In a circular orbit, is gravity absent, balanced away, or providing the inward acceleration?

Find the circular-orbit speed at radius \(7.5\times10^6\,\mathrm{m}\) around a planet of mass \(6.0\times10^{24}\,\mathrm{kg}\). Use \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\).

Why does the satellite mass not appear in \(v=\sqrt{GM/r}\) for a circular orbit?

A satellite moves in a circular orbit of radius \(7.5\times10^6\,\mathrm{m}\) with speed \(7.3\times10^3\,\mathrm{m\,s^{-1}}\). Estimate its period.

A satellite has circular-orbit period \(5400\,\mathrm{s}\) around a planet of mass \(5.0\times10^{24}\,\mathrm{kg}\). Find the orbital radius.

A circular orbit has radius \(8.0\times10^6\,\mathrm{m}\) and period \(7000\,\mathrm{s}\). Find the local gravitational field magnitude from the orbit data.

One circular orbit has radius \(r\). Another around the same body has radius \(4r\). Compare their speeds and periods.

Find the radius of a circular orbit around Earth with period \(86164\,\mathrm{s}\). Use \(M_\oplus=5.97\times10^{24}\,\mathrm{kg}\) and \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\).

A planet's mass is unknown, but a moon is observed in a circular orbit of radius \(1.8\times10^8\,\mathrm{m}\) with period \(3.0\times10^5\,\mathrm{s}\). Estimate the planet mass.

A spherical planet has radius \(R\) and surface field magnitude \(g_s\). Derive the circular-orbit speed and period at radius \(r=kR\), and interpret how both change as \(k\) increases.