Question

Earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.

Answer 1

The Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x $10^{24}$ Kg

Relationship between Linear and angular speed

Linear speed is the product of angular speed and the maximum displacement of the particle. That is,

V = Wr

Where

• V = Linear speed

• W = Angular speed

• r = Radius

Given that the earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.

a) To determine the Earth’s average orbital speed, we will make use of the below formula to calculate angular speed

W = 2$\pi$/T

W = (2 x 3.143) / (365.26 x 24)

W = 6.283 / 876624

W = 7.2 x $10^{-4}$ Rad/hr

The Earth’s average orbital speed V = Wr

V = 7.2 x  $10^{-4}$ x 149.6 x $10^{6}$

V = 107225.5 kilometers per hours.

b) Based on the information given in this question, to calculate the approximate mass of the Sun, we will use Kepler's 3rd law

M = (4$\pi ^{2}$$r^{3}$) / G$T^{2}$

M = (4 x 9.8696 x 3.35 x $10^{24}$) / (6.67 x $10^{-11}$ x 7.68 x $10^{11}$)

M = 1.32 x $10^{26}$ / 51.226

M = 2.58 x $10^{24}$ Kg

Therefore, the Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x $10^{24}$ Kg

Learn more about Orbital Speed here: brainly.com/question/22247460

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