task_id stringlengths 23 39 | topic stringclasses 2
values | subtopic stringlengths 8 23 | tier int64 1 3 | prompt stringlengths 140 281 | answer stringlengths 7 13 | gold_value_si float64 -10,772,972.97 5,201,570,780,000,000B | gold_unit stringclasses 4
values | rel_tol float64 0.02 0.02 | hand_curated bool 2
classes | params unknown |
|---|---|---|---|---|---|---|---|---|---|---|
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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