# Can we go anywhere in space with only THREE reaction wheels and ONE chemical thruster?

I had a discussion the other day with some of my peers and they were very keen on the fact the it is possible to change your orbit as desired using a single thruster and a three reaction wheels. The idea was that you point the thruster in any direction you want using the reaction wheels and boost it.

My intuition says that stability (maintaining a certain attitude) will be an issue as the reaction wheels are not able to withstand the forces of the thruster.

Assuming sufficient fuel is available and magnetorquers are available for desaturation of the wheel, is it possible to do orbital maneuvers with a single thruster on three-axis stabilized spacecraft?

• Could you expand on this " the reaction wheels are not able to withstand the forces of the thruster" ? Is not one system for rotational motion, and the other for translational? – Organic Marble Jan 3 at 14:06
• @OrganicMarble are gimbaled thrusters commonly used in small satellites? Up to my knowledge, thrust control is available but to achieve thrust vectoring (as done in gimbaled thrusters), a cluster of thrusters are needed. The technology of thrust vectoring as in gimbaled thrusters is used in rockets mainly. – John Jan 3 at 15:18
• Abstractly, a single fixed thruster can be mounted so as to point through the center of mass; the center of mass doesn't change as you rotate the spacecraft. As you expend fuel, the CoM will shift, but if the tanks are also mounted along the thrust line, the shift will occur along the thrust line as well. Real-world concerns like propellant slosh will affect this, of course; it's not clear to me how abstract our spacecraft is. – Russell Borogove Jan 3 at 19:19
• If a gimbaled truster is used why bother with the reaction wheels. – lijat Jan 3 at 20:26
• While the thruster can't be perfectly in line with the CoM, it can be close. The reaction wheels can be used to induce a spin in the craft around the direction of travel, which will prevent the the slight misalignment from pushing the vehicle off course. – JCRM Jan 4 at 9:26

I did some rough calculation.

E(Engine Force).             = 800 N
m(Mass of reaction wheel)    = 10 kg
r(radius of reaction wheel)  = 0.2 m
w(max spin rate of wheel)    = 6000rpm * 2pi / 60s
cgo(C.G offset)              = 0.01m

I     = m * r * r / 2        = 0.2 kgm^2
WheelCapacity = I * w        = 125.6 Nms

Torque experienced during engine firing due to C.G offset
= 800 * 0.01 = 8 Nm


These numbers are pretty reasonable number for a medium heavy satellite. So, within ~15s of firing the wheel can saturate to it full capacity. If C.G and thrust axis can be maintained accurately then it maybe possible.

Also, in the example the wheel should not only absorb all extra torque by engine but also be capable to provide sufficient torque else satellite can quickly become out of control. The typical value of wheel torque generally lies somewhere between 0.3 ~ 3 Nm.

Edit 1: I gave it some thought, and it appears to me that wheels can probably be designed for higher torque. Motors can probably just have to be made with more current capacity and powerful magnets. But the wheel capacity remains an issue.

• so if the vehicle spins at 2 rpm it could maintain attitude indefinitely? – JCRM Jan 5 at 15:37
• Given no disturbance torque. But SRP, drag gravity gradient are inescapable – Prakhar Jan 5 at 15:59
• @Prakhar space.stackexchange.com/questions/21465/… is another question you may enjoy answering. Seems mildly related. – Magic Octopus Urn Jan 6 at 19:20
• @Prakhar what's SRP? – SusanW Jul 4 at 9:02
• SRP= Solar radiation pressure – Prakhar Jul 4 at 9:15