Mechanics
Geosynchronous Orbit Radius
Radius of an orbit with a specific period. For geosynchronous orbit, T equals the planet's rotation period.
Variables
rm
Orbital radius
Distance from center of planet
GN·m²/kg²
Gravitational constant
6.674×10⁻¹¹
Mkg
Planet mass
Mass of planet
Ts
Orbital period
Time for one orbit (24 hrs for Earth geosync)
Derivation
From T = 2π√(r³/GM), solve for r: r³ = GMT²/(4π²), so r = (GMT²/4π²)^(1/3).
Your notes
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Common questions
What is the Geosynchronous Orbit Radius formula?
Geosynchronous Orbit Radius is written r = √[3]{GMT²/4π²}. Radius of an orbit with a specific period. For geosynchronous orbit, T equals the planet's rotation period. It belongs to Mechanics, under Gravitation.
What are the units in r = √[3]{GMT²/4π²}?
In SI units, r is orbital radius, measured in m; G is gravitational constant, measured in m³/(kg·s²); M is planet mass, measured in kg; T is orbital period, measured in s.
How is the Geosynchronous Orbit Radius formula derived?
From T = 2π√(r³/GM), solve for r: r³ = GMT²/(4π²), so r = (GMT²/4π²)^(1/3). The result is r = √[3]{GMT²/4π²}.