Gravitational fields · Orbital motion

Why does a satellite keep missing Earth?

Change only its sideways launch speed and watch gravity produce an impact, a circle, an ellipse or escape.

Learning goalExplain how inward gravity continually changes the direction of a satellite’s velocity.

Pathcircular orbit

Latest orbit eventLaunch 1 · circular-speed release

Watch: the velocity arrow remains tangent while gravity always points towards the body’s centre.

1 Choose the launch Central body Starting distance, r1.35R near surface8 body radii Sideways launch speed1.00v_c too slowabove escape speed

Changes describe the next launch. The satellite already in flight is never scrubbed backwards.

Prediction from the launch conditions Circular orbit

The sideways speed gives exactly the centripetal acceleration required at this radius.

Display speed1× Changes playback only—not the orbital physics.

Altitude2,230 km

Speed6.81 km s⁻¹

Field strength5.39 N kg⁻¹

Elapsed time0.0 min

Explain the path

Three pieces of orbital evidence

Values are per kilogram, so satellite mass does not change the path.

At launch Gravity provides exactly the required inward acceleration

gravity5.39 m s⁻²=v²/r5.39 m s⁻²

Specific energy Negative total energy: bound orbit

U/m −46.3 MJ kg⁻¹K/m 23.2 MJ kg⁻¹E/m −23.2 MJ kg⁻¹

Orbit shape Circle

Gravity points inward

It continually changes velocity direction, producing a curved path.

Speed selects the path

The same starting point can lead to impact, a circle, an ellipse or escape.

Mass cancels

Satellite mass changes force and energy, but not acceleration or trajectory.