This lecture discusses orbital perturbations included in the DAMAGE model for predicting space debris orbits. It covers the effects of third-body gravity from the Sun and Moon, known as luni-solar perturbations, which cause secular changes in the orbital elements of inclination, eccentricity, and longitude of ascending node, especially for geosynchronous and high Earth orbits. It also discusses solar radiation pressure perturbations, which have a small effect on low Earth orbit satellites but can considerably affect the eccentricity of geosynchronous satellites with large surface areas. The lecture concludes by recapping the different perturbation models covered in the previous three lectures.

1. Space Environment
Lecture 46 – Space Debris (Vol. 4)
Orbit propagator (Part 3)
Professor Hugh Lewis
SESA3038 Space Environment

2. Overview of lecture 46
• In this lecture we conclude our look at the orbital perturbations that are
included in DAMAGE and their effects on an ideal orbit
– In this lecture:
– Third-body gravity effects (i.e. due to the Sun and Moon)
– Solar radiation pressure
Space Environment – Space Debris (Vol. 4)

3. Third-body perturbations Space Environment – Space Debris (Vol. 4)
Luni-solar perturbations:
The effect of the direct gravitational attraction of the Moon and the Sun on the satellite:
Principal effects are secular changes in 𝑖𝑖, 𝑒𝑒, and 𝜔𝜔:
• For LEO satellites, perturbation is small
• For GEO and HEO satellites, effect can be significant

4. Third-body perturbations Space Environment – Space Debris (Vol. 4)
Effects of luni-solar gravity perturbations on
Integral orbit:
• Initial operational orbit: rev 11
• Initial orbit period 72 hours (3 days)
• Rev. 1000 (after ~8.2 years)

5. Solar Radiation Pressure (SRP)
perturbation
Space Environment – Space Debris (Vol. 4)
Direct electromagnetic radiation from the
Sun exerts a pressure on satellites of the
order of 10−6 N/m2 at Earth orbit (refer to
SESA3039 lectures on SRP torque)
For LEO satellites, the effect is small relative to
other surface forces (i.e. atmospheric drag)
For GEO satellites, the effect can be
considerable – particularly for satellites with
large array surface areas
• The principal effect is on eccentricity

6. Perturbation ‘filters’ Space Environment – Space Debris (Vol. 4)
To save computational time, not all
perturbations are computed for every
satellite/object:
Relative and approximate magnitudes of
perturbations for LEO
• Moderate solar activity with satellite area-to-
mass ratio of ~0.005 m2/kg
• Acceleration normalised to 1 g

7. Perturbation ‘filters’ Space Environment – Space Debris (Vol. 4)
To save computational time, not all
perturbations are computed for every
satellite/object:
• Active satellites: 𝐽𝐽2 and 𝐽𝐽3 ON
• Inactive satellites and debris:
• If altitude > 2000 km: luni-solar ON
• If altitude > 2000 km and
⁄
𝐴𝐴 𝑚𝑚 > 5 × 10−3 m2/kg: SRP ON
• If altitude < 2000 km and ⁄
𝐴𝐴 𝑚𝑚 > 1.0
m2/kg: SRP ON
• If altitude < 2000 km: drag ON

8. All perturbations Space Environment – Space Debris (Vol. 4)

9. Recap of lectures 44-46
• In the last three lectures we introduced the orbital propagation techniques
that are used in the DAMAGE model:
– Orbit propagation in DAMAGE is based on a general perturbations
approach where semi-analytical methods are employed.
– We introduced the different orbital perturbations that are included and
their effects on an ideal orbit
– Earth gravity anomalies
– Atmospheric drag
– Third-body gravity effects
– Solar radiation pressure
Space Environment – Space Debris (Vol. 4)