
#1
Feb308, 02:36 PM

P: 23

Problem:
The earth's orbit (assumed circular) around the sun is 1.5e11 m in radius, and it makes this orbit once a year. What is the centripetal acceleration of the earth? Equations: a = (v^2) / r T = (2*pi*r) / v My work: T = (2*pi*r) / v; 1 year = (365 days / 1 year)*(24 hours / 1 day)*(60 mins / 1 day)*(60 secs / 1 min) = 3.1536e7 s; 3.1536e7 s = (2*pi*1.5e11 m) / v; algebraically rearranged is: v = (2*pi*1.5e11 m) / (3.1536e7 s) v = 29885.8 m/s a = (v^2) / r; a = ((29885.8 m/s)^2) / (1.5e11 m); a = 0.005954 m/s^2 MY ANSWER My question is if this is correct? I've been bombarded with tough questions up until this one and I am curious to know if I solved this correctly. It 'seemed' too easy. Confirmation on the answer would be appreciated since I can't find any information on presumed circular rotation around the sun. Thank you. 



#3
Feb308, 02:46 PM

Emeritus
Sci Advisor
PF Gold
P: 4,975

I haven't plugged the numbers in but your working is correct.




#4
Feb1308, 01:53 PM

P: 12

Centripetal acceleration of Earth around Sun
The answer looks right. An alternative way of solving this question (to check your answer) would be to just ask what is the centripetal acceleration of earth around the sun, given the sun's gravitation force at our distance.
acceleration=G*m1/r(2) G=gravitational constant=6.67E11 m(3)kg(1)s(2) m1=mass of sun (1.00 E30) kg r=distance to the sun = 1.5E11 m Ie. acceleration = 6.67E11 m(3)kg(1)s(2) * (1.00 E30) m / [ (1.5E11 m) * (1.5E11 m)] Answer = 5.8987E03 ms(2) My mass of distance were approximations, but the answer is very close indeed. 


Register to reply 
Related Discussions  
Centripetal Acceleration of Earth  Introductory Physics Homework  7  
Centripetal Acceleration !!!  Introductory Physics Homework  2  
Centripetal acceleration, incorporating a change in acceleration around the circle...  Introductory Physics Homework  3  
Centripetal force question(involves satellite going around earth.  Introductory Physics Homework  11  
Centripetal acceleration of Earth around Sun?  Introductory Physics Homework  6 