🌌 SPACE & MATH EXPLORER

Interactive Mathematics • Orbital Mechanics • Planetary Science

Function Grapher

Plot any function of x. Use +, −, *, ^, sin, cos, tan, sqrt, log, abs, pi, e …

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x range: −10 to 10

Orbital Mechanics & Rocket Trajectory

How Earth’s spin affects a rocket’s path — as seen from the ground vs. from space.

Viewing: Rotating frame (ground view)

What you’re seeing

Earth’s surface at the equator moves ~1,670 km/h eastward. When a rocket launches, it carries that velocity with it.

Ground frame (red path): the rocket looks like it goes straight up, but Coriolis forces push it sideways as altitude increases.

Space / inertial frame (green path): from fixed stars, the rocket follows a curved arc — it drifts east because of the tangential velocity it inherited from Earth’s spin.

This is why launch sites prefer the equator and rockets always launch eastward — free speed from the planet’s rotation!

Surface speed (equator)  465 m/s
Escape velocity  11.2 km/s
LEO orbital speed  7.9 km/s
LEO period  ~90 minutes
East-launch bonus  ~0.46 km/s free

Legend

Earth (rotating)
Launch site / rocket
Ground-frame path (Coriolis)
Space-frame path (inertial)
Low Earth Orbit ring

Planetary Rotation Speeds

Equatorial surface speed of every planet. Jupiter’s day is only 10 hours — its equator moves at 45,300 km/h.

Equatorial Speed Comparison (km/h)

3D Surface Grapher

Plot a function of x and y. The result is z. Rotate with mouse, scroll to zoom.

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