Geosynchronous Orbit Radius
Radius of an orbit with a specific period. For geosynchronous orbit, T equals the planet's rotation period.
Variables
Derivation
From T = 2π√(r³/GM), solve for r: r³ = GMT²/(4π²), so r = (GMT²/4π²)^(1/3).
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Constants in this formula
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- G = 6.674 30 × 10⁻¹¹ N·m²/kg² (Gravitational constant)
- M = 2 kg (Planet mass)
- T = 3 s (Orbital period)
Result: r = 0.0003122 m
Other mechanics formulas with the same quantities
- Universal Gravitation (Gravitation) shares Gravitational constant
- Gravitational Field (Gravitation) shares Gravitational constant
- Gravitational Potential Energy (General) (Gravitation) shares Gravitational constant
- Escape Velocity (Gravitation) shares Gravitational constant
- Surface Gravity (Gravitation) shares Gravitational constant
Where this formula is listed
- Mechanics formulas, under Gravitation.
- In the mechanics list it comes after Surface Gravity.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Geosynchronous Orbit Radius formula?
Geosynchronous Orbit Radius is written r = ∛(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 = ∛(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 = ∛(GMT²/(4π²)).