Physics Lab

First-principles physics, one goal at a time

Goal

Launch a rocket

Start where every flight starts: a force, a mass, and Newton's laws. Push harder or fly lighter, and watch exactly how much faster you go.

Hand-sketched rocket lifting off on a blooming exhaust plume, the gantry falling away beside it and Earth's curve faint below.

  1. It all starts with one law: a force changes a mass's motion. Push harder, or make it lighter, and it speeds up faster.

    Force, Mass & Acceleration

    Newton’s second law: force (F) equals mass (m) times acceleration (a). The same push moves a lighter mass faster — this is the law every other rung here builds on.

    Acceleration 1.0000m/s2

    Assumes: Point mass · No friction

  2. Gravity pulls on every mass with a force we call weight. To leave the ground, something has to push back harder than this.

    Weight

    Weight is just mass (m) pulled by gravity (g): W = m·g. Same mass, different world, different weight — which is why gravity is the field you pick.

    Weight 980.66N

    Assumes: Point mass · Uniform gravity

  3. A rocket moves by throwing mass out the back. The momentum it gives the exhaust is the momentum it gains going forward.

    Momentum

    Momentum is mass in motion: p = m·v. A rocket gains forward momentum by throwing exhaust backward — Newton’s third law, action and reaction, in numbers.

    Momentum 1000.00kg*m/s

    Assumes: Point mass

  4. Now turn that momentum into a force. Hurl mass out the back at exhaust speed vₑ and, by Newton’s third law, the reaction pushes you forward: thrust F = ṁ·vₑ. This is the force the next step weighs against gravity.

    Thrust from Exhaust Flow

    Thrust is the exhaust’s momentum per second: F = ṁ·vₑ (mass flow ṁ times exhaust speed vₑ). It turns the momentum idea from the last card into the force this rocket actually pushes with.

    Thrust 750000.00N

    Assumes: Momentum thrust only — ignores the nozzle pressure term · Steady mass flow

  5. For liftoff, thrust has to beat weight. If the thrust-to-weight ratio is below one, the rocket never leaves the pad.

    Thrust-to-Weight Ratio

    Thrust-to-weight ratio: TWR = T / W = T / (m·g). It weighs the thrust (previous card) against the weight (weight card). Above 1 it lifts off; below 1 it sits on the pad.

    Thrust-to-weight ratio 1.5296

    Assumes: Rigid body · Uniform gravity

  6. Burning propellant builds up speed. The rocket equation ties how fast the exhaust leaves and how much propellant you carry to the delta-v you gain.

    The Rocket Equation

    The rocket equation. Δv is your speed budget — how much you can change your velocity. It grows with exhaust efficiency (Iₛₚ) and the wet/dry mass ratio m₀/m_f; the ln means every extra km/s costs exponentially more propellant.

    Delta-v 8.5290km/s
    5101520246810Mass ratioDelta-v (km/s)You are hereComputed · ascent/ascent-physicsIdeal — no gravity or drag losses

    Assumes: Ideal — no gravity or drag losses · Constant specific impulse

  7. Where on Earth you launch from is a free head start: the planet's spin already carries the pad eastward — fastest at the equator, nothing at the poles. That is why Ariane flies from Kourou, and why companies tow platforms out to sea.

    Launch Site

    Earth’s spin is a free head start: boost = v_eq·cosφ (the equator’s eastward speed times the cosine of your latitude φ). Maximum at the equator, zero at the poles — which is why launch sites hug the tropics.

    Rotation head-start 0.4628km/s
    02040608000.10.20.30.4Latitude (deg)Speed (km/s)You are hereSea (equator)KourouCanaveralBaikonurComputed · util/locationRigid body · Eastward (prograde) launch

    Assumes: Rigid body · Eastward (prograde) launch

  8. How much Δv does orbit actually demand? Not a magic number — it is the orbital speed you must reach (set by this world’s gravity and size) plus the losses fighting up through gravity and air. On Earth about 9.4 km/s; a smaller, airless world asks far less.

    Δv to Orbit

    The real price of orbit: v_req = v_orbit + v_loss — the orbital speed itself plus everything the climb steals (gravity and drag). Orbit is a speed, and you must buy more than the sticker price.

    Δv to reach orbit 9.3885km/s

    Assumes: Point mass · Ascent gravity + drag losses entered by hand (trajectory-dependent)

  9. Now add it up: your rocket's Δv plus the free head-start from your launch site, against what orbit demands. A better site buys margin — or lets you fly a smaller rocket for the same job.

    Reach Orbit

    margin = v_cap + v_boost − v_req: the rocket's Δv budget, plus the free eastward boost from Earth's spin (launch-site card), minus the cost of orbit. One line decides whether the design flies.

    8.5290km/s
    0.4628km/s
    9.3885km/s

    Assumes: Ideal — no gravity or drag losses · Eastward (prograde) launch

    Challenge Load the rocket heavier — raise the loaded mass in the rocket equation until this verdict flips red. That mass is the payload wall for this stack.