Find Center of Mass of Pluto & Charon System

Click For Summary

Homework Help Overview

The problem involves finding the center of mass of the Pluto and Charon system, given their diameters and the distance between them. The context is within astrophysics, focusing on gravitational systems and mass distribution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the center of mass formula and the implications of using diameters to determine positions. Questions arise regarding the lack of mass data and how to proceed with the calculations without explicit coordinates.

Discussion Status

Some participants confirm the correctness of the equation provided and suggest choosing a reference point for simplification. There is ongoing exploration of whether the problem can be treated as one-dimensional, with participants considering how to set up the coordinate system.

Contextual Notes

Participants note the absence of mass values and the challenge of determining angles between the two bodies, which may affect the interpretation of their positions.

elsternj
Messages
42
Reaction score
0

Homework Statement


Pluto's diameter is approximately 2370km , and the diameter of its satellite Charon is 1250km . Although the distance varies, they are often about 1.93×104km apart, center-to-center.
Assuming that both Pluto and Charon have the same composition and hence the same average density, find the location of the center of mass of this system relative to the center of Pluto.


Homework Equations



xcm=m1x1+m2x2 / m1 + m2

The Attempt at a Solution


Well the center of Pluto and its satellite would be half the diameter so it's center of mass, I am assuming, would be

Pluto: 1185km
Charon: 625km

where i am confused is that i don't have the masses or any actual coordinates. I'm assuming that the masses would end up canceling out? But can somebody guide me as to where to go from here? How do I get the coordinates with the distance they are from each other? Is my equation even right?
 
Physics news on Phys.org
The equation is correct, where x1, x2, and xcm are the distances from any arbitrarilly chosen reference point. It is simplest to choose that reference point at the center of one of the masses. Note that the mass of a sphere is is a function of its diameter cubed.
 
So am I to assume that this is one dimensional? ..For I have no idea the angle at which these spheres are from one another. Say I choose Pluto to be the reference point. Make that x position to be 0 and then Charon's position to be the given distance?
 
elsternj said:
So am I to assume that this is one dimensional? ..For I have no idea the angle at which these spheres are from one another. Say I choose Pluto to be the reference point. Make that x position to be 0 and then Charon's position to be the given distance?
Yes and Yes.
 

Similar threads

High School Is the barycentre of the Pluto - Charon system also the L1 point?
  • · Replies 3 ·
Replies
3
Views
2K
Center of mass and momentum- A question about systems
  • · Replies 25 ·
Replies
25
Views
2K
Infer diameter of Pluto from orbiting Charon
  • · Replies 6 ·
Replies
6
Views
3K
Determining the mass of Pluto using its moon
  • · Replies 5 ·
Replies
5
Views
5K
Finding the center of mass of a homogeneous object
  • · Replies 6 ·
Replies
6
Views
4K
Center of Mass (Subtraction over addition)
  • · Replies 7 ·
Replies
7
Views
3K
Pluto & Charon's Center of Mass - 6871.5 km
  • · Replies 1 ·
Replies
1
Views
16K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Determine the location of the center of mass of spheres
  • · Replies 3 ·
Replies
3
Views
5K
Finding the acceleration of the center of mass
  • · Replies 2 ·
Replies
2
Views
1K