Radius of Sphere of Influence( Black Hole) Calculator

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✖Black Hole Mass is expressed in solar mass is the mass of a particular black hole in evaluation.ⓘ Black Hole Mass [M_bh]			+10% -10%
✖Stellar Velocity Dispersion of the Host Bulge is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects.ⓘ Stellar Velocity Dispersion of the Host Bulge [σ]			+10% -10%

✖Sphere of Influence Radius is the radius of the region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy.ⓘ Radius of Sphere of Influence( Black Hole) [r_h]

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Formula

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Radius of Sphere of Influence( Black Hole)

Formula

`"r"_{"h"} = "[G.]"*("M"_{"bh"})/("σ")^2`

Example

`"530722.8km"="[G.]"*("4M☉")/("1000km/s")^2`

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Radius of Sphere of Influence( Black Hole) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2
r_h = [G.]*(M_bh)/(σ)^2
This formula uses 1 Constants, 3 Variables

Constants Used

[G.] - Gravitational constant Value Taken As 6.67408E-11

Variables Used

Sphere of Influence Radius - (Measured in Meter) - Sphere of Influence Radius is the radius of the region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy.
Black Hole Mass - (Measured in Kilogram) - Black Hole Mass is expressed in solar mass is the mass of a particular black hole in evaluation.
Stellar Velocity Dispersion of the Host Bulge - (Measured in Meter per Second) - Stellar Velocity Dispersion of the Host Bulge is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects.

STEP 1: Convert Input(s) to Base Unit

Black Hole Mass: 4 Solar Mass --> 7.952E+30 Kilogram (Check conversion here)
Stellar Velocity Dispersion of the Host Bulge: 1000 Kilometer per Second --> 1000000 Meter per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_h = [G.]*(M_bh)/(σ)^2 --> [G.]*(7.952E+30)/(1000000)^2

Evaluating ... ...

r_h = 530722841.6

STEP 3: Convert Result to Output's Unit

530722841.6 Meter -->530722.8416 Kilometer (Check conversion here)

FINAL ANSWER

530722.8416 ≈ 530722.8 Kilometer <-- Sphere of Influence Radius

(Calculation completed in 00.004 seconds)

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Created by Kaki Varun Krishna

Mahatma Gandhi Institute of Technology (MGIT), Hyderabad

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Sri sivasubramaniyanadar college of engineering (ssn college of engineering), Chennai

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< 8 Fundamental Parameters Calculators

Tsiolkovsky Rocket Equation

Go Change in Rocket Velocity = Specific Impulse*[g]*ln(Wet Mass/Dry mass)

Radius of Sphere of Influence( Black Hole)

Go Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2

Semi Major Axis of Phasing Ellipse

Go Semi Major Axis of Ellipse = ((Number of Periods*Gravitational Parameter^0.5)/(2*pi))^(2/3)

Radius of Sphere of Influence

Go Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5)

Angular Momentum of Trajectory given Parameter of Orbit

Go Angular Momentum of Orbit = sqrt(Parameter of Orbit*[GM.Earth])

Parameter of Orbit

Go Parameter of Orbit = Angular Momentum of Orbit^2/Standard Gravitational Parameter

Rocket Mass Ratio

Go Rocket Mass Ratio = e^(Change in Rocket Velocity/Rocket Exhaust Velocity)

Standard Gravitational Parameter

Go Standard Gravitational Parameter = [G.]*(Mass of Orbital Body 1)

Radius of Sphere of Influence( Black Hole) Formula

Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2
r_h = [G.]*(M_bh)/(σ)^2

If the black body is rotating, how does it effect radius of influence?

If the black hole is rotating, there will be a second radius of influence associated with the rotation.

How to Calculate Radius of Sphere of Influence( Black Hole)?

Radius of Sphere of Influence( Black Hole) calculator uses Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2 to calculate the Sphere of Influence Radius, The Radius of Sphere of Influence( Black Hole) is the radius of the region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy. Sphere of Influence Radius is denoted by r_h symbol.

How to calculate Radius of Sphere of Influence( Black Hole) using this online calculator? To use this online calculator for Radius of Sphere of Influence( Black Hole), enter Black Hole Mass (M_bh) & Stellar Velocity Dispersion of the Host Bulge (σ) and hit the calculate button. Here is how the Radius of Sphere of Influence( Black Hole) calculation can be explained with given input values -> 530.7228 = [G.]*(7.952E+30)/(1000000)^2.

FAQ

What is Radius of Sphere of Influence( Black Hole)?

The Radius of Sphere of Influence( Black Hole) is the radius of the region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy and is represented as r_h = [G.]*(M_bh)/(σ)^2 or Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2. Black Hole Mass is expressed in solar mass is the mass of a particular black hole in evaluation & Stellar Velocity Dispersion of the Host Bulge is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects.

How to calculate Radius of Sphere of Influence( Black Hole)?

The Radius of Sphere of Influence( Black Hole) is the radius of the region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy is calculated using Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2. To calculate Radius of Sphere of Influence( Black Hole), you need Black Hole Mass (M_bh) & Stellar Velocity Dispersion of the Host Bulge (σ). With our tool, you need to enter the respective value for Black Hole Mass & Stellar Velocity Dispersion of the Host Bulge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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