A satellite is in a circular orbit of radius 1.6×10⁷ m around Earth. Taking GM = 4.0×10¹⁴ m³/s², calculate the satellite's orbital speed.

Gravity Challenge #2 — Circular Orbits

The orbital speed
of a satellite.

Gravity Medium

Problem

A satellite moves in a circular orbit of radius \( r = 1.6 \times 10^7\ \mathrm{m} \) around Earth. Taking \( GM = 4.0 \times 10^{14}\ \mathrm{m^3/s^2} \), calculate the satellite’s orbital speed.

Orbit radius\( r = 1.6 \times 10^7\ \mathrm{m} \)
Earth’s GM\( GM = 4.0 \times 10^{14}\ \mathrm{m^3/s^2} \)
Answer inm/s

The orbit is circular — gravity supplies exactly the centripetal force.

Hint: set gravity equal to the centripetal requirement: \( \tfrac{GMm}{r^2} = \tfrac{mv^2}{r} \). The satellite’s own mass cancels — solve for \( v \).

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The orbital speedof a satellite.

Problem

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The orbital speed
of a satellite.