1. What is a Hohmann Transfer?

The Hohmann transfer is an orbital maneuver that moves a spacecraft between two circular orbits in the same plane using two engine impulses. It's the most fuel-efficient method for such transfers.

2. How Does the Calculator Work?

The calculator uses the Hohmann transfer equation:

Where:

• \( \Delta v_1 \) — First velocity change needed (m/s)
• \( \mu \) — Standard gravitational parameter of the central body (m³/s²)
• \( r_1 \) — Initial circular orbit radius (m)
• \( r_2 \) — Target circular orbit radius (m)

Explanation: The equation calculates the first velocity change needed to enter the transfer ellipse. A second burn is required at apoapsis to circularize the orbit.

3. Importance of Hohmann Transfer

Details: Hohmann transfers are fundamental to orbital mechanics and space mission planning. They're used for satellite deployments, interplanetary trajectories, and space station rendezvous.

4. Using the Calculator

Tips: Enter μ (for Earth: 3.986×10¹⁴ m³/s²), initial and target orbital radii. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Is Hohmann always the most efficient transfer?
A: For two circular, coplanar orbits, yes. For other cases, bi-elliptic transfers or other methods may be more efficient.

Q2: What's the second Δv needed?
A: The second burn is calculated similarly: \( \Delta v_2 = \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2 r_1}{r_1 + r_2}} \right) \)

Q3: How does transfer time work?
A: Transfer time is half the period of the transfer ellipse: \( t = \pi \sqrt{\frac{(r_1 + r_2)^3}{8\mu}} \)

Q4: Can this be used for interplanetary transfers?
A: Yes, but simplified as patched conic approximations, treating each planet's sphere of influence separately.

Q5: What are the main limitations?
A: Assumes instantaneous burns, circular orbits, and no perturbations from other bodies or non-spherical gravity.