Orbit computation and on sky positions.

Given a set of orbital elements, compute the on-sky position of an object.

import kete

Define an object through cometary orbital elements:

elements = kete.CometElements(
    desig="Ceres",
    epoch=2460200.5,
    eccentricity=0.0789,
    inclination=10.58688,
    lon_of_ascending=80.25498,
    peri_time=2459919.898,
    peri_arg=73.4218,
    peri_dist=2.5489,
)

# These can be converted to cartesian coordinates
state = elements.state

# States for objects may also be queried from JPL Horizons
# state = kete.HorizonsProperties.fetch("Ceres").state

print("State information from orbital elements:\n")
print(state)

# This state may be viewed in several frames
# These share the exact definitions used by SPICE
# state.as_equatorial, state.as_ecliptic, state.as_galactic, state.as_fk4

State information from orbital elements:

State(desig="Ceres", jd=2460200.5, pos=[-1.9589083041617754, -1.7916187518626496, 0.3041714202955882], vel=[0.006441217443010055, -0.00842341454823092, -0.0014530324527460736], frame=Ecliptic, center_id=10)

By default, kete uses TDB scaled JD time, the Time object automatically handles conversions to and from this scaling:

jd = kete.Time.from_ymd(2024, 6, 1.5).jd

# Currently the state of the object above is not at this date
# lets perform orbit propagation to bring it to this date:
state = kete.propagate_n_body([state], jd)[0]

Lets try to make an observation of ceres from the ground

obs_info = kete.mpc.find_obs_code("Palomar Mountain")

# Location of palomar mountain in lat/lon/elevation
print(
    "\nInformation about Palomar, these values are with respect to "
    "WGS84 Earth Coordinates."
)
print("lat, lon, elevation, Obs code, and name")
print(obs_info)

# Load the position of the observer in the solar system:
observer = kete.spice.mpc_code_to_ecliptic("Palomar Mountain", jd)

Information about Palomar, these values are with respect to WGS84 Earth Coordinates.
lat, lon, elevation, Obs code, and name
(33.35412, 243.13746, 1.69615, 'Palomar Mountain', '675')

We can now compare the position of ceres with respect to the observatory:

observer_to_object = state.pos - observer.pos

print("\nVector from the observatory to the object (no light delay):")
print(observer_to_object)

# Unfortunately, light takes a measurable amount of time to move, so we need to add a
# correction for it. In this case we can just use the two-body approximation for motion.
# Note that in general the two-body approximation will result in incorrect
# position calculations when propagation time exceeds a few days.
# But its an excellent approximation over the minutes time scale.
light_delay_state = kete.propagate_two_body([state], state.jd, observer.pos)[0]

print("\nThe light delayed position of the object vs the instantaneous:")
print(light_delay_state.pos)
print(state.pos)
# it is a small difference, but it is measurable.

# lets compute the vector from the observer to this light delayed state
# and convert it to the equatorial frame:
observer_to_object = (light_delay_state.pos - observer.pos).as_equatorial

Vector from the observatory to the object (no light delay):
Vector([0.698685392937, -1.889062712782, -0.158580439884], Ecliptic)

The light delayed position of the object vs the instantaneous:
Vector([0.370884041446, -2.848778331127, -0.158471893462], Ecliptic)
Vector([0.370997851354, -2.848770361948, -0.158492608031], Ecliptic)

print(f"\nAt {kete.Time(jd).iso} UTC from the {obs_info[-1]} observatory")
print(
    f"{state.desig} is visible at:\n"
    f"{observer_to_object.ra_hms} RA  {observer_to_object.dec_dms} DEC"
)

At 2024-06-01T12:00:00+00:00 UTC from the 675 observatory
Ceres is visible at:
19 30 47.625 RA  -26 21 19.92 DEC