<p>If your simulation is starting from the Earth's surface, or from somewhere close to the Earth (e.g., orbit insertion), you want to use some kind of Earth-centered inertial (ECI) frame initially. At some critical distance from the Moon, your simulation should switch to some kind of Moon-centered inertial (MCI) frame.</p>
<p>Which ECI frame, and which MCI frame, it doesn't matter much. The J2000 frame (very similar to the International Celestial Reference Frame, or ICRF) is widely used. Note that this is not a &quot;true&quot; equatorial frame. It was a &quot;mean&quot; equatorial frame at the J2000 epoch (noon TT on 1 Jan 2000), but it is no longer truly Earth equatorial as the Earth's orientation has precessed and nutated since that time. As the equations of motion take on their simplest form in an inertial (non-rotating) frame, many have migrated to the J2000 frame or the ICRF frame (or the ECI equivalent).</p>
<p>Regarding the critical distance for the switch from ECI to MCI (and if the spacecraft is returning to the Earth, a corresponding switch from MCI to ECI on exceeding a critical distance from the Moon): You will get erroneous results if you don't perform these switches and if you use finite precision arithmetic (e.g., <code>double</code> in C, C++ and numpy, <code>float</code> in python). The switch point has to be somewhere reasonable. Not switching at all is not at all reasonable. Switching from ECI to MCU shortly after translunar injection is not reasonable, nor is switching shortly before lunar landing. The Apollo program used the Moon's gravitational sphere of influence (about 66300 km from the center of the Moon) as the switch point. Another option is the Moon's Hill sphere (about 61600 km from the center of the Moon). Both work.</p>

CC BY-SA 4.0
2023-05-10T08:34:27.317Z
2023-05-10T08:34:27.317Z
David Hammen
<p>Which coordinate system is most suited for this type of problem? ecliptic? equatorial?</p>

CC BY-SA 4.0
2023-05-09T18:32:40.507Z
I would expect the easiest to work with would be one centered on Earth, using the plane of the Moon's orbit as Z=0.  I'm not aware if there is a specific name for it.
Greg Miller
CC BY-SA 4.0
2023-05-09T18:53:18.610Z
I suggest using J2000.0 ecliptic coords, since the trajectory is close to the ecliptic, and you can easily get data using J2000 from Horizons.
PM 2Ring
CC BY-SA 4.0
2023-05-09T21:02:52.310Z
This is likely answerable also on [space.se]
James K
CC BY-SA 4.0
2023-05-10T08:36:17.777Z
I answered from the perspective of a [Space Exploration](https://space.stackexchange.com/) question, which is where this question should be migrated.
David Hammen
CC BY-SA 4.0
2023-05-10T22:43:16.840Z
I’m voting to close this question because it's not on-topic in Astronomy SE. Luckily however it's a great fit in Space Exploration SE so it might end up getting migrated there.
uhoh
<observational-astronomy><orbit><astrophysics><space>
Which coordinate system should one use for simulating a spacecraft trajectory to the moon?
Blobmou
# Which coordinate system should one use for simulating a spacecraft trajectory to the moon?

(Asked by: username_0 on 2023-05-09)

Which coordinate system is most suited for this type of problem? ecliptic? equatorial?

**Tags:** observational-astronomy, orbit, astrophysics, space

> **Comments:**
> **username_1**: I would expect the easiest to work with would be one centered on Earth, using the plane of the Moon's orbit as Z=0.  I'm not aware if there is a specific name for it.  
> **username_2**: I suggest using J2000.0 ecliptic coords, since the trajectory is close to the ecliptic, and you can easily get data using J2000 from Horizons.  
> **username_3**: This is likely answerable also on [space.se]  
> **username_4**: I answered from the perspective of a [Space Exploration](https://space.stackexchange.com/) question, which is where this question should be migrated.  
> **username_5**: I’m voting to close this question because it's not on-topic in Astronomy SE. Luckily however it's a great fit in Space Exploration SE so it might end up getting migrated there.  

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## 1 answers

### Answer by username_4 on 2023-05-10. Score: 1

If your simulation is starting from the Earth's surface, or from somewhere close to the Earth (e.g., orbit insertion), you want to use some kind of Earth-centered inertial (ECI) frame initially. At some critical distance from the Moon, your simulation should switch to some kind of Moon-centered inertial (MCI) frame.

Which ECI frame, and which MCI frame, it doesn't matter much. The J2000 frame (very similar to the International Celestial Reference Frame, or ICRF) is widely used. Note that this is not a "true" equatorial frame. It was a "mean" equatorial frame at the J2000 epoch (noon TT on 1 Jan 2000), but it is no longer truly Earth equatorial as the Earth's orientation has precessed and nutated since that time. As the equations of motion take on their simplest form in an inertial (non-rotating) frame, many have migrated to the J2000 frame or the ICRF frame (or the ECI equivalent).

Regarding the critical distance for the switch from ECI to MCI (and if the spacecraft is returning to the Earth, a corresponding switch from MCI to ECI on exceeding a critical distance from the Moon): You will get erroneous results if you don't perform these switches and if you use finite precision arithmetic (e.g., `double` in C, C++ and numpy, `float` in python). The switch point has to be somewhere reasonable. Not switching at all is not at all reasonable. Switching from ECI to MCU shortly after translunar injection is not reasonable, nor is switching shortly before lunar landing. The Apollo program used the Moon's gravitational sphere of influence (about 66300 km from the center of the Moon) as the switch point. Another option is the Moon's Hill sphere (about 61600 km from the center of the Moon). Both work.


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