Astrophysics and Energy: Orbits, Gravity, and Photons
Orbital velocity, gravitational force, photon energy, and spring potential energy — four calculations spanning orbital mechanics and energy storage.
From satellites in orbit to the energy in a single photon, these four calculations span vastly different scales of physics.
Orbital velocity: the speed needed to stay in orbit
An object orbiting Earth at low Earth orbit altitude (about 6,771 km from Earth's center) needs a velocity of roughly 7,672 m/s (about 27,600 km/h) to maintain a stable circular orbit — the speed at which gravitational pull exactly matches the centripetal force needed for that orbit.
Gravitational force: Newton's law, applied to real masses
Using F = G × m₁m₂/r², a 1,000 kg object at Earth's surface (6,371 km from Earth's center) experiences a gravitational force of about 9,820 N — dividing by mass recovers the familiar 9.8 m/s² gravitational acceleration.
Photon energy: light's smallest possible packet
Photon energy is E = h × f, where h is Planck's constant (6.626×10⁻³⁴ J·s). A photon at 5×10¹⁴ Hz (roughly visible light frequency) carries about 3.31×10⁻¹⁹ joules of energy — an almost incomprehensibly small number for a single photon, which is why light is normally discussed in terms of enormous numbers of photons at once.
Spring potential energy: energy stored in deformation
Elastic potential energy is ½kx². A spring with a 2,500 N/m constant compressed 0.02m stores 0.5 joules — since energy scales with the square of displacement, doubling the compression quadruples the stored energy, not just doubles it.
From orbits to photons, the same underlying rigor
Orbital mechanics, gravitational force, photon energy, and spring energy all follow exact, calculable relationships despite their vastly different scales. Try the orbital velocity calculator, gravitational force calculator, photon energy calculator, and spring potential energy calculator.