Solar Sail Questions: Analyzing & Approximating Motion

In summary, the conversation discusses a simulation of a solar sail in Java and the surprising results of the constant slope of dr/dt. The conversation also touches on analytical approximations and other methods for approximating solar sail motion.
  • #1
JoAuSc
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I did a simulation of a solar sail in Java. It seems to be accurate; when you face the sail in one direction, it approaches the sun, in the other direction it goes outward, when it's parallel to the sun's rays it moves in an ellipse and when it's perpendicular, the ellipse is elongated. (This simulation is for a solar sail whose angle relative to the sun is constant. I should also mention the solar radiation force term is something like S/r^2, split into components based on the sail angle, where S was derived with the assumption that the maximum acceleration at the Earth's distance from the sun due to the sail was 0.25 mm/s^2, which I got from a paper.)

One thing that surprised me, though, is that dr/dt (where r is the radius) seems to be roughly constant. After taking a closer look at it and letting the end time of the simulation be much longer (~100 years), r is not quite linear, but curves towards the sun the closer to the sun you get at a rate that increases as well, whether you're looking at r >> 150 million km, or r << 150 million km.


Here are my questions:

1.) Is there a way to analytically get an approximate value for the slope of dr/dt?

(This is neglecting variations due to eccentricity. My simulation has a slider which varies the intial velocity, but it assumes it's all perpendicular to the sun, so while you can smooth out an elliptical orbit to get a circular one, you can't smooth out an elliptical spiral, at least not until I allow the direction of the initial velocity to vary with sail angle.)


2.) Also, do you guys have any idea of better ways to approximate solar sail motion? My simulation solves the set of 2nd-order equations that come from Newton's 2nd law in polar coordinates, but I've heard about other methods, such as "Lagrange's planetary equations for orbital perturbations". Can anyone provide me with methods of determining the path of a solar sail that'd be better than simply solving Newton's 2nd law?
 
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  • #2


Hello,

Thank you for sharing your simulation with us. It seems like you have put a lot of thought and effort into your project.

To answer your first question, there are several analytical approximations for the slope of dr/dt that can be used for solar sail motion. One approach is to use the concept of specific orbital energy, which is the sum of the kinetic and potential energies per unit mass of a spacecraft. For a solar sail, the specific orbital energy can be calculated using the following equation:

ε = -μ/2a

Where μ is the standard gravitational parameter of the sun and a is the semi-major axis of the spacecraft's orbit. The slope of dr/dt can then be approximated using the following equation:

dr/dt ≈ √(2μ/r - 2ε)

This approximation holds true for circular orbits and small eccentricities. For more accurate results, you can also take into account the effect of solar radiation pressure on the specific orbital energy.

As for your second question, there are indeed other methods for approximating solar sail motion. One approach is to use perturbation methods, such as the Lagrange's planetary equations that you mentioned. These equations take into account the gravitational influence of other celestial bodies on the spacecraft's orbit. Another method is to use numerical integration techniques, which can provide more accurate results but may require more computational resources.

I hope this helps in your research. Keep up the good work!
 
  • #3


Thank you for sharing your simulation and questions about solar sail motion. It is great to see people using programming and simulations to better understand scientific concepts.

To answer your first question, yes, there are analytical methods for approximating the slope of dr/dt. One approach is to use Kepler's third law, which relates the period of an orbit to the semi-major axis of the orbit. This can be used to calculate the rate of change of the semi-major axis, which is related to dr/dt. Another approach is to use the vis-viva equation, which relates the kinetic and potential energies of an orbiting body. This can also be used to approximate the rate of change of the semi-major axis and therefore dr/dt.

As for your second question, there are indeed other methods for approximating solar sail motion. One approach is to use numerical integration methods, such as the Runge-Kutta method, to solve the differential equations of motion for the sail. This can provide more accurate results compared to analytical methods. Another approach is to use perturbation methods, which involve breaking down the motion of the sail into smaller components and solving them separately. This can be useful for more complex scenarios, such as when the sail is affected by multiple gravitational forces.

Overall, the best method for approximating solar sail motion will depend on the specific scenario and level of accuracy needed. It is always good to compare results from different methods and validate them against known data or observations. Keep up the great work in exploring solar sail motion and finding new ways to approximate it!
 

1. What is a solar sail?

A solar sail is a type of spacecraft propulsion system that uses the energy from sunlight to propel the spacecraft forward. It consists of a large, lightweight sail made of reflective material, such as mylar, that reflects photons from the sun to create a small amount of thrust.

2. How does a solar sail work?

A solar sail works by utilizing the momentum of photons from sunlight to create thrust. The sail is positioned so that it reflects the photons from the sun, which creates a small force in the opposite direction. This continuous force eventually accelerates the spacecraft to high speeds.

3. What is the advantage of using a solar sail compared to traditional propulsion systems?

The biggest advantage of using a solar sail is that it does not require any fuel or propellant to operate. This makes it a cost-effective and sustainable option for long-term space travel. Additionally, solar sails can reach very high speeds, making them ideal for deep space missions.

4. Can a solar sail be used to travel to other planets?

Yes, a solar sail can be used to travel to other planets. However, it is not as efficient as traditional propulsion systems for short distance travel within a planet's orbit. It is better suited for long-distance space travel between planets or outside of the solar system.

5. How do scientists analyze and approximate the motion of a solar sail?

Scientists use various mathematical models and simulations to analyze and approximate the motion of a solar sail. These models take into account factors such as the size and shape of the sail, the distance from the sun, and the solar wind. They also use data from previous solar sail missions to improve their approximations and make more accurate predictions.

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