Problem involving Kepler's Law

In summary, Halley's comet orbits the sun every 76 years and has a closest approach that is within the solar system. The mean distance from the sun at its closest is approximately 2.95 X 10^6 km, which is the sum of the farthest and nearest distance from the sun. The given equation (T1/T2)^2 = (R1/R2)^3 can be used to calculate the semi-major axis of the orbit and compare it with other known values of objects orbiting the sun. The farthest point in our solar system is approximately 5900 X 10^6 km from the sun. The only given information was the closest approach of Halley's comet, which is within the solar
  • #1
pinkerpikachu
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1. Halley's comet orbits the sun roughly once every 76 years. It comes very close to the surface of the sun on its closest approach. Roughly how far our from the sun is it at its closest? Is it still 'in' the solar system? What planet's orbit is nearest when it is out there? [Hint: the mean distance in Kepler's third law is 1/2 the sum of the nearest and farthest distance from the sun.

2. (T1/T2)^2 = (R1/R2)^3


Any help is appreciated.
 
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  • #2
Can you work out the semi-major axis of the orbit? You may want to compare it with the known values of something else that orbits the sun.

Were you given any other info?
 
  • #3
Did you really mean "at its closest"? Yes, of course Halley's closest approach to the sun is inside the solar system. Otherwise we wouldn't be able to see it! Surely you must mean "farthest".
 
  • #4
That was the only information given, and yes, i mean the closest.

The mean different is the farthest point in our solar system (relative to the sun), and the closest which IS the sun.

So pluto is the farthest being 5900 X 10^6 km from the sun.

(5900 X 10^6 +0)/2 = 2.95 X 10^6

76 days may or may not have to be converted into seconds

and...that is all I know
 

1. What are Kepler's laws?

Kepler's laws are three scientific principles proposed by astronomer Johannes Kepler in the early 17th century that describe the motion of planets around the sun. They are based on observations made by Tycho Brahe and are considered fundamental laws of planetary motion.

2. What is the first law of Kepler?

The first law, also known as the law of ellipses, states that the orbit of a planet around the sun is an ellipse with the sun at one of the two foci.

3. What is the second law of Kepler?

The second law, known as the law of equal areas, states that a line that connects a planet to the sun will sweep out equal areas in equal amounts of time. This means that a planet moves faster when it is closer to the sun and slower when it is further away.

4. What is the third law of Kepler?

The third law, also known as the law of harmonies, states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. This means that the further a planet is from the sun, the longer its orbital period will be.

5. How are Kepler's laws used in modern astronomy?

Kepler's laws are still used in modern astronomy to study and predict the motion of planets and other celestial bodies. They also serve as the foundation for understanding the laws of gravity and the motion of objects in space.

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