Kepler's Law to Determine Period of Asteroid

In summary, the newly discovered asteroid orbits at twice the Earth-Sun distance, and using Kepler's third law with K = 1 and R = 2, we can determine that its period of orbit is √8 or about 2.83 years.
  • #1
scrambledeggs
3
0

Homework Statement



A newly discovered asteroid orbits at twice the Earth-Sun distance. Find its period of orbit (in years).

Homework Equations



I know that I'm supposed to use Kepler's third law to determine this.
T2 = Kr3
K = 4∏2/GM

and the Earth-Sun distance is of course 1 Au

The Attempt at a Solution



I know that the answer should be √8 or about 2.83 years I just don't know how to get there. So frustrating because I know that this is a simple question.

Could it be that K = 1, and R=2 therefore R3 = 8?
 
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  • #2
scrambledeggs said:

Homework Statement



A newly discovered asteroid orbits at twice the Earth-Sun distance. Find its period of orbit (in years).

Homework Equations



I know that I'm supposed to use Kepler's third law to determine this.
T2 = Kr3
K = 4∏2/GM

and the Earth-Sun distance is of course 1 Au

The Attempt at a Solution



I know that the answer should be √8 or about 2.83 years I just don't know how to get there. So frustrating because I know that this is a simple question.

Could it be that K = 1, and R=2 therefore R3 = 8?

Think about the relationship between this asteroid's orbit and the Earth's orbit.
 

1. How can Kepler's Law be used to determine the period of an asteroid's orbit?

Kepler's Law states that the square of an object's orbital period is directly proportional to the cube of the semi-major axis of its orbit. By measuring the semi-major axis and using this equation, we can calculate the asteroid's orbital period.

2. What is the semi-major axis of an asteroid's orbit?

The semi-major axis is half of the longest diameter of an elliptical orbit. It is the average distance between the asteroid and the object it is orbiting around, such as the sun or a planet.

3. Can Kepler's Law be used for any type of asteroid orbit?

Yes, Kepler's Law can be applied to any type of orbit, including circular, elliptical, and parabolic orbits. However, it is most accurate for elliptical orbits.

4. How do we measure the semi-major axis of an asteroid's orbit?

The semi-major axis can be measured using a variety of methods, such as radar or optical observations. In some cases, the asteroid's trajectory can also be used to determine its semi-major axis.

5. Can Kepler's Law also be used to determine the period of a comet's orbit?

Yes, Kepler's Law can be used to determine the period of a comet's orbit as well. However, comets typically have highly elliptical orbits, so the calculation may be less accurate compared to objects with more circular orbits.

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