Calculate the orbital period and acceleration of a weather forecasting satellite's

Question

Calculate the orbital period and acceleration of a weather forecasting satellite that is launched to orbit the earth at a height of 300km above the surface of the earth.

Answer 1

h = 300 km

= 300 x 10³ m

h = .300 x 10⁶ m

R + h = 6.38 x 10⁶ + .300 x 10⁶

R + h = 6.68 x 10⁶ m

v₀ = \(\sqrt{\cfrac{9R^2}{(R+h)}}\) 

v₀ = \(\sqrt{\cfrac{9.8\times(6.32\times10^6)^2}{6.68\times10^6}}\) 

v₀ = \(\sqrt{\cfrac{398.90\times10^{12}}{6.68\times10^6}}\)

v₀ = \(\sqrt{59.71\times10^6}\)

v₀ = 7.72 x 10³ m/s

T = \(\cfrac{2\pi(R+h)}{v_0}\)

T = \(\cfrac{2\times3.14\times6.68\times10^6}{7.72\times10^3}\)

T = 5.4 x 10³ sec