Interplanetary Transfer API

The Interplanetary Transfer API solves Lambert’s problem for ballistic transfers between solar system planets. It provides both single-solution computation and grid-based pork chop plot generation for visualizing optimal launch windows. All orbital mechanics calculations use pg_orrery’s lambert_transfer() and lambert_c3() SQL functions.

Solve Transfer

Compute a single Lambert transfer solution between two planets for a given departure and arrival time.

GET /api/transfer/solve

Query Parameters

Parameter	Type	Required	Description
dep_body	int	Yes	Departure body ID (1-8)
arr_body	int	Yes	Arrival body ID (1-8)
dep_time	string	Yes	Departure time (ISO 8601)
arr_time	string	Yes	Arrival time (ISO 8601)

Body IDs

ID	Planet
1	Mercury
2	Venus
3	Earth
4	Mars
5	Jupiter
6	Saturn
7	Uranus
8	Neptune

Response

{
  "departure_body": "Earth",
  "arrival_body": "Mars",
  "departure_time": "2028-05-01T00:00:00Z",
  "arrival_time": "2029-01-15T00:00:00Z",
  "c3_departure_km2s2": 12.4,
  "c3_arrival_km2s2": 8.7,
  "v_inf_departure_km_s": 3.52,
  "v_inf_arrival_km_s": 2.95,
  "tof_days": 259.0,
  "transfer_sma_au": 1.31
}

Tip

C3 (characteristic energy) is the square of the hyperbolic excess velocity — the primary metric for sizing a launch vehicle. Lower C3 means less propellant needed to escape the departure planet’s gravity well. Typical Earth→Mars transfers have departure C3 values between 8 and 15 km²/s².

Response Fields

Field	Type	Description
departure_body	string	Departure planet name
arrival_body	string	Arrival planet name
departure_time	string	ISO 8601 departure timestamp
arrival_time	string	ISO 8601 arrival timestamp
c3_departure_km2s2	float	Departure characteristic energy (km²/s²)
c3_arrival_km2s2	float	Arrival characteristic energy (km²/s²)
v_inf_departure_km_s	float	Departure hyperbolic excess velocity (km/s)
v_inf_arrival_km_s	float	Arrival hyperbolic excess velocity (km/s)
tof_days	float	Time of flight in days
transfer_sma_au	float	Transfer orbit semi-major axis in AU

Example

Solve an Earth→Mars transfer departing May 2028, arriving January 2029:

GET /api/transfer/solve?dep_body=3&arr_body=4&dep_time=2028-05-01T00:00:00Z&arr_time=2029-01-15T00:00:00Z

---

Pork Chop Plot

Generate a grid of departure C3 values across a range of departure and arrival dates. The resulting data can be contour-plotted to identify optimal launch windows — regions of low C3 form the characteristic “pork chop” shape.

POST /api/transfer/porkchop

Request Body

{
  "departure_body": 3,
  "arrival_body": 4,
  "dep_start": "2028-04-01T00:00:00Z",
  "dep_end": "2028-08-01T00:00:00Z",
  "arr_start": "2028-12-01T00:00:00Z",
  "arr_end": "2029-06-01T00:00:00Z",
  "dep_step": 5,
  "arr_step": 5
}

Request Fields

Field	Type	Default	Description
departure_body	int	—	Departure body ID (1-8, required)
arrival_body	int	—	Arrival body ID (1-8, required)
dep_start	string	—	Start of departure date range (ISO 8601, required)
dep_end	string	—	End of departure date range (ISO 8601, required)
arr_start	string	—	Start of arrival date range (ISO 8601, required)
arr_end	string	—	End of arrival date range (ISO 8601, required)
dep_step	int	5	Departure date grid spacing in days
arr_step	int	5	Arrival date grid spacing in days

Note

The grid automatically filters out cells where the arrival time is before or equal to the departure time. Smaller step values produce higher-resolution plots but increase computation time — a 1-day step over a 6-month window generates thousands of Lambert solutions.

Response

{
  "departure_body": "Earth",
  "arrival_body": "Mars",
  "cells": [
    {
      "departure_time": "2028-04-01 00:00:00+00",
      "arrival_time": "2028-12-01 00:00:00+00",
      "c3_km2s2": 18.3
    },
    {
      "departure_time": "2028-04-01 00:00:00+00",
      "arrival_time": "2028-12-06 00:00:00+00",
      "c3_km2s2": 16.1
    },
    {
      "departure_time": "2028-04-06 00:00:00+00",
      "arrival_time": "2028-12-01 00:00:00+00",
      "c3_km2s2": 15.7
    }
  ],
  "min_c3": 8.2,
  "optimal_departure": "2028-05-15 00:00:00+00",
  "optimal_arrival": "2029-01-20 00:00:00+00"
}

Response Fields

Field	Type	Description
departure_body	string	Departure planet name
arrival_body	string	Arrival planet name
cells	array	Grid of C3 values for each departure/arrival combination
cells[].departure_time	string	Departure timestamp for this grid cell
cells[].arrival_time	string	Arrival timestamp for this grid cell
cells[].c3_km2s2	float	Departure C3 for this transfer (km²/s²)
min_c3	float	Lowest C3 value found in the grid (km²/s²)
optimal_departure	string	Departure time corresponding to min_c3
optimal_arrival	string	Arrival time corresponding to min_c3

Tip

Pork chop plots are a standard mission design tool. The low-C3 valleys in the plot correspond to Hohmann-like transfer opportunities that recur on synodic period cycles — roughly every 26 months for Earth→Mars. The min_c3 and optimal_departure/optimal_arrival fields give you the best transfer in the grid without needing to process the full cell array.

---

C3 Reference Values

For context on what the C3 numbers mean in practice:

Transfer	Typical C3 (km²/s²)	Notes
Earth → Mars	8-15	Most common interplanetary target
Earth → Venus	5-12	Lower C3 due to closer proximity
Earth → Jupiter	75-90	Requires heavy-lift vehicle or gravity assists
Earth → Mercury	50-100+	Often uses Venus gravity assists to reduce C3

Caution

C3 values above ~50 km²/s² typically exceed the capability of most launch vehicles for meaningful payload mass. Real missions to the outer planets use gravity assists (flybys) to reduce the required departure C3, which this single-arc Lambert solver does not account for.