# Can a solar sail craft change an orbit's inclination (from polar to equatorial)?

How much maneuvering can you do with a solar sail in space?

Can you change your inclination (go from a polar orbit to an equatorial) in a single star system?

Can this be done in a binary system?

• Perhaps this will interest you. But the question is still unclear. – HDE 226868 Dec 9 '14 at 18:51
• One. With the proper angling of the sail, you can produce either a prograde or retrograde acceleration, which will raise or lower your orbit respectively. See: Can you tack against the sun using a solar sail? Of course, as your distance from the star decreases, the effectiveness of the sail will decrease, meaning changes will take place more slowly. The mass of the planets is largely inconsequential (though may affect time to reach escape/insertion velocity). – Caleb Hines Dec 9 '14 at 20:00
• The accepted answer for your linked answers is no for one sun. How do you deal with something like a inclination change with a solar sail? – Mellester Dec 10 '14 at 14:52

In general, inclination change is the costliest component of orbital maneuvers.

For solar sails, like for every other craft, the easiest solution is launching directly into the required orbit. Barring that, we have to expend resources on plane change. Here the differences between normal spacecraft and sailcraft begin to emerge:

• a normal spacecraft has limited propellant supply, and our proposed solution should focus on minimizing propellant use and hence, $\Delta V$ (operational lifetime may be also constraining our maneuver schedule);

• an ideal solar sailcraft has "unlimited fuel", and does not use any propellants for attitude control (i.e. is equipped with variable reflectivity solar vanes, or magnetorquers for LEO operations). We would like to minimize time till maneuver completion.

• a more realistic sailcraft is characterized by solar sail and attitude control degradation (due to solar wind and galactic cosmic rays, and finite resource of attitude control surfaces/actuators). Here, the most relevant objective to minimize may be a combination of time-to-completion and number of attitude changes.

The 90 degrees' plane change stipulated in the question has been shown to be achievable through three burns for high-thrust spacecraft (we'll adapt the scheme to low-thrusters shortly):

• boost the orbit's apoapsis by a prograde burn so that the necessary node for plane change (ascending or descending) is also moved higher, away from your planet's influence;
• at the necessary node, fire in the normal/antinormal direction;
• at the next periapsis do a retrograde burn to get back to target orbit (equatorial in your case).

Some spacecraft with thermal protection and half-decent brick-like aerodynamics can do plane changes in the upper atmosphere. Because of mass constraints, most spacecraft including solar sailcraft can not afford this (nor do they really need it).

Low-thrusters suffer from gravity losses so raising apoapsis takes many more revolutions. Yet, the underlying sequence of steps stays more or less the same:

• first, get the periapsis as close to the planet as possible and at the right argument of periapsis (taking care to stay outside the influence of atmospheric drag) to get the most of Oberth effect during subsequent revolutions. Altitude of periapsis (PeA) and argument of periapsis (AgP) are crucial for efficiency of the maneuver and they will have to stay mostly the same (you have to take into account the planet's oblateness - the $J_2$ term of the gravity field will perturb AgP). Timing also matters: you want periapsis to be located over the sunny hemisphere of the planet.

• second, raise the apoapsis aiming to maximize the prograde component of solar pressure (here, efficiency $\frac{dApA}{dt}$ depends on the solar angle ($\beta$) and the maximum sustained attitude rate allowed by your attitude control subsystem) while passing the periapsis. Somewhere between the apses there will be a region for another attitude change so that during the apoapsis you can contribute to the maneuver's objectives by a) changing inclination (every little bit helps), b) maintaining altitude of the periapsis, c) getting into the right prograde attitude for the next periapsis pass. The exact sequence depends on the location of the node you need.

In general, the whole maneuver has to be optimized in a special piece of software. Again, I urge you to consider injecting the craft into the right orbit right from the start (or doing midcourse corrections in case of interplanetary/interstellar flights).

In a binary system (let's just call the planet you're orbiting Tattooine), the nearest star will contribute the most pressure, and the resulting force will be a geometric sum of the three vectors (pressure from the 1st sun, 2nd sun, and the reflected sunlight from Tattooine) instead of two. Thermal control may be complicated because of this. There may be other interesting corner cases I haven't yet thought through.