How Fast Will the Comet Travel at the Midpoint Between Two Stars?

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In summary, the problem involves a binary star system with two stars of equal mass separated by a large distance. A comet, initially at rest, is pulled towards the stars by gravity and travels along a straight line passing through the midpoint between the stars. Using the equations for potential and kinetic energy, the comet's speed at the midpoint can be calculated to be v= sqrt(4(GMsun/r)), where r is the distance from the midpoint to one of the stars.
  • #1
rebeldiiamond
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ok so here's the problem
A binary star system has two stars, each with the same mass as our sun, separated by 8.00 x 10^11 . A comet, far away from both stars is essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line that passes through the midpoint between the two stars.
What is the comet's speed at the midpoint?

here's what i tried (but it was wrong)
pe initial(comet)= ke intial = 0
pe final (comet)= ke final= -GMsun/r
since 2 masses --> 2(GMsun/r)


ke = 1/2mvr^2---> v= sqrt(4(GMsun/r))
it says i have the wrong answer...
Is my method completely wrong? What can I do to fix it? Any help is greatly appreciated!:confused:
 
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  • #2
why do you have 1/2mvr^2 for the kinetic energy? You do end up with the correct expression for v. What did you use for r? r is half the distance between the stars.
 
  • #3
Method looks fine to me, if r is the distance from midpoint to star.
 

1. What are Kepler's Laws and why are they important in astronomy?

Kepler's Laws are three principles that describe the motion of planets around the sun. They were developed by Johannes Kepler in the 17th century and are important because they helped us understand the nature of our solar system and laid the foundation for modern astronomy.

2. What is the first law of Kepler and how does it relate to the orbits of planets?

The first law, also known as the law of orbits, states that all planets move in elliptical orbits with the sun at one of the foci. This means that the distance between the planet and the sun varies throughout its orbit, with the closest point being the perihelion and the farthest point being the aphelion.

3. How does the second law of Kepler explain the speed of planets in their orbits?

The second law, also known as the law of areas, states that a line drawn from the sun to a planet will sweep out equal areas in equal time intervals. This means that a planet will move faster when it is closer to the sun (at perihelion) and slower when it is farther away (at aphelion).

4. What is the third law of Kepler and how does it relate to the orbital periods of planets?

The third law, also known as the law of periods, states that the square of the orbital period of a planet is proportional to the cube of its average distance from the sun. This means that the farther a planet is from the sun, the longer its orbital period will be. This law also allows us to calculate the orbital period of a planet if we know its distance from the sun.

5. How can I use Kepler's Laws to solve a problem involving the motion of a planet?

To solve a problem involving Kepler's Laws, you will need to know at least two of the following variables: orbital period, distance from the sun, or speed of the planet at a specific point in its orbit. You can then use the equations derived from Kepler's Laws to calculate the missing variable. It is important to remember that these laws are based on idealized scenarios and may not perfectly describe the motion of all planets in our solar system.

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