Foundations of Astrophysics
Bridge high school physics and university astrophysics by exploring the cosmic tug-of-war between gravity and pressure. Calculate orbital maneuvers, decode starlight spectra, model stellar collapse, and map the expanding metric of spacetime.
Like Duolingo, but for Foundations of Astrophysics. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 12 levels across 2 sections, about 24 minutes end to end, roughly 5 days at five minutes a day. It moves through Orbital Dynamics and Starlight and Stellar Collapse and Spacetime. It assumes you already know the basics.
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Key ideas in Foundations of Astrophysics
- Orbital velocity decreases as distance from the central attracting mass increases
- Setting gravity equal to centripetal force yields speed proportional to the inverse square root of radius
- Quadrupling the orbital radius cuts the required circular speed by a factor of two
- Specific mechanical energy depends solely on the semi-major axis and remains constant throughout an orbit
- The vis-viva equation shows speed increases as current orbital distance decreases
- Gravitational potential energy converts to kinetic energy as an object falls toward periapsis
- Escape velocity equals circular orbital speed multiplied by the square root of two
- Escape velocity sets the total mechanical energy of the spacecraft to zero
- The factor of root two (~1.414) comes from setting kinetic energy equal to gravitational potential energy
- Work equals force times displacement, meaning an engine does more mechanical work per second at higher speeds
- Burning propellant at high speed leaves the exhaust with less kinetic energy, transferring more energy to the craft
- The Oberth effect yields higher final energy from the same delta-v when applied at the lowest orbital point
- Kepler's Third Law relates the orbital period squared to the semi-major axis cubed divided by central mass
- A more massive central object forces orbiting bodies at a given distance to complete orbits faster
- Measuring a companion star's period and separation reveals the enclosed gravitational mass
- Wien's law states peak emission wavelength is inversely proportional to surface temperature
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Foundations of Astrophysics the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
When you equate Newton's gravity with the required centripetal force, how does circular speed depend on orbital radius?
Get it right to open this lesson and 11 more in the app.
Where Foundations of Astrophysics takes you
- 1
Orbital Dynamics and Starlight
- Calculating Orbits and Escape Trajectories
- Decoding Starlight Through Spectroscopy
- 2
Stellar Collapse and Spacetime
- Balancing Hydrostatic Equilibrium and Degeneracy
- Mapping Spacetime Curvature and Cosmic Expansion
2 sections · 4 units · 12 levels. Built to play, not to enroll.
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- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
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You pick the voice
Foundations of Astrophysics is taught in the Professor style: clear, structured, thorough. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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