Respuesta :
The radius of its orbit, measured from Earth's center, will be 1.44 × 10⁷ mm.
What is Newton's law of gravitation?
Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data in problem is;
The mass of Earth is, [tex]\rm m_E = 5.98 \times 10^{24} \ kg[/tex]
Gravitational constant, G =6.674 × 10⁻¹¹ N m₂/kg²
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
[tex]\rm F_g = \frac{Gm_sm_e}{r^2}[/tex]
The centripetal force due to rotation of the satellite;
[tex]\rm F_c = \frac{m_s v^2}{r}[/tex]
The centripetal and the gravitational force are equal;
[tex]\rm F_g = F_c \\\\ \frac{Gm_sm_e}{r^2} = \frac{m_s v^2}{r} \\\\ r = G \frac{m_E }{v^2 } \\\\ r = G \frac{m_E }{(r \omega )^2 } \\\\ r = \sqrt[3]{\frac{Gm_E}{\omega^2}} \\\\ r = \sqrt[3]{\frac{6.67 \times 10^{-11}(5.98 \times 10^{24})}{(3.63 \times 10^{-4})^2}} \\\\ r = 1.44 \times 10^7 \ mm[/tex]
Hence, the radius of its orbit measured from Earth's center will be 1.44 × 10⁷ mm.
To learn more about Newton's law of gravitation, refer to the link.
https://brainly.com/question/9699135.
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