Physics

Problem

Two identical communication satellites A and B are moving in separate circular orbits around the Earth. Satellite A is at a distance of

8.0\times10^{6}\,\text{m}

from the Earth’s centre, while satellite B is at

1.6\times10^{7}\,\text{m}

from the centre. a. (i) Obtain the ratio of their orbital speeds

v_A : v_B

. b. (ii) Calculate the numerical values of

v_A

and

v_B

. Use

GM_E = 3.986\times10^{14}\,\text{N\,m}^2\!\text{/kg}

. c. (iii) Find the ratio of their orbital periods

T_A : T_B

Intuitive explanation

Orbital mechanics hinges on the balance between gravity pulling inward and the centripetal force needed to keep an object moving in a circle. Since both satellites are identical and in stable orbits, you can use Kepler's third law or the gravitational force equation to relate their orbital radii to their speeds and periods—notice that the radius ratio is 1:2, which will create a clean relationship. The key is recognizing that orbital velocity and period depend on radius in predictable ways, so you can compare the satellites without needing Earth's mass explicitly.

Intuitive explanation

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