# At which direction do you apply thrust to perform an inclination change maneuver?

Assume that the vehicle is already at the orbital node. No combined plane changes are included.

At which direction is the thrust applied to do an inclination change maneuver?

So far, Google hasn't given me any useful answers. Some of the answers say to fire the thrust perpendicular to the velocity vector at the initial orbit to do a simple inclination change maneuver and some say to fire it tangentially which I could guess is related to the combined plane change maneuver.

• Intuitively, firing thrusters in the direction you're already moving (tangential to velocity) won't make you move in a different direction, which is the goal of an inclination change maneuver. Feb 12 at 20:09
• Some intuition for why a normal burn is what you want: consider two extremely low ordbits. Like, 20 cm above the ground. Notice that you don't really need orbital velocity now, you can just put some wheels on the ground and roll on these at any speed. The orbits have become two intersecting earth-rounding roads, and your spaceship is a car switching between them. How do you do that? Well, by turning the steering wheel. What does that accomplish? Well, it imposes a force perpendicular to the moving direction. Feb 13 at 8:07
• If you want to change your inclination by a lot, you indeed start off by firing prograde (tangentially) to raise your apoapsis somewhere near the Hill sphere (a very expensive maneuver), wait till apoapsis where you're crawling at a couple m/s, apply the normal burn to change the inclination for next to no cost, then burn retrograde at perigee to circularize the orbit again. Very expensive but still less than turning the orbit 90 degrees at LEO.
– SF.
Feb 14 at 14:14

## 2 Answers

To change an orbit's inclination, you need to apply thrust in the normal/anti-normal direction. The normal/anti-normal direction are some of the 6 main directions you can change your velocity.

There are the 6 main directions:

• Prograde
• Retrograde
• Normal
• Anti-normal
• Radial
• Anti-radial

This description from the answer you saw online is correct.

Fire the thrust perpendicular to the velocity vector at the initial orbit to do a simple inclination change maneuver

However somebody who is unfamiliar with some of the terms might find it a bit confusing. To try to make it clearer, I drew this picture below in paint.net depicting all the 6 main directions to change your velocity. The purple arrows are the normal/anti-normal direction. Changing the velocity in one of those 2 directions will change the inclination.

To visual it better, I drew this image below depicting different orbits with varies inclinations. The more the velocity changes in the normal/anti-normal direction, the more inclined the orbit will be. (I know my drawing skills aren't great, but I hope the images can help you understand it).

Further reading

• Orbital Normal follows the right-hand rule for rotations: curl your fingers (on your right hand) in the direction of the orbit, and your thumb will point to Normal. Feb 13 at 2:27
• No worries. I'll delete the previous comment just to make sure nobody thinks the images are still backwards. Your orbits are all retrograde from a north-is-up perspective (assuming that's earth) but that shouldn't be too confusing. It might be worth including something about the right-hand rule in the answer since "which way is normal" is a pretty common issue. Feb 13 at 15:19
• For an impulsive burn, you need a mix of normal/anti-normal and retrograde to keep the orbit from changing shape, because a pure normal/anti-normal burn relative to your current orbit is partially prograde to your destination orbit. As the burn duration gets longer, the burn gets closer to pure normal/anti-normal, but that's relative to your current orbit, not your start or end orbit.
– Mark
Feb 14 at 0:12
• Yeah, basically, you burn along the difference vector between your initial velocity and your new orbit's velocity. Burning normal or anti-normal to your orbital plane will get you there but will spend more delta-v, up to about 57% more in the bonkers situation where you're trying to do a 180° plane change. Feb 14 at 13:13

Comment with a drawing, illustrating points made by previous comments:

Green is current orbit

Red is the new, desired orbit

Orange orbit has the same inclination as the desired orbit, but higher apogee

"a" is desired inclination change

"b" is optimum thrust direction

Blue vector is the thrust vector to achieve red orbit inclination "a" without affecting scalar velocity or apoapsis

Purple vector is the thrust vector at right angle to the green orbit needed to achieve desired new orbital inclination "a". However, it also changes scalar velocity so it will raise apoapsis above that for the red orbit. Higher orbit from purple thrust is illustrated in orange.

Since Red-Blue-Green is an isosceles triangle, b=1/2(180*-a)

This description assumes the usual disclaimer used for Hohmann transfers: the thrust is applied as an instantaneous impulse. In reality, the thrust duration for a large inclination change would be a significant portion of the launch burn and occupy a significant orbital phase angle. This would necessitate changing thrust angle and graded (not instantaneous) course changes. Rocket science, in other words.