Gravitation & Astronomy
Every gravitation & astronomy calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
8 calculators in this section
- Delta-v and Hohmann Transfer Calculator: Two Burns Between Two OrbitsMoving between two circular orbits takes two burns and a long coast between them, and the cheapest way to do it was worked out by Walter Hohmann in 1925. Put in two radii and get both Δv figures, the total, the transfer time, and the angle the destination must be at when you leave — which is what a launch window actually is.
- Exoplanet Transit Detection Calculator: Depth, Duration and What Is DetectableWhen a planet crosses its star, the star dims by the ratio of the areas — nothing else. An Earth in front of the Sun blocks 84 parts per million, which is the number the Kepler mission was built around. Put in a planet, a star and a period and get the depth, the transit duration, the chance of the orbit being lined up at all, and an honest answer about whether a telescope on the ground could ever see it.
- Kepler’s Third Law Calculator: Orbital Period from the Semi-Major AxisKepler's third law is not “T squared is proportional to a cubed”. It is T² = 4π²a³/GM, and the constant on the right belongs to the central body alone — which is why one number works for every planet round the Sun and a different one for every moon round Jupiter. Give a semi-major axis and get the period in seconds, days and years, the perihelion and aphelion distances, the two speeds there, and a check that a³/T² really is 1.000 in astronomical units and years.
- Orbital Period and Altitude Calculator: Speed, Period and the Geostationary CaseType an altitude and get the orbital period, the orbital speed, the gravity out there, how many times a day you go round and how far west the ground track slides each time — plus the altitude that makes the period exactly one sidereal day, which is what “geostationary” really means and is 77 km lower than the 24-hour answer.
- Rocket Thrust and Specific Impulse Calculator: Thrust, vₑ and IspThrust is how hard the engine pushes. Specific impulse is how economically it pushes, and it is measured in seconds — which confuses every student who meets it, because a second is not a force. Put in a mass flow and an exhaust velocity and get the thrust, the pressure term that makes a sea-level engine weaker than the same engine in vacuum, the effective exhaust velocity and the Isp that follows from it.
- Synodic Period Calculator: Why Mars Oppositions Come Round When They DoMars goes round the Sun in 687 days, but a Mars opposition comes round every 780. The difference is the synodic period: how long one body takes to lap another as seen from the Sun, and it is the quantity that sets launch windows, eclipse seasons and when a planet is worth looking at. One subtraction of angular rates does the whole job.
- Thrust-to-Weight Ratio Calculator: Will It Leave the Pad?A rocket with a thrust-to-weight ratio below 1 does not rise slowly. It does not rise at all — it sits on the pad burning its propellant away. Put in a thrust and a mass and get the ratio, the acceleration that is left over after gravity has taken its share, and the ratio on the Moon and on Mars. The diagram lifts off only when the number does.
- Tsiolkovsky Rocket Equation Calculator: Delta-v from the Mass RatioΔv = ve ln(m₀/mf). The speed you can gain grows only as the logarithm of the mass ratio, which is the cruellest arithmetic in engineering and the reason a rocket is a thin shell wrapped round a tank. Put in a mass ratio and get the Δv; put in a Δv you want and get the propellant fraction it demands.