Source: NIE
Subject: Science and Technology
Context: ISRO confirmed that the Chandrayaan-3 Propulsion Module (PM) re-entered the Moon’s Sphere of Influence (MSI) during its high-altitude Earth-bound orbit, undergoing two lunar flybys.
About Moon’s Sphere of Influence (MSI):
What it is?
- The Moon’s Sphere of Influence (MSI) is the region around the Moon where its gravitational influence dominates over Earth’s for orbital calculations.
- Inside this region, it is mathematically more accurate to treat a spacecraft as orbiting the Moon, with Earth acting as a perturbing body.
Located in:
- The MSI is an imaginary, approximately spherical (or oblate spheroid) region surrounding the Moon.
- For the Earth–Moon system, the MSI radius is roughly ~66,000 km from the Moon’s center (approximate, varies with models).
How to Calculate It (SOI Radius)?
Using the classical patched-conic approximation:
- a = Moon’s semi-major axis around Earth (~384,400 km)
- m = Mass of Moon
- M = Mass of Earth
- Gives a practical estimate used for mission planning.
(Note: For precise mission design, ISRO uses numerical N-body simulations, not this crude formula.)
Features of the Sphere of Influence:
- Dominant gravitational region: Moon’s gravity governs trajectory integration more strongly than Earth’s.
- Not a physical boundary: It is a mathematical convenience, not a sharp gravitational cutoff.
- Both Earth & Moon still influence motion: Earth still perturbs the orbit inside MSI; Moon still perturbs outside it.
- Useful for “patched conic” method: Helps switch from one two-body solution (Earth–craft) to another (Moon–craft).
- Shape is not perfectly spherical: It is closer to an oblate spheroid, influenced by orbital eccentricity and the Sun.
Significance:
- Trajectory Planning: Determines when spacecraft navigation should shift from Earth-centric to Moon-centric calculations.
- Critical for Lunar Flybys & Insertions: Ensures optimal timing for orbit circularisation, braking, or slingshot manoeuvres.
- Avoids Orbital Uncertainty: Helps predict perturbations from Earth, Sun, and other lunar orbiters.
