any ideas on how to find the average acceleration of the earth moving around the sun for an eight month time interval?

Do you mean the angular acceleration?

 

If is a formula for it:

 

a=v²/r

 

Where v is the tangent velocity at any point and r is the distance from the centre of the sun.

Either use the a from above or calculate it out explicitely (and possibly more correctly) by using Newtonian Gravity.

The average is [math] \frac{\int_T a(t) \, dt}{8 \text{ month}} [/math] where T is the time-interval of length 8 month you are taking the average over.

 

Care to tell us what you need that for in exchange for possibly better-suited answers?

Thanks for you help so far. However, this is a grade 12 physics course and we have not learned either of those two formulas yet so I assume it is not permitted in our anwser. First of all, I must assume a perfectly circular path, find the average radius of the earth's orbit, find the circumference of the orbital path and then divide that by the number of seconds in a year to get the speed. Now what?

I wouldn't assume it's "not permitted." Most teachers would like it if you go above and beyond what they teach.

Thanks for you help so far. However, this is a grade 12 physics course and we have not learned either of those two formulas yet so I assume it is not permitted in our anwser. First of all, I must assume a perfectly circular path, find the average radius of the earth's orbit, find the circumference of the orbital path and then divide that by the number of seconds in a year to get the speed. Now what?

 

Average acceleration will be the vector difference of the velocities, divided by the elapsed time. With a circular orbit, the speed will be the same, but the direction won't, which is why you have to make sure you are doing a vector calculation (because the answer isn't zero)

Average acceleration will be the vector difference of the velocities, divided by the elapsed time. With a circular orbit, the speed will be the same, but the direction won't, which is why you have to make sure you are doing a vector calculation (because the answer isn't[/i'] zero)

 

exactly

your teacher probably wants you to calculate the distance travelled (circumference of the orbit) and divide it by time of orbit to get velocity ... then use the centripetal acceleration formula given by Klaynos... this acceleration acts toward the centre of orbit.