physics.basic_orbital_capture

These two functions will return the radii of impact for a target object of mass M and radius R as well as it’s effective cross sectional area sigma. That is to say any projectile with velocity v passing within sigma, will impact the target object with mass M. The derivation of which is given at the bottom of this file.

The derivation shows that a projectile does not need to aim directly at the target body in order to hit it, as R_capture>R_target. Astronomers refer to the effective cross section for capture as sigma=π*R_capture**2.

This algorithm does not account for an N-body problem.

Functions

capture_area(→ float)	Input Param:
capture_radii(→ float)	Input Params:

Module Contents

physics.basic_orbital_capture.capture_area(capture_radius: float) → float

Input Param:

capture_radius: The radius of orbital capture and impact for a central body of mass M and a projectile moving towards it with velocity v

SI units: meters | m

Returns:

>>> capture_area(17209590691)
9.304455331329126e+20
>>> capture_area(-1)
Traceback (most recent call last):
    ...
ValueError: Cannot have a capture radius less than 0

Returned SI units:

meters*meters | m**2

physics.basic_orbital_capture.capture_radii(target_body_radius: float, target_body_mass: float, projectile_velocity: float) → float

Input Params:

target_body_radius: Radius of the central body SI units: meters | m target_body_mass: Mass of the central body SI units: kilograms | kg projectile_velocity: Velocity of object moving toward central body

SI units: meters/second | m/s

Returns:

>>> capture_radii(6.957e8, 1.99e30, 25000.0)
17209590691.0
>>> capture_radii(-6.957e8, 1.99e30, 25000.0)
Traceback (most recent call last):
    ...
ValueError: Radius cannot be less than 0
>>> capture_radii(6.957e8, -1.99e30, 25000.0)
Traceback (most recent call last):
    ...
ValueError: Mass cannot be less than 0
>>> capture_radii(6.957e8, 1.99e30, c+1)
Traceback (most recent call last):
    ...
ValueError: Cannot go beyond speed of light

Returned SI units:

meters | m