Question

A russian satellite moves round the earth in an orbit at an altitude of about 800km.Determine(1) the value of g at this altitude (2)the linear velocity of the satellite and (3)the period of the satellite

Answer 1

(1) $g = \dfrac{GM_{\oplus}}{(R_{\oplus}+h)^2} = \dfrac{6.67\cdot10^{-11}\,\mathrm{N m^2/kg^2}\cdot6\cdot10^{24}\,\mathrm{kg}}{(6.4\cdot10^6+800\cdot10^3 \,\mathrm{m})^2} = 7.72\,\mathrm{m/s^2}.$

(2) The linear velocity $v = \sqrt{g\cdot(R_{\oplus}+h)} = \sqrt{7.72\,\mathrm{m/s^2}\cdot(6.4\cdot10^6+800\cdot10^3\,\mathrm{m})} = 7455\,\mathrm{m/s}.$

(3) $T = \dfrac{2\pi (R_{\oplus}+h)}{v} = 6068\,\mathrm{s} = 1.69\,\mathrm{h}.$