top of page

For an interesting comparison, we can consider the recent Juno mission. The Juno spacecraft weighted approximated 1500 kg and travelled to from Earth to Jupiter using chemical propulsion. With an additional gravity assist maneuver from Earth, Juno completed its trip in approximated 5 years. Using SunSail, we find that this trip would take 9.89 years to complete if the spacecraft were propelled by a 71 m x 71 m square sail.

Orbit Specs: 
Initial Orbit: 1.0 AU 
Sail Density: 12.0 g/m^2 
Sail Area:  5000 m^2 
Cargo mass: 1500 kg 
Sail Inclination:  0.0 degrees 
 
Results: 
Final Orbit: 5.20 AU 
Final Velocity: 29.94 km/s 
Travel Time: 9.89 years 
Bound to Sun?: No 

 

These results seem promising regarding the viability of solar sails for interplanetary missions, although there are many engineering challenges that must be surmounted to create reliable sails of such a size.

Returning to the initial settings, SunSail can also be used to investigate the dependence of trajectory on different variables.

SunSail - Modeling Solar Sails

ASTR 350 Final Project

by Rae Holcomb

About

Model Design and Capabilities

Example Usage and Results

Acknowledgements

About
Background
Derivations
Model Design
Usage and Results

SunSail is a Matlab program that simulates the orbit of a solar sail spacecrafts. It allows the user to set parameters such as the initial position and velocity, size, material density, mass of cargo,  and angle of inclination of the sail and calculates the trajectory of the probe to a target orbit size. 

This code was created by Rae Holcomb, as Junior in Astrophysics at Rice University. It is the final project for ASTR 350 - Introduction Astrophysics of Stars at Rice University. For more information, please contact Rae at rjh9@rice.edu

SunSail can be downloaded here:

A solar sail is a device that using photonic pressure from the Sun to propel a spacecraft. Since this method requires essentially no extra fuel, it is great interest for missions with long lifespans.

Although solar sails are still in their early stages of research and development, radiation pressure already plays an important role in the spacecraft of today. Interplanetary probes have accounted for displacement due to radiation pressure when planning their trajectories since the 1960s. In 1973, Mariner 10 became the first mission to use active solar pressure control to regulate its attitude and conserve fuel. In 2014, the Kepler Space Telescope began using solar pressure to position and stabilize itself after two of its four reaction wheels broke.

Today, several organizations are working on missions to further develop and test solar sails technology. In 2010, the Japanese Aerospace Exploration Agency deployed IKAROS, the first interplanetary solar sail spacecraft, and successfully demonstrated that it experienced propulsion from solar radiation. The Planetary Society aims to launch LightSail2 in early 2018 to explore the uses of controlled solar sailing within Earth's orbit. Other future missions, such as CubeSail and the Near-Earth Astroid Scout plan to use solar sails to propel micro-satellites at low cost throughout the solar system. Solar sails have also been proposed as a passive means to deorbiting damaged satellites, such as the European Space Agency's Gossamer mission. Breakthrough Starshot, an ambitious project by Breakthrough Initiatives, plans to use high-power laser beams to propel a small probe to Alpha Centauri in the space of a few decades.

Acknowledgments

Background

Derivations

The propulsion provided by a solar sail can be found by considering the force exerted by the sun's pressure. In general, a probe is far enough from the sun so that we can assume that the sun's light hits is isotropically. Thus, the energy hitting the sail per second per unit area, also known as Poynting's vector or flux, is a function of the star's luminosity:

Where the luminosity can be found assuming that the sun is a black body:

The momentum of a photon is the photon's energy divided by the speed of light. Thus the momentum transferred to the sail per second, or force, can be found can be found by integrating the flux across the projected area of the sail.
 

 

Thus the acceleration experienced by a solar sail as a function of its distance from the host star can be found by

 

where theta is the angle between the incoming light and the vector normal to the surface of the sail.

SunSail uses Euler's method to numerically calculate a sail's trajectory given the following input parameters:

r0AU   =  the initial orbital radius of the sail given in AU

dens   =   the area density of the sail's materials in kg/m^2

temp   =   the effective temperature of the host star in Kelvin

area    =  the area of the sail in m^2

cargo  =  the mass of the sail's cargo in kg

theta  =  the orientation of the sail in radians, where 0 indicates that the sail's surface is fully perpendicular to the incoming light

The user may also specify some initial perturbation velocity of the probe relative to the probe's initial orbit. Several suggestions of sail densities based on existing sail materials are provided within the code.

SunSail provides the following primary functions:

runorbit - calculates the orbital trajectory across a given amount of time

traveltime - calculates time needed for the sail to reach a target orbit size and the trajectory across that timescale

And several helper functions:

 

display - prints information on the sail's orbit to the console in a readable format

plotorbit - creates a plot of the sail's orbit relative to it's initial and target orbits

orbitalvel - calculates the tangential velocity needed to maintain circular orbit at a given radius

orbitalfreq - calculates the orbial frequency needed to maintain circular orbit at a given radius

kineticenergy - calculates the kinetic energy of the sail at a given time

potentialenergy - calculates the potential energy of the sail at a given time 

isbounded - evaluates whether the sail is in an orbit bound to the sun at a given point in time
 

There are several flexibilities built into SunSail. The default state of the code assumes that the probe launches from Earth's orbit around the Sun and has a destination at the orbit of Jupiter. However, all these can be adjusted with simple changes to the code. By changing the global variable rsun describing the radius of the host star and the initial condition temp, SunSail is able to model the behavior of a sail around stars of different luminosities. 

Additionally, the primary functions runorbit and traveltime are designed to perform their calculations using a helper function called force, which calculates the acceleration due to radiation pressure experienced by the craft at a given radius. Thus, these primary functions are capable of calculating orbital trajectories created by different forcing functions. For example, should the user wish to compare the trajectories of a probe using chemical propulsion to a solar sail, they could simply write an additional forcing function that provides constant acceleration and give it as an input to runorbit or traveltime. A similar method could be applied to model the trajectories of laser-propelled sails.

This project would not have been possible without the tutelage of Dr. Patrick Hartigan, my instructor for this course. I would also like to extend my thanks to Matt Schwartz for his feedback on this project and to the whole of the Physics and Astronomy Department at Rice University for continuing to feed my curiosity and wonder about the universe.

Here's to sailing towards a brighter future!

Below are examples of the results generated by SunSail. In its default state, SunSail calculates the orbit of a probe from Earth to Jupiter made of Kapton film (a common material in the design of solar sails today) with a sail area of 500 m^2, a cargo of 10 kg, and an inclination of 0 degrees. Under these conditions, the sail reaches the orbit of Jupiter in 3.17 years.

Orbit Specs: 
Initial Orbit: 1.0 AU 
Sail Density: 12.0 g/m^2 
Sail Area:   500 m^2 
Cargo mass:   10 kg 
Sail Inclination:  0.0 degrees 
 
Results: 
Final Orbit: 5.20 AU 
Final Velocity: 30.95 km/s 
Travel Time: 3.17 years 
Bound to Sun?: Yes 

SunSail also allows us to examine how a sail's velocity and acceleration vary across its orbit.

Each of the graphs above display the time it takes for 500 m^2 Kapton film sail to travel from Earth to Jupiter carrying 10 kg of cargo as a function of one of the input variables.

As expected, a probe experiences the quickest transit time when its surface is angled perpendicular to the incoming light. This orientation maximizes the area of the sail exposed to light. As the angle of the sail increases, it experienced more acceleration in the tangential direction, but this effect is overruled by the decreasing area of the sail exposed to the sun's radiation.

Transit time decreases rapidly as the sail size increases. As area increases, it allows the sail to collect more light and thus the probe experiences more propulsion. There is some opposite effect in that increasing sail size increasing the total mass of the spacecraft, thus slowing it. However, for sails of a low enough density, this effect is small compared to the increase in propulsion.

As sail density increases, the sail takes longer to complete its orbit. This increase curves slightly below a linear relationship, since total sail mass is a function of both the sail's density times its area and the cargo carried by the sail. The final plot also shows how transit time increases as a function of the cargo mass carried.

As might be expected, the acceleration of the sail decreases as a function of 1/r^2 since as the sail gets further from the host star, the flux of the incoming light also decreases as the inverse square of distance. Accordingly, we see that the probe's speed increases rapidly early on in its orbit while it is closest to the sun and continues to increase more slowly as the probe gets further away.

If we inspect the sail's energy, we find that it's potential energy decreases as the inverse square of distance, where as kinetic energy increases as the square of the speed.  Around 35 AU, the sail's kinetic energy exceeds its potential energy. At this point the probe is no longer gravitationally bound to the sun and it would escape the solar system even if the sail were removed.

 

However, not all initial conditions allow a sail to escape the solar system. Below is an example of a sail that will remain gravitationally bound to the sun indefinitely.

Orbit Specs: 
Initial Orbit: 1.0 AU 
Sail Density: 12.0 g/m^2 
Sail Area:    50 m^2 
Cargo mass:   10 kg 
Sail Inclination:  0.0 degrees 
 
Results: 
Final Orbit: 9.99 AU 
Final Velocity: 30.01 km/s 
Travel Time: 15.00 years 
Bound to Sun?: Yes

Artist's depiction of the IKAROS spacecraft. Image from Wikimedia Commons.

bottom of page