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While playing around with the animation on https://www.nasa.gov/specials/trackartemis/ I noticed that Orion capsule seems not be pointing directly into its direction of flight. If this would be case the main engine of the SM shout point more or less to earth, shouldn't it?

However, in the animation the engine is pointing more into the opposite direction. Thus it seems that the space craft was rotated after the TLI burn. Is this correct?

Is this just how the animation is created or is this the real orientation?

If this is the real orientation, is there a specific reason for it? Of course the capsule could be rotated into any direction without changing the flight path itself. But are there any "real" constraints on the orientation (e.g. pointing solar panels to sun) or could a later crew (more or less) choose what they would like to see? Why is Artemis I pointed into this direction?

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Probably a partial (wasn't sure if I should leave it as just a comment):

TL;DR:

the main engine of the SM shout point more or less to earth, shouldn't it?

It did.

Thus it seems that the space craft was rotated after the TLI burn. Is this correct?

Yes

Is this just how the animation is created or is this the real orientation?

Seems to be real

If this is the real orientation, is there a specific reason for it?

Seems to be for the sun, as referenced below, the panels face the sun and the radiators face deep space, a power and thermal-balanced attitude. Results in an attitude that does not always reflect direction of travel.

Information on Orion attitude:

https://www.nasaspaceflight.com/2018/08/digging-details-orions-em-1-test-flight/#more-57538

Most of the time on the long coast periods outbound to and returning from the Moon, Orion will be in a tail-to-Sun attitude. “Our vehicle design is the tail-to-Sun flight attitude, so that way your arrays get full Sun and the radiators are around the barrel [are] looking at deep space. So that tail-to-Sun is sort of our baseline power/thermal-balanced attitude.”

“Nominally, the vehicle could just sit there in ‘tail to sun’ indefinitely, but we do have other things that you have to do, like the IMUs (Inertial Measurement Units) will need to be aligned and you’ll need to do star-tracker takes and stuff,” she added. “So there will be times you’ll go out of attitude just to get data and align the IMUs, but you’ll just keep going back to tail to sun.”

The spacecraft doesn’t have to hold the coast attitude precisely. “It’s got a big plus or minus 20-degree deadband,” Merancy said.

“You don’t have to hold it that tight. So when you’re sitting tail-to-Sun you can just bounce around in there, because it just drives up your prop quantity [consumption] to hold it really tight and you don’t need to. The arrays can track plenty and you’ve 40 degrees worth of ‘slosh,’ so GNC doesn’t need a tight deadband on that.”

Additional:

https://blogs.esa.int/orion/2022/11/15/artemis-i-short-mission-overview/

Twenty minutes after the boost, two hours after launch, the ICPS will detach from Orion and this is when the launch is considered a success, from here on Orion and its European Service Module are on their own.

On to the Moon

Meanwhile Orion and the European Service Module will be en route to the Moon. Roughly eight hours after launch the European Service Module will perform its first of several trajectory correction burns using the main Orbital Maneuvering System (OMS) engine, providing a delta-v of 35 m/s.

  • that should account for the engine pointing in the direction you assume - that is pointing at Earth with nose towards its destination.

From here, Orion will cruise to the Moon with minor corrections done by the European Service Module’s six clusters of reaction control engines. These are scheduled on flight day two, five and four.

Throughout the 10-day trip to the Moon the European Service Module will be pointing its four solar arrays in the best way to get as much sunlight to convert into electricity. Both the solar arrays and the spacecraft itself can be turned and rotated to track the Sun during the voyage to the Moon and back.

  • that should account for the change in attitude during its journey.

Edit: info on panels:

https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/Orion/Power

more:

https://www.eoportal.org/satellite-missions/artemis-i#esm-layout

SADM of the ESM has a unique design incorporating a two axis gimbal. An inner axis provides rotation of the SAW about an axis perpendicular to the ESM longitudinal axis, and an outer axis which rotates the SAW about its own longitudinal axis. The two-axis capability is necessary for two reasons:

  1. allow maximum sun tracking to meet the power requirements for particular vehicle attitudes of certain mission phases. Insufficient power is generated by the SAW with a single (roll) axis SADM not providing the avoidance capability of the shadowing effect of both the Orion vehicle on the SAW and the SAWs on each other

  2. insure the structural integrity of the SAWs under injection maneuvers. For the trans-lunar injection performed with the upper stage of the Space Launch System rocket, actually the iCPS (interim Cryogenic Propulsion Stage), the arrays are canted backwards to sustain in deployed configuration the 1 g acceleration load. For the trans-earth injection performed with the ESM main engine, the acceleration is less severe and the arrays have to be canted forwards to prevent damages from the OMS-E engine plume while minimizing the load on the SAWs.

The SADM also allows repositioning (canting) of the SAW to reduce the loads on the SAW and SADM during the different Orion orbital maneuvers. At TLI (Trans-Lunar Injection), a 0.5 g acceleration is generated by the iCPS engine and at LOI (Lunar Orbit Insertion) and TEI (Trans-Earth Injection) a 0.3 g deceleration is generated by the OMS-E engine.

The Solar Array orientation is controlled by the two-axis Solar Array Drive Mechanism (SADM). The Sun-tracking mechanism can swivel between –35° and +25° on the inner axis, while the outer axis can rotate fully: 0° to +360°

This GIF shows the view of Earth before the attitude change, whilst the rear was still pointing towards Earth.

enter image description here

attitude change of both Orion and panels here:

Timelapse of NASA's Orion Spacecraft Leaving Earth:

More detail about the panels in this answer to Do Orion's solar panels have adjustable sweep?:

https://space.stackexchange.com/a/29767/40489

I did wonder if it was for communications:

enter image description here

From this position, the phased array antenna is generally angled aft, but this type of antenna has a wide scanning range and does not need to be mechanically directed.

but O2O is for the crewed flight not this one:

enter image description here

Optical Communications System (O2O) will bring laser communications to the Moon aboard NASA's Orion spacecraft O2O will be capable of transmitting high-resolution images and video

and seems to have full articulation so it could be reasonably independent of Orion attitude.

and i haven't seen references stating attitude required for communications.

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