Respuesta :
The Earth ‘s orbital period and Orbital speed will be 2.6×10²⁸ second and 4.3 ×10¹⁵ m/sec, respectively.
What is earth orbital period?
The time required to complete an orbit around a planet is called as the orbital period.
The given data in the problem is;
r is the mean distance = 1.5 x 10 ^11 m
M is the sun’s mass = 1.99 x10^30 Kg
T is the Earth ‘s orbital period
V is the orbital speed.
The Earth ‘s orbital period is found as;
[tex]\rm T = \frac{2 \times \pi r^\frac{3}{2} }{\sqrt{GM_{sun}} } \\\\\ \rm T = \frac{2 \times 3.14 (6.94 \times 10^{18})^\frac{3}{2} }{\sqrt{6.67 \times 10^{-11} 1.99 \times 10^{30}} } \\\\\ T =2.6 \times 10^{28} \ m/sec[/tex]
Hence, the Earth ‘s orbital period will be 2.6×10²⁸ second.
The orbital speed is found as;
[tex]\rm V = \sqrt{\frac{GM_{sun}}{r } }\\\\[/tex]
[tex]\rm V = \sqrt{\frac{GM_{sun}}{r } }\\\\\rm V = \sqrt{\frac{6.67 \times 10^{-11} \times 1.99 \times 10^{30}}{6.96 \times 10^8} }\\\\V=4.36 \times 10^{13}[/tex]
Hence, orbital speed will be 4.3 ×10¹⁵ m/sec.
To learn more about the orbital speed, refer to the link;
https://brainly.com/question/541239
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