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Flybys and Foci

This repository contains libraries for numerically approximating the flight time of a spacecraft on a hyperbolic escape trajectory. The libraries were written for the appendix of my short novel Flybys and Foci and are used to calculate three values:

  1. Focal distance of a solar gravitational lens
  2. Hyperbolic excess velocity of a spacecraft
  3. Flight time to points a specified distance away from the sun

Below is a description of each subdirectory in this repo. The full scientific appendix can be found on my website and the book can be purchased on Amazon.

Config

The config directory stores Excel files for specifying the inputs used in the flight time calculations. The inputs specify a flight plan and are parsed by flight_time.py. Please see flight_profile_template.xlsx for an example.

Graphs

The graphs directory is where charts from all of the calculations are saved.

Output

The results of flight time calculations from flight_time.py are stored in the output directory.

Source

The flybys and foci library calculates three values:

  1. Focal distance of a solar gravitational lens (focal.py)
  2. Hyperbolic excess velocity of a spacecraft (oberth.py)
  3. Flight time to points a specified distance away from the sun (flight_time.py)

There are several additional source files used across multiple calculations. orbit.py is a library for calculating orbital parameters and astro_constants.py has a list of astronomical and physical constants. The evaluate.py file simply calls functions in other files with specified parameters.

Focal distance

focal.py

Plots the focal distance from the sun of a gravitational lens given the closest approach light makes to the surface of the sun. To run the function, use the commands:

python3
>>> import focal
>>> focal.plot_foci(5)

The argument passed to plot_foci specifies the upper limit for what is plotted. The gravitational focal point of light passing between 1 and 5 solar radii from the sun will be plotted with the given arguments and saved to the graphs directory.

Hyperbolic excess velocity

oberth.py

This file calculates the hyperbolic escape velocity of a spacecraft for two scenarios given a starting heliocentric orbit:

  1. A single instantaneous burn
  2. Two burns, the first in a retrograde direction bringing the spacecraft close to the sun followed by a second prograde burn.

There are two separate functions - the compare function compares the hyperbolic escape velocity of the one burn and two burn scenario. Import the oberth.py library and call compare:

python3
>>> import oberth
>>> oberth.compare(20000)

which will generate a plot comparing the hyperbolic excess velocity of the two scenarios given a total delta-v budget of 100km/s. Note that the argument to compare is the delta-v budget in meters per second. The graphs are saved in the graphs directory. Below is an example of the generated graph.

Alt text

The second function is two_burns which plots the hyperbolic escape velocity under the two burn scenario (a retrograde burn to bring the perihelion near the sun and a second prograde escape burn). The delta-v budget is split between the two burns, and the final hyperbolic escape velocity for all combinations is plotted.

python3
>>> import oberth
>>> oberth.two_burns(25000)

The argument passed is the maximum delta-v of the second burn, again in m/s. Below is an example of the generated graph

Alt text

Flight time

flight_time.py spacecraft.py

The third and most complicated calculation is flight time. The library calculates the flight time to points a specified distance from the sun assuming a non-instantaneous burn. Inputs to the calculation are specified in an excel file in the config folder, includuing the delta-v budget, the burn length, starting velocity, and final position. The functions use a numerical approximation to calculate the time to reach the specified final position. The results are saved as a text file in the output folder.

To run the calculation, save a new flight profile using the template in the config folder. If the flight profile is named einstein_550.xlsx invoke the script using the commands:

python3
>>> import flight_time
>>> flight_time.open_flight_profile("einstein_550.xlsx")

flight_time.py parses the arguments and creates a new spacecraft object defined in spacecraft.py. This class contains methods for advancing the spacecraft through space while updating the velocity, position, time elapsed, and other parameters. For details on how the calculations are performed, see the inline documentation in spacecraft.py. The calculated flight time to reach the specified position is saved in the output folder.