Aerospace & Aeronautical Engineering / Hohmann Orbital Transfer
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LABORATORY 42 · AEROSPACE & AERONAUTICAL ENGINEERING

Hohmann Coplanar Orbital Transfer and Delta-V Velocity Budgets

Calculate impulse velocity increments Delta V_1 and Delta V_2 required to transfer between circular orbits and evaluate delta-v budgets across orbit radius ratios. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

FIRST BURN DELTA V_1—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with x_radius = 0.2 dimensionless.

0.2 dimensionless
Central body: Earth (mu = 3.9860 x 10^14 m^3/s^2)

Adjust x_radius, then execute aerospace trial.

Aeronautical telemetry and flight states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity aerodynamic modeling.

Aeronautical assumptions and boundary condition limits

Hohmann transfer assumes impulsive (infinitesimally short) velocity changes; continuous low-thrust ion engines require spiral trajectories. Linear regression of the first-burn velocity increment Delta V_1 against the radius parameter yields a baseline circular velocity v_1 = 7.7800 km/s with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Astrodynamics Orbital Maneuver Simulator

Propagates 2-impulse and continuous-thrust orbital transfers with gravitational Ephemeris models.

Spacecraft Liquid Apogee Engine (LAE) Model

Simulates bipropellant rocket engine firing (I_sp = 320 s, thrust = 450 N) with mass depletion tracking.

Tsiolkovsky Delta-V Mass Budget Calculator

Computes propellant mass fractions and payload capacity from the rocket equation.

3D Inertial Orbit State Visualizer

Renders initial circular orbit, elliptical transfer trajectory, and final target circular orbit.

Porkchop Plot Interplanetary Trajectory Tool

Evaluates launch energy C3 and arrival v_inf across launch windows (e.g. Earth to Mars).

Orbital Telemetry Station

Logs velocity increments Delta V_1, Delta V_2, transfer flight times, and orbital element changes.

FOLLOW THE METHOD

A reason behind every step.

Calculate impulse velocity increments Delta V_1 and Delta V_2 required to transfer between circular orbits and evaluate delta-v budgets across orbit radius ratios. Standardized parameter settings: 0.08, 0.14, 0.2, 0.26, 0.32, 0.38 dimensionless.

01

Initial LEO Orbit Configuration

Set initial circular Low Earth Orbit at altitude h_1 = 300 km (r_1 = 6678.14 km), confirming circular speed v_1 = 7.780 km/s.

02

Target Orbit Altitude Stepping

Define target circular orbit radii r_2 corresponding to parameter x = sqrt(2*r_2/(r_1+r_2)) - 1 = 0.08, 0.14, 0.20, 0.26, 0.32, and 0.38.

03

First Tangential Burn Execution

Apply impulsive tangential burn Delta V_1 at periapsis to inject spacecraft into the Hohmann transfer ellipse.

04

Transfer Orbit Propagation

Propagate the spacecraft along the elliptical arc over transfer time t_trans = pi * sqrt(a_trans^3 / mu) until apoapsis arrival.

05

Second Circularization Burn

Apply circularizing impulse Delta V_2 at apoapsis to match target circular speed v_2, recording total delta-v budget.

06

Delta-V Linear Regression

Plot Delta V_1 versus the radius parameter x, perform linear regression to determine slope v_1 = 7.780 km/s, and verify Tsiolkovsky propellant mass.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Hohmann Orbital Transfer mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
\Delta V_1 = v_1 \left[\sqrt{\frac{2 r_2}{r_1 + r_2}} - 1\right] \implies \Delta V_1 = m \cdot x + b
#Transfer Radius Parameter (dimensionless)First Burn Delta V_1 (km/s)Radius Ratio Parameter sqrt(2*r_2 / (r_1+r_2)) - 1First Burn Velocity Increment Delta V_1 (km/s)Remove

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CHECK YOUR UNDERSTANDING

Explain what the aerodynamic metrics mean.

What type of trajectory connects the initial and target circular orbits in a classic two-impulse Hohmann transfer?

According to Tsiolkovsky's Rocket Equation, how does propellant mass scale with mission delta-v?

For a baseline circular LEO velocity v_1 = 7.780 km/s and radius parameter x = 0.200, what is the required first burn velocity increment Delta V_1?

Why is it advantageous to perform orbital inclination plane changes at the highest possible altitude (apoapsis)?