What is the orbital period of an asteroid between Earth and Jupiter?

In summary, the conversation discusses finding the orbital period of an asteroid that extends from Earth's orbit to Jupiter's orbit, assuming circular and co-planar planetary orbits and known values for G, Ms, ma, LE, and LJ. The solution involves using the equation T = 2π (a3/μ)1/2, where T is the period, a is the semi-major axis of the orbit, and μ is the gravitational mass of the sun. The correct answer is found by identifying the major axis and using the semi-major axis instead of the orbital radius of Jupiter's orbit.
  • #1
TheBigDig
65
2

Homework Statement


The orbit of an asteroid extends from the Earth’s orbit to Jupiter’s orbit, just touching both. Assume that the planetary orbits are circular and co-planar and that Newton’s constant G, the mass of the sun Ms, the mass of the asteroid ma and the radii of the Earth’s and Jupiter’s orbit respectively, (LE, LJ ), are known.
1. Find the orbital period of the asteroid.Express all of your answers in terms of the given quantities of the problem: G, Ms, ma,LE and LJ

Homework Equations


T = 2π (a3/μ)1/2 where T is the period, a is the semi-major axis of the orbit and μ is the gravitational mass of the sun (μ = GMs)

The Attempt at a Solution


I'm actually really stuck on this one though it seems simple. It seems like the answer is T = 2π (LJ3/μ)1/2 but I am almost certain that is wrong. It just seems to easy to me.
 
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  • #2
TheBigDig said:
3. I'm actually really stuck on this one though it seems simple. It seems like the answer is T = 2π (LJ3/μ)1/2 but I am almost certain that is wrong. It just seems to easy to me.
That is because for a you used the orbital radius of Jupiter's orbit. What you found was the period of Jupiter's orbit. What you need here is the semi-major axis. Try a diagram.
 
  • #3
Make a sketch of the orbit and identify the major axis.
 

Related to What is the orbital period of an asteroid between Earth and Jupiter?

1. What is the orbital period of an asteroid?

The orbital period of an asteroid is the time it takes for the asteroid to complete one full orbit around the sun.

2. How long is the orbital period of an asteroid?

The length of an asteroid's orbital period varies depending on its size, shape, and distance from the sun. Generally, the orbital period can range from a few months to several years.

3. How is the orbital period of an asteroid calculated?

The orbital period of an asteroid is calculated using Kepler's Third Law of Planetary Motion, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. Scientists also take into account the gravitational pull of other celestial bodies in the asteroid's path.

4. Can the orbital period of an asteroid change over time?

Yes, the orbital period of an asteroid can change over time due to a variety of factors such as collisions with other objects, gravitational pulls from other planets, and the Yarkovsky effect (a force that can alter an asteroid's orbit due to uneven heating from the sun).

5. Is there a way to predict the orbital period of an asteroid?

Yes, scientists can use mathematical models and observations to predict the orbital period of an asteroid. However, due to the unpredictable nature of space, there may be slight variations in the predicted and actual orbital periods.

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