Solving for Diameter and Mass of a New Kuiper Object with a Satellite

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Homework Help Overview

The discussion revolves around calculating the true diameter and mass of a new Kuiper object based on its angular size and distance, as well as determining its density and composition. The problem involves concepts from astronomy and physics, particularly related to angular measurements and gravitational dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to apply angular size and distance to find the true diameter of the Kuiper object. Participants raise questions about the relationship between angular size and physical dimensions, and some seek clarification on terminology related to angles.

Discussion Status

Participants are exploring the relationship between angular size and distance, with some providing diagrams and examples to clarify concepts. There is an ongoing exchange of ideas, but no consensus has been reached regarding the specific calculations or methods to apply.

Contextual Notes

The original poster expresses uncertainty about applying the given angular size and distance to the problem, indicating a potential gap in understanding the relevant equations or concepts. There is also a mention of a diagram provided by a participant to aid in understanding.

astronomystudent
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PROBLEM
If the size of a new Kuiper object is 0.0150 arc sec in angular size as seen from a distance of 42.00 AU, what is the true diameter? If it has a satellite with a period of 5.50 hours at a semimajor axis of 12500.0 km, what is the mass? What is the resulting density? What do you it is composed of?

What I know:
I know that I use V=4/3(pi)r^3 to get the density and previous equations to solve for mass. I don't know how I am supposed to apply the 0.0150 arc seconds or distance to solve for the diameter. What is the equation for that?
 
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What is the relationship of the some length of segment on the circumference of a circle and the angle subtended by that segment?
 
I have no idea what you mean when you say "angle subtended..."
 
Is the concept of angular size the trouble here. Here is a diagram, with this you should know what to do...
http://www.berrys.plus.com/hh5.gif

So the furthur away the object is, the smaller the angular size will become.

Hope this helps...
Sam
 
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