Understanding Kepler's Third Law: Calculating Aphelion Distance of a Comet

[kylewoodloveast]

A comet has a perihelion distance of 0.29 A.U. and an orbital period of 77 years. To the nearest thousandth of an A.U., what is its aphelion distance from the Sun?

I know that keplers third law plays a part in this p2=a3 but I just can't plug it in right. I know the answer is 35.908 but I don't know how to get to that point.

 

[kylewoodloveast]

Taking the mass of Earth as 6 x 1024 kg and its radius to be 6400 km, (corresponding to a value for g of 9.77 m/s2 at the Earth's surface) what is the value for g to 2 decimal places at an elevation of 1700 km?

I know that Newtons laws fall into here somewhere but I am having some trouble realizing how. I know that G'6.67 x 10-11...

 

[hage567]

It's best to start a new thread for a new problem.

For the question in the original post: show your work, so we can see what you're doing.

 

[kylewoodloveast]

what i did was square 77 which is 5929 and then I got the cube root of that which is 18.

 

[hage567]

OK, so what is that number? What does it represent in the shape of the orbit?

 

[hage567]

For the second question: yes, you need Newton's laws here. Two of them. Do you know which ones?

 

[kylewoodloveast]

I have no idea. I have the law of centrpetal acc. and law of universal gravitation right here beside me.

 

[hage567]

Let's concentrate on the Kepler's law question, so things don't get confused!

 

[kylewoodloveast]

ok, i am ready.,

 

[hage567]

What does Kepler's law tell you? What does the number 18 represent? Do you know about ellipses? Do you know what aphelion and perihelion mean?

 

[kylewoodloveast]

keplers law tells me that the square of the period is equal to the cube of the au. aphelion is the farthest distance from the sun and perihelion is the closest.

 

[hage567]

"cube of au"? OK, but do you know what that is? It's the length of the semi-major axis of the orbit. So draw out a picture of an ellipse, and label it. Put the aphelion and perihelion on it. All you need to solve this problem is to understand the geometry of the orbit. Your calculation of "a" is correct (but watch the rounding). But "a" is not what the final answer is. You now need to use this value to get the aphelion distance.