the orbit's history. We were surprised by the outcome. This paper describes our observations.

We utilized the information now available on Space-Track.com to look into this spacecraft's first 50 years of space flight history. This website "publishes" the, now famous, TLEs (two-line elements) dating back to 1958 when NORAD (now CSpOC) began its role of maintaining the catalog of all space objects. In order to discover if the satellite had progressed slowly forward in its sun-synchronous orbit as we had expected, we needed to track the sun angle (φ) over time. To simplify the procedure of following the mean sun time of the orbit, we describe a method for sampling the AO-7 orbit RAAN value at Vernal Equinox of each year.

Our search for the drift in our SSO led to the unexpected finding that both the elements RAAN (**Ω**) and inclination (**i**) exhibit a sinusoidal variation with a period of approximately 29 years. We further identified this to be caused by a solar gravity gradient torque, which perturbs LEO sun-synchronous orbits. We, here, provide in Appendix 2 the full analysis confirming that the solar gravity-gradient torque acting on the plane of the orbit is the cause of the observed oscillation. The differential equation we derived is essentially the same as that of the classical pendulum equation, which can be linearized to become a simple harmonic oscillator. While we initially believed we had discovered a new form of orbit perturbation, we've now uncovered an earlier finding of this phenomenon described in a NASA X-document by Ken Duck. Quite ironically, this discovery by K. Duck, a NASA/GSFC employee, used the ITOS series orbit to demonstrate his version of the solution to this differential equation. This is the same orbit into which AO-7 was injected. While we cannot, therefore, claim the discovery of this solar gravity-gradient perturbation along with the coupling of this effect with the Earth's J_{2} perturbation, we are able to use 50 years of NORAD data to demonstrate that K. Duck's discovery is valid over nearly two cycles of the perturbation. And, we've verified this not only using the data for the still functional AO-7 spacecraft, but we've also verified this using the TLEs for the NOAA-4 spacecraft, the primary Δ-104 passenger (now non-functional); this spacecraft also experienced the same solar gravity-gradient perturbation.