City of DisCosmicism without consolation

Launch and orbital motion · Part III

Launch direction and Earth rotation

Once a rocket has turned sideways, the direction of that sideways motion matters. Earth is already rotating eastwards, so a prograde launch can inherit some velocity for free. Latitude and azimuth also constrain the orbital plane that can be reached directly.

The launch pad is already moving

A point on Earth's equator moves eastwards at roughly 465 m/s because the planet rotates. Away from the equator that speed falls with the cosine of latitude. A vehicle launched eastwards therefore starts with an inertial velocity advantage that a westward launch must first cancel and then overcome.

vrotation = ω r cos(latitude)

This does not mean every mission should launch due east. The required orbital inclination, downrange safety, populated areas, launch windows, rendezvous targets and vehicle performance can all dictate another direction. But for a low-inclination prograde orbit, an eastward launch from a low latitude is energetically attractive.

Configure a horizontal launch vector

This calculator treats your chosen speed as horizontal velocity relative to a frame rotating with Earth at the selected altitude. Azimuth is measured clockwise from north: 0° north, 90° east, 180° south and 270° west. PHP adds Earth's eastward rotational velocity to obtain a simple inertial horizontal vector.

Earth rotation at surface408.3 m/s east
Rotating-frame east component7,370.0 m/s
Rotating-frame north component0.0 m/s
Inertial east component7,791.1 m/s
Inertial horizontal speed7,791.1 m/s
Inertial azimuth90.00°
Idealised direct inclination28.50°
Circular speed at altitude7,788.5 m/s
Difference from circular+2.6 m/s
Configured horizontal inertial velocity vectorNorth and east components of the chosen velocity after adding Earth's rotation.ENlatitude 28.5° · rotating-frame azimuth 90.0°vector display is scaled for direction and component comparison
inertial totaleast component including rotationnorth component

Latitude sets a geometric floor

For an idealised direct launch into an orbital plane, a due-east trajectory from latitude φ naturally produces an inclination close to |φ|. Launching from Cape Canaveral therefore does not directly produce an equatorial orbit without a later plane change. A site near the equator can reach very low inclinations much more naturally.

cos(i) = cos(φ) · sin(A)

Here i is inclination, φ is latitude and A is the inertial horizontal azimuth. The relation is a geometric idealisation: real launch trajectories are finite, guided and constrained by safety corridors and target conditions.

Why not simply launch straight east from everywhere?

Because the desired orbital plane may not be eastward. Sun-synchronous and many Earth-observation missions use near-polar orbits. A spacecraft rendezvousing with an existing orbital station must enter a compatible plane. Some launch sites also cannot safely fly over particular directions. Launch direction is therefore a compromise between orbital geometry, performance and geography.

The complete picture

The three pages in this series now fit together. First, the rocket climbs enough to survive the atmosphere and clear the ground. Second, it pitches and builds tangential velocity because angular momentum is what keeps the trajectory from intersecting Earth. Third, the direction of that tangential velocity determines the orbital plane, while Earth's rotation can either help or hinder.

A launch vehicle is not chiefly a machine for going up. It is a machine for manufacturing the right velocity vector at the right place and time.

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