center of mass?

Question

Pluto's diameter is approximately 2370 km, and the diameter of its satellite Charon is 1250 km. Although the distance varies, they are often about 1.95×104 km 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.

Answer 1

The ratios of the two masses are proportional to the ratios of the cubes of the diameters. So for Pluto, the relative mass is 2370^3 = 13312053000
and for Charon the relative mass is
1250^3 = 1953125000
... and the two masses have a ratio of 6.816

That means that the center of gravity must be 6.816 times closer to Pluto than to Charon, or 2861 km from the center of Pluto.

Answer 2

Center of mass of Pluto lies at the center of Pluto and center of mass for Charon lies at the center of Charon.

The distance between two center of mass points
= 2370/2 + 19500 + 1250/2
= 21310 km

Both the objects in the system are actually orbiting around the center of mass point of the system to keep the system in balance.

Thus if r is the distance of center of mass of the system from center of pluto, then

mass of pluto x r = mass of Charon x (21310 - r)
density of pluto x Volume of pluto x r = density of Charon x Volume of Charon x (21310 - r)

Since both densities are same as per the question, therefore
Volume of pluto x r = Volume of Charon x (21310 - r)

solving for r = 3664.174 km from center of pluto

Answer 3

I simply move my scale so that the main body is located at 0. The other one at whatever distance.


Charon has a diameter of 0.527 times that of Pluto. Assuming equal density, then its mass will be 0.527^3 times that of pluto. We'll set the mass of Pluto at 1 (that is; one 'Pluto Mass Unit'); then the mass of Charon is 0.1467

Moment = mass times distance.

Pluto = 1 times 0 = 0
Charon = 0.1467 times 1.95x10^4 km = 2861

Total mass = 1.1467
Total moment = 2861

Location of barycentre = moment / mass

286.1 / 1.1467 = 2495 km (from Pluto's centre).

Answer 4

Pluto Diameter Km

Answer 5

the center of mass (i will abbreviate as cm) is the WEIGHTED average of the cms by their masses.
that is of a bunch of masses it's (m1x1 + m2x2+ m3x3)/(m1+m2+m3)
but the x's have to be relative to the reference pt. usually it's easier to pick the reference pt. at the center of one fo the objects.
so for ur example u would just have (Mp*0 + Mc*(distance))/(Mp + Mc) where Mc and Mp are the masses of Charon and Pluto respectively.