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astro-ap-parallax_distance-10000
astrophysics
parallax_distance
1
A star has a measured parallax of p = 0.230 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \boxed{value unit}.
4.348 pc
134,159,894,800,000,000
m
0.02
false
{ "p_arcsec": 0.23 }
astro-orb-specific_orbital_energy-10001
orbital_mechanics
specific_orbital_energy
1
For an Earth orbit with semi-major axis a = 18,500 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \boxed{value unit}.
-10.77 MJ/kg
-10,772,972.972973
J/kg
0.02
false
{ "a_km": 18500 }
astro-orb-kepler_third_law-10002
orbital_mechanics
kepler_third_law
1
A satellite is in an Earth orbit with semi-major axis a = 29,700 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \boxed{value unit}.
14.15 hr
50,938.469871
s
0.02
false
{ "a_km": 29700 }
astro-orb-leo_period-10003
orbital_mechanics
leo_period
2
A satellite orbits at altitude h = 1,760 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \boxed{value unit}.
121.6 min
7,296.71129
s
0.02
false
{ "h_km": 1760 }
astro-orb-circular_velocity-10004
orbital_mechanics
circular_velocity
1
A satellite is in a circular Earth orbit of radius r = 34,100 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \boxed{value unit}.
3.419 km/s
3,418.93983
m/s
0.02
false
{ "r_km": 34100 }
astro-orb-altitude_from_period-10005
orbital_mechanics
altitude_from_period
3
An Earth satellite has an orbital period of T = 14.5 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \boxed{value unit}.
2.382e+04 km
23,817,360.059146
m
0.02
false
{ "T_hr": 14.5 }
astro-orb-leo_period-10006
orbital_mechanics
leo_period
2
A satellite orbits at altitude h = 1,910 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \boxed{value unit}.
125 min
7,499.553336
s
0.02
false
{ "h_km": 1910 }
astro-orb-altitude_from_period-10007
orbital_mechanics
altitude_from_period
3
An Earth satellite has an orbital period of T = 5.2 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \boxed{value unit}.
8867 km
8,867,062.439897
m
0.02
false
{ "T_hr": 5.2 }
astro-orb-hohmann_transfer-10008
orbital_mechanics
hohmann_transfer
3
Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 10,800 km and r₂ = 33,400 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \boxed{value unit}.
2433 m/s
2,432.976091
m/s
0.02
false
{ "r1_km": 10800, "r2_km": 33400 }
astro-orb-leo_period-10009
orbital_mechanics
leo_period
2
A satellite orbits at altitude h = 1,480 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \boxed{value unit}.
115.4 min
6,923.069432
s
0.02
false
{ "h_km": 1480 }
astro-orb-circular_velocity-10010
orbital_mechanics
circular_velocity
1
A satellite is in a circular Earth orbit of radius r = 17,800 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \boxed{value unit}.
4.732 km/s
4,732.151564
m/s
0.02
false
{ "r_km": 17800 }
astro-orb-kepler_third_law-10011
orbital_mechanics
kepler_third_law
1
A satellite is in an Earth orbit with semi-major axis a = 23,200 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \boxed{value unit}.
9.769 hr
35,167.637853
s
0.02
false
{ "a_km": 23200 }
astro-orb-escape_velocity-10012
orbital_mechanics
escape_velocity
1
From a distance r = 16,300 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \boxed{value unit}.
6.993 km/s
6,993.423729
m/s
0.02
false
{ "r_km": 16300 }
astro-ap-distance_modulus-10013
astrophysics
distance_modulus
2
A star has apparent magnitude m = 13.5 and absolute magnitude M = 1.5. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \boxed{value unit}.
2512 pc
77,508,716,490,000,000,000
m
0.02
false
{ "m": 13.5, "M": 1.5 }
astro-ap-hubble_law-10014
astrophysics
hubble_law
1
A galaxy recedes at v = 5,500 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \boxed{value unit}.
78.57 Mpc
2,424,460,957,000,000,000,000,000
m
0.02
false
{ "v_kms": 5500 }
astro-orb-vis_viva-10015
orbital_mechanics
vis_viva
2
A spacecraft is on an Earth orbit with semi-major axis a = 34,600 km. At an instant its distance from Earth's center is r = 51,600 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \boxed{value unit}.
1.982 km/s
1,982.26668
m/s
0.02
false
{ "a_km": 34600, "r_km": 51600 }
astro-orb-hohmann_transfer-10016
orbital_mechanics
hohmann_transfer
3
Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,300 km and r₂ = 30,500 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \boxed{value unit}.
2192 m/s
2,192.424607
m/s
0.02
false
{ "r1_km": 11300, "r2_km": 30500 }
astro-orb-circular_velocity-10017
orbital_mechanics
circular_velocity
1
A satellite is in a circular Earth orbit of radius r = 28,600 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \boxed{value unit}.
3.733 km/s
3,733.237595
m/s
0.02
false
{ "r_km": 28600 }
astro-ap-schwarzschild_radius-10018
astrophysics
schwarzschild_radius
2
A black hole has mass M = 4.85e+06 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \boxed{value unit}.
1.433e+07 km
14,326,148,964.775715
m
0.02
false
{ "m_solar": 4850000 }
astro-ap-hubble_law-10019
astrophysics
hubble_law
1
A galaxy recedes at v = 11,800 km/s. Using Hubble's law with H₀ = 70 km/s/Mpc, compute its distance in Mpc. Give your final answer as \boxed{value unit}.
168.6 Mpc
5,201,570,780,000,000,000,000,000
m
0.02
false
{ "v_kms": 11800 }
astro-orb-vis_viva-10020
orbital_mechanics
vis_viva
2
A spacecraft is on an Earth orbit with semi-major axis a = 19,000 km. At an instant its distance from Earth's center is r = 14,000 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \boxed{value unit}.
5.997 km/s
5,996.991727
m/s
0.02
false
{ "a_km": 19000, "r_km": 14000 }
astro-ap-parallax_distance-10021
astrophysics
parallax_distance
1
A star has a measured parallax of p = 0.671 arcsec. Compute its distance in parsecs (d = 1/p). Give your final answer as \boxed{value unit}.
1.49 pc
45,986,253,080,000,000
m
0.02
false
{ "p_arcsec": 0.671 }
astro-orb-hohmann_transfer-10022
orbital_mechanics
hohmann_transfer
3
Compute the total Δv for a Hohmann transfer between two coplanar circular Earth orbits of radii r₁ = 11,600 km and r₂ = 28,300 km. Use μ = 3.986×10^14 m³/s². Sum the two burns and give the total in m/s. Give your final answer as \boxed{value unit}.
2011 m/s
2,011.001431
m/s
0.02
false
{ "r1_km": 11600, "r2_km": 28300 }
astro-orb-escape_velocity-10023
orbital_mechanics
escape_velocity
1
From a distance r = 14,500 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \boxed{value unit}.
7.415 km/s
7,414.80346
m/s
0.02
false
{ "r_km": 14500 }
astro-orb-synodic_period-10024
orbital_mechanics
synodic_period
2
Two planets orbit the Sun with sidereal periods T₁ = 547.5 days and T₂ = 1,971.0 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \boxed{value unit}.
758.1 days
65,497,846.153846
s
0.02
false
{ "T1_d": 547.5, "T2_d": 1971 }
astro-ap-wien_law-10025
astrophysics
wien_law
1
A star has surface temperature T = 26,700 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \boxed{value unit}.
108.5 nm
0
m
0.02
false
{ "T_K": 26700 }
astro-orb-synodic_period-10026
orbital_mechanics
synodic_period
2
Two planets orbit the Sun with sidereal periods T₁ = 419.7 days and T₂ = 1,186.2 days. Compute their synodic period (1/T_syn = |1/T₁ − 1/T₂|) in days. Give your final answer as \boxed{value unit}.
649.6 days
56,126,571.428571
s
0.02
false
{ "T1_d": 419.75, "T2_d": 1186.25 }
astro-ap-wien_law-10027
astrophysics
wien_law
1
A star has surface temperature T = 15,600 K. Using Wien's displacement law λ_peak = b/T with b = 2.898×10^-3 m·K, compute the peak emission wavelength in nm. Give your final answer as \boxed{value unit}.
185.8 nm
0
m
0.02
false
{ "T_K": 15600 }
astro-orb-vis_viva-10028
orbital_mechanics
vis_viva
2
A spacecraft is on an Earth orbit with semi-major axis a = 9,600 km. At an instant its distance from Earth's center is r = 7,700 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \boxed{value unit}.
7.875 km/s
7,874.746612
m/s
0.02
false
{ "a_km": 9600, "r_km": 7700 }
astro-orb-altitude_from_period-10029
orbital_mechanics
altitude_from_period
3
An Earth satellite has an orbital period of T = 18.8 hours. Using μ = 3.986×10^14 m³/s² and Earth radius R = 6.371×10^6 m, solve Kepler's third law for the semi-major axis, then report the altitude above Earth's surface in km. Give your final answer as \boxed{value unit}.
2.952e+04 km
29,523,900.397144
m
0.02
false
{ "T_hr": 18.8 }
astro-orb-kepler_third_law-10030
orbital_mechanics
kepler_third_law
1
A satellite is in an Earth orbit with semi-major axis a = 25,700 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \boxed{value unit}.
11.39 hr
41,002.55371
s
0.02
false
{ "a_km": 25700 }
astro-ap-transit_radius-10031
astrophysics
transit_radius
2
An exoplanet transit has fractional depth ΔF/F = 0.012140. The host star radius is R_★ = 2.3 R_⊙ (R_⊙ = 6.957×10^8 m, R_⊕ = 6.371×10^6 m). Using ΔF/F = (R_p/R_★)², compute the planet radius in Earth radii (R_⊕). Give your final answer as \boxed{value unit}.
27.67 R_earth
176,302,789.050242
m
0.02
false
{ "depth": 0.012140000000000001, "r_star_rsun": 2.3 }
astro-orb-specific_orbital_energy-10032
orbital_mechanics
specific_orbital_energy
1
For an Earth orbit with semi-major axis a = 25,600 km and μ = 3.986×10^14 m³/s², compute the specific orbital energy ε = −μ/(2a) in MJ/kg. Give your final answer as \boxed{value unit}.
-7.785 MJ/kg
-7,785,156.25
J/kg
0.02
false
{ "a_km": 25600 }
astro-orb-circular_velocity-10033
orbital_mechanics
circular_velocity
1
A satellite is in a circular Earth orbit of radius r = 13,000 km. With μ = 3.986×10^14 m³/s², compute the circular orbital speed v = √(μ/r) in km/s. Give your final answer as \boxed{value unit}.
5.537 km/s
5,537.2862
m/s
0.02
false
{ "r_km": 13000 }
astro-orb-vis_viva-10034
orbital_mechanics
vis_viva
2
A spacecraft is on an Earth orbit with semi-major axis a = 9,900 km. At an instant its distance from Earth's center is r = 8,850 km. With μ = 3.986×10^14 m³/s², use the vis-viva equation v = √(μ(2/r − 1/a)) to find its speed in km/s. Give your final answer as \boxed{value unit}.
7.058 km/s
7,058.078335
m/s
0.02
false
{ "a_km": 9900, "r_km": 8850 }
astro-orb-leo_period-10035
orbital_mechanics
leo_period
2
A satellite orbits at altitude h = 1,280 km above Earth's surface. With Earth radius R = 6.371×10^6 m and μ = 3.986×10^14 m³/s², compute its orbital period in minutes. Give your final answer as \boxed{value unit}.
111 min
6,660.21922
s
0.02
false
{ "h_km": 1280 }
astro-orb-kepler_third_law-10036
orbital_mechanics
kepler_third_law
1
A satellite is in an Earth orbit with semi-major axis a = 41,200 km. Earth's standard gravitational parameter is μ = 3.986×10^14 m³/s². Compute the orbital period in hours. Give your final answer as \boxed{value unit}.
23.12 hr
83,225.62116
s
0.02
false
{ "a_km": 41200 }
astro-orb-escape_velocity-10037
orbital_mechanics
escape_velocity
1
From a distance r = 15,600 km from Earth's center, with μ = 3.986×10^14 m³/s², compute the escape velocity v = √(2μ/r) in km/s. Give your final answer as \boxed{value unit}.
7.149 km/s
7,148.605745
m/s
0.02
false
{ "r_km": 15600 }
astro-ap-schwarzschild_radius-10038
astrophysics
schwarzschild_radius
2
A black hole has mass M = 83 solar masses (M_⊙ = 1.989×10^30 kg). With G = 6.674×10^-11 m³ kg⁻¹ s⁻² and c = 2.998×10^8 m/s, compute the Schwarzschild radius r_s = 2GM/c² in km. Give your final answer as \boxed{value unit}.
245.2 km
245,169.147232
m
0.02
false
{ "m_solar": 83 }
astro-ap-distance_modulus-10039
astrophysics
distance_modulus
2
A star has apparent magnitude m = 14.5 and absolute magnitude M = 2.0. Using the distance modulus m − M = 5·log₁₀(d/10 pc), compute the distance d in parsecs. Give your final answer as \boxed{value unit}.
3162 pc
97,577,692,820,000,000,000
m
0.02
false
{ "m": 14.5, "M": 2 }
astro-orb-leo_period_hours-20000
orbital_mechanics
leo_period_hours
2
A satellite orbits at altitude h = 1,480 km (R = 6.371×10^6 m, μ = 3.986×10^14 m³/s²). Report the orbital period in HOURS. Give your final answer as \boxed{value unit}.
1.923 hr
6,923.069432
s
0.02
true
{ "h_km": 1480 }
astro-orb-mars_circular_velocity-20001
orbital_mechanics
mars_circular_velocity
1
A probe is in a circular orbit of radius r = 10,800 km about Mars (μ_Mars = 4.283×10^13 m³/s²). Compute the circular speed in km/s. Give your final answer as \boxed{value unit}.
1.991 km/s
1,991.416767
m/s
0.02
true
{ "r_km": 10800 }
astro-ap-schwarzschild_meters-20002
astrophysics
schwarzschild_meters
2
A black hole of mass M = 15 M_⊙ (M_⊙ = 1.989×10^30 kg, G = 6.674×10^-11 m³ kg⁻¹ s⁻², c = 2.998×10^8 m/s). Compute the Schwarzschild radius r_s = 2GM/c² in METERS. Give your final answer as \boxed{value unit}.
4.431e+04 m
44,307.677211
m
0.02
true
{ "m_solar": 15 }
astro-ap-hubble_in_pc-20003
astrophysics
hubble_in_pc
2
A nearby galaxy recedes at v = 4,900 km/s (H₀ = 70 km/s/Mpc). Give its distance in PARSECS (not Mpc). Give your final answer as \boxed{value unit}.
7e+07 pc
2,159,974,307,000,000,000,000,000
m
0.02
true
{ "v_kms": 4900 }

Kepler astro-bench v0.1

The benchmark behind Orionfold/Kepler-GGUF — a verifier-checked set of astrodynamics and quantitative-astrophysics word problems, each with a single numeric gold answer and a programmatic verifier that doubles as a reinforcement-learning reward.

What's here

File Rows Purpose
pool.jsonl 120 Training / selection pool — 16 formula families (9 orbital, 7 astrophysics), 3 difficulty tiers.
heldout.jsonl 44 External curveball held-out — different seeds + hand-curated edge cases, disjoint from the pool. The number on the model card is measured here.
verifier.py astro_numeric_match(...) — the scorer.
units.py SI-unit parsing/normalization used by the verifier.

Row schema

{
  "task_id": "astro-orb-leo_period-0000",
  "topic": "orbital_mechanics",
  "subtopic": "leo_period",
  "tier": 2,
  "prompt": "A satellite orbits at altitude h = 1,030 km ... Give your final answer as \\boxed{value unit}.",
  "answer": "105.6 min",
  "gold_value_si": 6336.46,
  "gold_unit": "s",
  "rel_tol": 0.02,
  "hand_curated": false,
  "params": {"h_km": 1030}
}

All physical constants are given in the prompt — the task tests reasoning, not memorization. The expected answer is a single \boxed{value unit}.

The verifier is the reward

astro_numeric_match extracts the \boxed{} answer, normalizes units to SI, and checks the value against the gold within a per-row relative tolerance (default ±2%). It returns a binary score, so it plugs directly into an RLVR loop as the reward — the same scorer used to build Kepler's SFT corpus, to gate the SFT checkpoint, and to run the head-to-head comparison.

from verifier import astro_numeric_match  # needs units.py alongside

reward = astro_numeric_match(
    completion=model_output,        # the model's full text, containing \boxed{...}
    expected="105.6 min",           # the row's "answer" field
    rel_tolerance=0.02,             # the row's "rel_tol" field
)  # -> 1.0 if correct within tolerance, else 0.0

Known coverage gaps

Honest about its weak spots: the families hohmann_transfer (two-burn transfers) and altitude_from_period (inverse Kepler) are the hardest rows and where models — including Kepler — most often miss. Treat them as the frontier of this benchmark.

Methods

Full construction + measurement protocol: The Gate Before the GPU — Deciding SFT vs RL vs RLVR Before You Spend the Run.


Published by Orionfold LLC · orionfold.com · Methods at ainative.business/field-notes.

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