Question

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?

Answer 1

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

Step-by-step 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{(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=(v^2)/(r)` (2)

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

`a_r=(1)/(r)(GM_s)/(r)=(GM_s)/(r^2)\\\\a_r=((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)(m)/(s^2)`

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