How Do You Calculate Sun's Gravitational Acceleration at an Asteroid's Orbit?

[pumpernickel]

Hi. I am a little stuck and I would appreciate some help.

What is the acceleration due to gravity of the sun at the distance of 1.6 X 10^11 m? The asteroid revolves around the sun in 398 Earth days.

2. Homework Equations :

F= (m*V^2)/r3. The Attempt at a Solution :

First I found the circumference: 1.00 * 10 ^12 m
Converted 398 to seconds --> 85968000 sec

So I used that to come up with a velocity --> 1.00 * 10 ^12 m/85968000 sec = 11694 m/s

And did F= (V^2)/r and came up with .000855

I know I am doing this wrong but I just don't know what to do.

Thanks for your help!

 

[paisiello2]

Not sure why you think you are doing this wrong except maybe you assumed that the asteroid is moving in uniform circular motion which it probably is not in reality. Even though it might be a good approximation the exact answer is Newton's law of gravitation where you will need to look up the mass of the sun M and the gravitational constant G.

Try that and see how close the answer is.

 

[TheDemx27]

And did F= (V^2)/r and came up with .000855

Aren't you omitting m in that equation?

I would agree with paisiello in that you would need to know the mass of the sun, and apply that to Newtons law.

g = GM/r^2

 

[Filip Larsen]

I get a different number of seconds for the period of revolution (somehow you got your period in seconds a factor 2.5 too high). If you correct that and write "a" instead of "F" in your last expression (since F/m = a), then you should be good.

(You don't need to use Newtons law of gravitation).

 

[paisiello2]

Doesn't that assume the asteroid is moving uniformly in a perfect circle? That assumption needs to be stated somewhere.

Otherwise you'll need to use Newton's law.

 

[Filip Larsen]

Doesn't that assume the asteroid is moving uniformly in a perfect circle? That assumption needs to be stated somewhere.

The topic of this thread says "Circular motion" and the poster used an equation for centripetal force in a uniform circular motion, so I guess we can safely assume that this is an exercise on the topic of circular motion. Granted, it is always a good habit and it never hurts to state your assumption in case they are not obvious to the reader (or, in this case, the teacher checking your work).