Orbital radius and speed

  • #1
236
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Homework Statement



The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. What are the asteroid's orbital radius and speed?

Homework Equations



T = 2pi sqrt(r/g)

The Attempt at a Solution



I tried manipulating the above equation to solve for r. I got 4.383, but it was wrong.
 

Answers and Replies

  • #3
236
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I used 9.81 for the value of g.
 
  • #4
D H
Staff Emeritus
Science Advisor
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Why did you do that? You need to use the universal gravitational constant G, not the Earth's standard gravitational acceleration, g. Moreover, this equation,

[tex]T = 2\pi \sqrt{\frac r g}[/tex]

is not quite. What are Kepler's laws?
 
  • #5
236
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I have no idea. We didn't discuss them in depth.
 
  • #6
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
686
You were trying to use one of Kepler's laws here,

[tex]T = 2\pi \sqrt{\frac r g}[/tex]

but you did it wrong. Where did you get that equation from? Look over your text and your notes.
 

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