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Radius of Sphere of Influence( Black Hole) Formula

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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. Check FAQs

r h = [G.] \cdot \frac{M bh}{{(σ)}^{2}}

r_h - Sphere of Influence Radius?M_bh - Black Hole Mass?σ - Stellar Velocity Dispersion of the Host Bulge?[G.] - Gravitational constant?

Radius of Sphere of Influence( Black Hole) Example

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Here is how the Radius of Sphere of Influence( Black Hole) equation looks like with Values.

Here is how the Radius of Sphere of Influence( Black Hole) equation looks like with Units.

Here is how the Radius of Sphere of Influence( Black Hole) equation looks like.

530989.8048 = 6.7E-11 \cdot \frac{8E+30}{{(1000)}^{2}}

530989.8048km = 6.7E-11 \cdot \frac{8E+30kg}{{(1000km/s)}^{2}}

530989.8048 = 6.7E-11 \cdot \frac{8E+30}{{(1000)}^{2}}

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Radius of Sphere of Influence( Black Hole) Solution

Follow our step by step solution on how to calculate Radius of Sphere of Influence( Black Hole)?

FIRST Step Consider the formula

r h = [G.] \cdot \frac{M bh}{{(σ)}^{2}}

Next Step Substitute values of Variables

∴

r h = [G.] \cdot \frac{8E+30kg}{{(1000km/s)}^{2}}

Next Step Substitute values of Constants

∴

r h = 6.7E-11 \cdot \frac{8E+30kg}{{(1000km/s)}^{2}}

Next Step Convert Units

∴

r h = 6.7E-11 \cdot \frac{8E+30kg}{{(1E+6m/s)}^{2}}

Next Step Prepare to Evaluate

∴

r h = 6.7E-11 \cdot \frac{8E+30}{{(1E+6)}^{2}}

Next Step Evaluate

∴

r h = 530989804.8m

LAST Step Convert to Output's Unit

∴

r h = 530989.8048km

Radius of Sphere of Influence( Black Hole) Formula Elements

Variables

Constants

Sphere of Influence Radius

Symbol: r_h

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Sphere of Influence Radius

Black Hole Mass

Black Hole Mass is expressed in solar mass is the mass of a particular black hole in evaluation.

Symbol: M_bh

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Black Hole Mass

Stellar Velocity Dispersion of the Host Bulge

Stellar Velocity Dispersion of the Host Bulge is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects.

Symbol: σ

Measurement: SpeedUnit: km/s

Note: Value should be greater than 0.

Formulas to find Stellar Velocity Dispersion of the Host Bulge

Gravitational constant

Gravitational constant is a fundamental constant in physics that appears in Newton's law of universal gravitation and Einstein's theory of general relativity.

Symbol: [G.]

Value: 6.67408E-11

Other formulas in Fundamental Parameters category

Go Rocket Mass Ratio

M R = e^{\frac{ΔV}{V e}}

Go Tsiolkovsky Rocket Equation

ΔV = I sp \cdot [g] \cdot \ln (\frac{M wet}{M dry})

Go Standard Gravitational Parameter

μ std = [G.] \cdot (M 1)

Go Parameter of Orbit

p = \frac{h^{2}}{μ std}

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

Radius of Sphere of Influence( Black Hole) evaluator uses Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2 to evaluate 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 evaluate Radius of Sphere of Influence( Black Hole) using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Sphere of Influence( Black Hole)

What is the formula to find Radius of Sphere of Influence( Black Hole)?

The formula of Radius of Sphere of Influence( Black Hole) is expressed as Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2. Here is an example- 530.9898 = [G.]*(7.956E+30)/(1000000)^2.

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

With Black Hole Mass (M_bh) & Stellar Velocity Dispersion of the Host Bulge (σ) we can find Radius of Sphere of Influence( Black Hole) using the formula - Sphere of Influence Radius = [G.]*(Black Hole Mass)/(Stellar Velocity Dispersion of the Host Bulge)^2. This formula also uses Gravitational constant .

Can the Radius of Sphere of Influence( Black Hole) be negative?

No, the Radius of Sphere of Influence( Black Hole), measured in Length cannot be negative.

Which unit is used to measure Radius of Sphere of Influence( Black Hole)?

Radius of Sphere of Influence( Black Hole) is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Radius of Sphere of Influence( Black Hole) can be measured.

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Radius of Sphere of Influence( Black Hole) Formula

Radius of Sphere of Influence( Black Hole) Example

Radius of Sphere of Influence( Black Hole) Solution

Radius of Sphere of Influence( Black Hole) Formula Elements

Other formulas in Fundamental Parameters category

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

FAQs on Radius of Sphere of Influence( Black Hole)

Variable Name