Answer to Question #222691 in Classical Mechanics for Fletcher Madden

Question

The earth revolves round the sun with constant speed on an orbit of radius r=1.5x10^11m. Find the earth's acceleration towards the sun.

Answer 1

$v = \frac{s}{T}$

$s = 2\pi r$

$T = 1 \text{ year }\approx 365*24*3600s$

$v= \frac{2\pi*1.5*10^{11}}{365*24*3600}=29.89*10^3\frac{m}{s}$

$a =\frac{v^2}{r}= \frac{29.89^2*10^6}{1.5*10^{11}}=0.00595\frac{m}{s^2}$

$\text{Answer: }a =0.00595\frac{m}{s^2}$