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:
[tex]v=\sqrt{\frac{GM_s}{r}}[/tex] (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:
[tex]a_r=\frac{v^2}{r}[/tex] (2)
You replace the equation (1) into the equation (2) and replace the values of all parameters:
[tex]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}[/tex]
The radial acceleration of the Earth, towards the sun is 5.86*10^-3 m/s^2
