SPM Physics: AHA! Artificial Satellites – Gravity Becomes Centripetal Force!

Every satellite in orbit—whether near Earth or geostationary—moves because gravity acts as the centripetal force that keeps it circling the planet.

From the equation

$$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$$

we can derive four key relationships:

• Acceleration $a=\frac{GM}{r^2}$ → decreases as $r$ increases.

• Orbital speed $v=\sqrt{\frac{GM}{r}}$ → decreases as $r$ increases.

• Angular velocity $\omega =\sqrt{\frac{GM}{r^3}}$ → decreases as $r$ increases.

• Orbital period $T=\frac{4{\pi }^2{r}^3}{GM}$ → increases as $r$ increases.

Geostationary satellites stay fixed above the equator with a 24-hour period, ideal for communication and broadcasting.

Non-geostationary satellites move at different speeds and heights, used for GPS and Earth imaging.

Exam tip: When orbit radius increases, remember the trend—

$r\uparrow \Rightarrow a\downarrow ,v\downarrow ,\omega \downarrow ,T\uparrow \uparrow$

AHA! Gravity becomes centripetal force. Not by sight, but by INSIGHT!

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