What is the predicted mass of the Coma cluster using a simple model?

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SUMMARY

The predicted mass of the Coma cluster using a simple model is approximately 2 x 1043 kg, based on the velocities of galaxies averaging around 2000 km/s. The relevant equation used is GMm/R2 = Mv2/R, where G is the gravitational constant, M is the mass of the cluster, and R is the radius of the cluster, estimated at 1021 m. Discussions highlighted discrepancies in mass estimates, with Wikipedia citing a range of 2 x 1044 to 2 x 1045 kg, indicating a significant difference from the simple model's prediction.

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  • Understanding of gravitational physics and the equation GMm/R2 = Mv2/R
  • Familiarity with the concept of galaxy clusters and their dynamics
  • Basic knowledge of astrophysical measurements, including mass and velocity
  • Ability to interpret scientific literature, such as Wikipedia entries on astronomical topics
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Astronomy students, astrophysicists, and researchers interested in galaxy cluster dynamics and mass estimation methodologies.

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Homework Statement


An estimate of the mass of the Coma cluster can be made from the velocity of the galaxies relative to the centre of mass of the cluster; the velocities are around 2000 km s-1. The stars that form the cluster have been together for a long time. Show that a simple model will predict a mass of the cluster of the order of 2*10^43kg. The radius of the Coma cluster is about 10^21m.

Homework Equations


GMm/R^2 =Mv^2/R

The Attempt at a Solution


Tried a few things. First i tried to consider that as a spherical hollow shell. I calculated by using the above equation ( just plugin in values ) and i was off by a factor of 3. Next i tried to consider 2000 as being the AVERAGE speed. This time i was wrong by a factor of about 10.
I tried to model it as a disk but that seemed to complex
 
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Wikipedia says the Coma cluster has est. ##10^{14} - 10^{15}## sun masses, i.e. ##\; 2\cdot 10^{44}-2\cdot 10^{45}\,kg##.
Isn't this your factor ##10##?
 
fresh_42 said:
Wikipedia says the Coma cluster has est. ##10^{14} - 10^{15}## sun masses, i.e. ##\; 2\cdot 10^{44}-2\cdot 10^{45}\,kg##.
Isn't this your factor ##10##?
Maybe but the problem wants me to obtain 2*10^43
 

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