Return to Question

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m] ??

Thanks in advance

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m]?

Thanks in advance.

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m] ??

Thanks in advance

OK Alex , Ulrich, Stephen have done an excellent job. Now, how is it possible to go further using an Interpolating function instead of an analytical function ?

Example for Milky Way

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m] ??

Thanks in advance

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m] ??

Thanks in advance

Rotation speed vc[R] in reduced units for M33 looks like

0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955]

Knowing e=0.995, I am trying to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2  Rho[m])/  Sqrt[-e^2 m^2 + R^2], {m, 0, R}]

This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

Using trial and error, I obtain a "good" solution for Rho[m], but it is very time expensive.

Does anybody knows how to solve this equation to get Rho[m] ??

Thanks in advance

OK Alex , Ulrich, Stephen have done an excellent job. Now, how is it possible to go further using an Interpolating function instead of an analytical function ?

Example for Milky Way