The radius of he Earth orbit around the sun (assumed circular) is 1.50 X 10^8km, with T=365d. What is the radial acceleration of Earth towar

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The radius of he Earth orbit around the sun (assumed circular) is 1.50 X 10^8km, with T=365d. What is the radial acceleration of Earth towards the sun?

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Thiên Di 3 years 2021-08-18T22:59:27+00:00 1 Answers 12 views 0

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  1. thucuc
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    2021-08-18T23:00:27+00:00
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    Answer:

    ar = 5.86*10^-3 m/s^2

    Explanation:

    In order to calculate the radial acceleration of the Earth, you first take into account the linear speed of the Earth in its orbit.

    You use the following formula:

    v=\sqrt{\frac{GM_s}{r}}         (1)

    G: Cavendish’s constant = 6.67*10^-11 m^3 kg^-1 s^-2

    Ms: Sun’s mass = 1.98*10^30 kg

    r: distance between Sun ad Earth = 1.50*10^8 km = 1.50*10^11 m

    Furthermore, you take into account that the radial acceleration is given by:

    a_r=\frac{v^2}{r}             (2)

    You replace the equation (1) into the equation (2) and replace the values of all parameters:

    a_r=\frac{1}{r}\frac{GM_s}{r}=\frac{GM_s}{r^2}\\\\a_r=\frac{(6.67*10^{-11}m^3kg^{-1}s^{-2})(1.98*10^{30}kg)}{(1.50*10^{11}m)^2}\\\\a_r=5.86*10^{-3}\frac{m}{s^2}

    The radial acceleration of the Earth, towards the sun is 5.86*10^-3 m/s^2

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