Question

Satellite C revolves around Earth 10 times a day. What is the radius of its orbit, measured from Earth's center? Assume that Earth generates the only significant gravitation attraction on the satellite. Note: The mass of Earth is 5.98 × 1024 kg, and the constant of universal gravity (G) equals 6.674 × 10-11 N m2/kg2.

Answer 1

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, $\rm m_E = 5.98 \times 10^{24} \ kg$

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.

$\rm F_g = \frac{Gm_sm_e}{r^2}$

The centripetal force due to rotation of the satellite;

$\rm F_c = \frac{m_s v^2}{r}$

The centripetal and the gravitational force are equal;

$\rm F_g = F_c \\\\ \frac{Gm_sm_e}{r^2} = \frac{m_s v^2}{r} \\\\ r = G \frac{m_E }{v^2 } \\\\ r = G \frac{m_E }{(r \omega )^2 } \\\\ r = \sqrt[3]{\frac{Gm_E}{\omega^2}} \\\\ r = \sqrt[3]{\frac{6.67 \times 10^{-11}(5.98 \times 10^{24})}{(3.63 \times 10^{-4})^2}} \\\\ r = 1.44 \times 10^7 \ mm$

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.

brainly.com/question/9699135.

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