ZICORE Orbital Mechanics

Orbit Parameters

Central Body

Semi-Major Axis (km)

Eccentricity

Inclination (°)

RAAN (°)

Arg. Periapsis (°)

True Anomaly (°)

Altitude

400

Velocity

7.67

km/s

Period

92.4

min

Hohmann Transfer

Initial Orbit Altitude (km)

Target Orbit Altitude (km)

Transfer Results

ΔV₁ (burn 1)—

ΔV₂ (burn 2)—

Total ΔV—

Transfer Time—

Phase Angle—

Bi-Elliptic Transfer

Intermediate Apoapsis (km alt)

Bi-Elliptic Results

ΔV₁—

ΔV₂—

ΔV₃—

Total ΔV—

Transfer Time—

vs Hohmann—

Delta-V Budget

Launch to LEO

9.4 km/s

Orbit Insertion

0.7 km/s

Total ΔV 10.1 km/s

Mission feasibility: FEASIBLE — within typical chemical propulsion budget (~15 km/s)

Reference ΔV Values

LEO → Lunar Orbit3.9 km/s

LEO → GEO3.9 km/s

LEO → Mars Transfer3.6 km/s

Lunar Landing1.87 km/s

Mars EDL~1.5 km/s

Live Calculations

Orbital Velocity (vis-viva)

7.672

v = √(GM(2/r − 1/a)) km/s

Orbital Period

5547.6

T = 2π√(a³/GM) seconds

Escape Velocity

10.847

v_esc = √(2GM/r) km/s

Specific Energy

-28.93

ε = −GM/(2a) km²/s²

Current State Vector

Position (km)

Velocity (km/s)

Orbit Comparison

Add orbits to compare

Gravity Assist

Flyby Body

Flyby Altitude (km)

Approach Velocity (km/s)

Gravity Assist Results

Closest Approach—

Deflection Angle—

ΔV Gained—

Post-flyby Velocity—

SOI Radius—

Gravity assists use a planet's gravitational field and orbital velocity to change a spacecraft's trajectory and speed without using propellant. The maximum ΔV gain equals twice the planet's orbital velocity for a 180° deflection.

Preset Missions

ISS Resupply

LEO 400km → ISS. Simple orbit insertion and phasing.

ΔV: ~0.7 km/s | Time: 6 hours

Lunar Orbiter

LEO → Trans-Lunar Injection → Lunar Orbit. Hohmann-like transfer.

ΔV: ~3.9 km/s | Time: 3 days

Mars Transfer

LEO → Hohmann transfer → Mars orbit capture.

ΔV: ~5.7 km/s | Time: 9 months

GEO Station

LEO → GTO → GEO circularization.

ΔV: ~3.9 km/s | Time: 12 hours

Lagrange Point L1

LEO → Earth-Sun L1. Halo orbit insertion.

ΔV: ~3.2 km/s | Time: 4 months

Lagrange Point L2

LEO → Earth-Sun L2. Webb telescope destination.

ΔV: ~3.3 km/s | Time: 3 months

Celestial Body Database

Body	Mass (kg)	Radius (km)	GM (km³/s²)	SOI (km)	g (m/s²)
Earth	5.972e24	6,371	398,600	925,000	9.81
Moon	7.342e22	1,737	4,904	66,100	1.62
Mars	6.417e23	3,390	42,828	577,000	3.72
Venus	4.867e24	6,052	324,900	616,000	8.87
Jupiter	1.898e27	69,911	126,700,000	52,000,000	24.79

Kepler's Laws

1st Law: Orbits are ellipses with the central body at one focus.
2nd Law: Equal areas swept in equal times (conservation of angular momentum).
3rd Law: T² ∝ a³ (period squared proportional to semi-major axis cubed).

Useful Equations

      v = √(GM(2/r − 1/a))

      T = 2π√(a³/GM)

      v_esc = √(2GM/r)

      r_p = a(1−e) | r_a = a(1+e)

      ε = v²/2 − GM/r = −GM/(2a)

      h = √(GM·a(1−e²))