Intuition The ONE core ideaSunlight is a river of tiny momentum-carrying bullets called photons, and even though each one is impossibly small, the Sun fires so many that they add up to a steady, gentle push on anything in space. To predict that push we only need to count how much light-energy hits a surface each second, turn that energy into momentum, and account for whether the light sticks or bounces.
This page assumes nothing . Before you read Solar radiation pressure — sorry, before you read the parent topic Solar radiation pressure — every letter, ratio, and Greek symbol it throws at you is built here from the ground up. Read top to bottom; each brick rests on the one before it.
Definition Energy — the symbolE Energy is the "capacity to make something change" — to heat it, move it, or light it up. We label it with the letter E joule (J as light , and this same E
Definition Power, and the wattPower is energy per second — how fast energy is delivered. Its unit is the watt (W 1 W = 1 J/s
Why do we need both E steady stream . "Per second" is baked into the entire topic. Force itself, as we'll see, is a "per second" quantity.
Look at the figure below. The orange bulb emits a fixed power (60 W). Each tick of the clock, another identical 60-joule packet flies out — the figure spells out that "power = energy delivered every second." Keep that per-second heartbeat in mind: it is the same beat that later turns intercepted light-energy into a steady force.
Definition Speed of light — the symbolc c c ≈ 3 × 1 0 8 m/s c celeritas , Latin "swiftness") is universal in physics. It appears because light's momentum is tied to how fast it moves — you cannot separate light's push from its speed.
is , in a picture
Momentum is "how hard it is to stop something that's moving." A rolling bowling ball has lots of momentum (hard to stop); a rolling ping-pong ball has little. When a moving thing hits you and stops, it hands over its momentum — that handover is a push.
Definition Momentum — the symbolp momentum p = m v m v kg⋅m/s
Look at the figure below. The key idea for the whole topic is the bottom row : when a bullet hits a wall and sticks , the wall gains the bullet's momentum p bounces straight back , it leaves with momentum − p p − ( − p ) = 2 p twice the push. Hold that "twice" in mind; it is the mirror-vs-black-paint fact the parent topic hinges on.
Common mistake "Light has no mass, sop = m v = 0 Why it feels right: the only momentum formula you've met is p = m v m = 0 The fix: p = m v slow-object rule. Light obeys a different rule (next section) that gives it momentum without mass. Momentum is not "always mass times velocity" — it is a conserved book-keeping quantity, and light has some. See Photon momentum and relativity .
Light is not a smooth continuous stream — it comes in tiny indivisible packets called photons . Picture a machine gun firing millions of light-bullets per second. Each photon carries a specific amount of energy E E
Intuition Why this single formula unlocks everythingIf you know how much light-energy lands on a surface each second, you multiply by 1/ c momentum lands each second — and momentum-per-second is a force . The whole topic is: count energy, divide by c
Definition Force — the symbolF force is a push or pull. Newton's insight: force is momentum delivered per second . If a stream hands over momentum p is a force of p newton (N 1 N = 1 kg⋅m/s 2
Definition Pressure — the symbolP Pressure is force spread over area: P = F / A pascal (Pa 1 Pa = 1 N/m 2
Why does the topic talk about pressure first and force second? Because sunlight arrives per square metre — it is naturally a pressure. To get the force on your actual spacecraft you multiply pressure by its area. That is the logical order the parent note follows.
Definition Acceleration and mass — the symbolsa m Mass m kg Acceleration a F = ma a = F / m acceleration , not force — orbits respond to a
Definition Luminosity — the symbolL ⊙ L ⊙ total power the Sun radiates in every direction: L ⊙ ≈ 3.83 × 1 0 26 W ⊙
Definition Distance — the symbolr r astronomical units (AU 1 AU ≈ 1.5 × 1 0 11 m
Intuition Why the same light gets weaker far away — the sphere pictureThe Sun's power streams out equally in all directions. At distance r r 4 π r 2 quadruples → the light is four times thinner. This "spread over 4 π r 2 1/ r 2
Now the chain snaps together: S c pressure :
P rad = c S .
Definition The surface normal, and the angleθ normal is an arrow sticking straight out of a surface, perpendicular to it — like a pencil balanced on a tabletop. The angle θ to the Sun . If the surface faces the Sun dead-on, θ = 0 θ = 9 0 ∘
Definition Reflectivity — the symbolη η 0 1 η = 0 η = 1 ( 1 + η ) × 1 × 2
Common mistake "A surface tilted past edge-on still catches sunlight."Why it feels right: you plug any θ cos θ The fix: for θ > 9 0 ∘ away from the Sun — its lit side is in shadow, so no sunlight lands and the force is zero, not negative. Mathematically cos θ clamp : use max ( cos θ , 0 ) 0 ≤ θ ≤ 9 0 ∘
Every symbol is now defined. Watch them click into one expression, one factor at a time.
Definition Area-to-mass ratio — the symbolA / m A m A / m A / m A / m Solar sails versus a heavy orbiter, and its role as a perturbation in Orbital perturbations .
Each node names a symbol and its plain meaning, so you can map the diagram straight back to the definitions above.
Power = E per second, watts
Radiation pressure Prad = S over c
Intensity S = power per area
Sphere area 4 pi r squared
Force F = Prad times A times one plus eta times cos theta
Acceleration a = F over m
Area to mass ratio A over m
Read it as a river: energy E c L ⊙ 4 π r 2 S c P rad cos θ F
Cover the right side and test yourself. If any answer surprises you, re-read that section before opening the parent note.
What is power, in one phrase, and its unit? Energy delivered per second; the watt (W = J/s
What letter denotes energy, and its unit? E J
What is the value and meaning of c The speed of light, ≈ 3 × 1 0 8 m/s
Ordinary momentum formula and its unit? p = m v kg⋅m/s
The light-momentum rule and why it's not p = m v p = E / c p = m v
Why does a mirror get pushed twice as hard as black paint? A bounced photon reverses momentum (p → − p 2 p p
Force stated as a "per second" idea? Force = momentum delivered per second; unit newton (N
Definition of pressure and its unit? Force per area, P = F / A Pa = N/m 2
Newton's link between force, mass, acceleration? F = ma a = F / m
What does L ⊙ Total power the Sun radiates in all directions, ≈ 3.83 × 1 0 26 W
Why does light get weaker as 1/ r 2 Fixed power spreads over a sphere of area 4 π r 2 r 2
Definition of intensity S Power per area, S = L ⊙ / ( 4 π r 2 ) ≈ 1361 W/m 2
What is the angle θ The surface normal and the direction to the Sun.
What happens to the force for θ > 9 0 ∘ Surface faces away, no light lands — clamp cos θ 0
What does η η = 0 η = 1 Reflectivity; 0 1
The full simple force formula on a plate? F = ( S / c ) A ( 1 + η ) cos θ 0 ≤ θ ≤ 9 0 ∘
Why do orbits care about A / m SRP acceleration scales with area-to-mass, so light high-area craft feel it strongly.
Solar radiation pressure — the parent topic these foundations unlock.Photon momentum and relativity — where p = E / c Inverse-square law — why intensity falls as 1/ r 2 Solar sails — the extreme high-A / m Orbital perturbations — where the resulting acceleration matters. 
