Elliptical Orbit Question

In summary, the comet's speed at perihelion is 54.6 km/s and its distance from the Sun is 8.823 x 10^10 m. At aphelion, the greatest distance between the comet and the Sun is 6.106 x 10^12 m. When asked if the speed at aphelion is greater or less than 54.6 km/s, the answer is less than. Attempts to calculate the speed at aphelion using conservation of energy and angular momentum have not been successful. Showing the actual calculation may help to troubleshoot the solution.
  • #1
lakersgrl786
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Homework Statement


A particular comet has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of 8.823 1010 m and moves with a speed of 54.6 km/s. The greatest distance between this comet and the Sun (aphelion) is 6.106 1012 m.
(a) Is the speed of the comet greater than or less than 54.6 km/s when it is at aphelion?
-this is less than
(b) Calculate its speed at aphelion.


Homework Equations


I tried using conservation of energy where Ki + Ui = Kf + Uf where K = to 1/2mv^2 based on the velocities of the comet at both locations. I set U = (-GMm/r) where G = the gravitational constant, M = the mass of the sun, m = the mass of the comet, and r = the distance from the sun (the given values in the problem). You can cancel out m as the mass of the comet is present in all terms and is not given in the problem. However, each time I solved this problem with the values given, I'm not getting the correct answer. Is there another approach?
I tried the conservation of angular momentum as well, but that did not work.
 
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  • #2
There is a similar problem on another thread. I'd suggest, though, that you show here the actual calculation you did -- it's awfully hard to troubleshoot your solution if we can't see it...
 
  • #3
It seems like the speed at aphelion should be greater than 54.6 km/s, but I'm not sure how to calculate it exactly.

Thank you for sharing your approach and thoughts on this problem. It seems like you have a good understanding of the relevant equations and concepts. However, there may be a few things that could be causing your calculations to not match the expected answer.

Firstly, make sure that you are using the correct values for the gravitational constant (G) and the mass of the Sun (M). These values can vary depending on the units used, so double check that they match the units used in the problem.

Secondly, when using the conservation of energy equation, make sure that you are using the same units for all values. In this case, it may be helpful to convert all distances to meters and all velocities to m/s to ensure consistent units.

Lastly, it may be helpful to double check your calculations and make sure that you are correctly solving for the final velocity at aphelion. It may also be useful to try solving the problem using different equations or approaches to see if you get the same answer.

Overall, it seems like you are on the right track and just need to double check your calculations and make sure all values are consistent. Keep up the good work!
 

1. What is an elliptical orbit?

An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, follows an elliptical path around another object due to the gravitational pull between the two bodies.

2. How is an elliptical orbit different from a circular orbit?

An elliptical orbit is different from a circular orbit in that it is not a perfect circle. Instead, it is an oval-shaped path, with the object being closer to the center of the orbit at some points and further away at others.

3. What causes an object to have an elliptical orbit?

The shape of an object's orbit is determined by its velocity and the strength of the gravitational force between it and the object it is orbiting. If the velocity and gravitational force are just right, an elliptical orbit will form.

4. How do astronomers measure the eccentricity of an elliptical orbit?

Astronomers measure the eccentricity of an elliptical orbit by calculating the distance between the two foci of the ellipse and dividing it by the length of the major axis. The result is a number between 0 and 1, with 0 representing a perfect circle and 1 representing a highly eccentric orbit.

5. Can an object have both a circular and an elliptical orbit?

Yes, an object can have both a circular and an elliptical orbit. This is known as a Hohmann transfer orbit, in which an object starts in a circular orbit, then uses a carefully calculated amount of energy to transition to an elliptical orbit and back again.

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