Radius of Sphere of Influence Calculator

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✖Planet 1 radius is the radius of the first considered planetary body.ⓘ Planet 1 radius [R₁]			+10% -10%
✖Planet 1 Mass is the mass of the first planetary body.ⓘ Planet 1 Mass [M₁]			+10% -10%
✖Planet 2 Mass is the mass of the second planetary body.ⓘ Planet 2 Mass [M₂]			+10% -10%

✖Planet 2 radius is the radius of the second considered planetary body.ⓘ Radius of Sphere of Influence [R₂]

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Formula

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Radius of Sphere of Influence

Formula

`"R"_{"2"} = ("R"_{"1"}/0.001)*("M"_{"1"}/"M"_{"2"})^(2/5)`

Example

`"1.1E^8km"=("14E6km"/0.001)*("5E24kg"/"1E30kg")^(2/5)`

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Radius of Sphere of Influence Solution

STEP 0: Pre-Calculation Summary

Formula Used

Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5)
R₂ = (R₁/0.001)*(M₁/M₂)^(2/5)
This formula uses 4 Variables

Variables Used

Planet 2 radius - (Measured in Meter) - Planet 2 radius is the radius of the second considered planetary body.
Planet 1 radius - (Measured in Meter) - Planet 1 radius is the radius of the first considered planetary body.
Planet 1 Mass - (Measured in Kilogram) - Planet 1 Mass is the mass of the first planetary body.
Planet 2 Mass - (Measured in Kilogram) - Planet 2 Mass is the mass of the second planetary body.

STEP 1: Convert Input(s) to Base Unit

Planet 1 radius: 14000000 Kilometer --> 14000000000 Meter (Check conversion here)
Planet 1 Mass: 5E+24 Kilogram --> 5E+24 Kilogram No Conversion Required
Planet 2 Mass: 1E+30 Kilogram --> 1E+30 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R₂ = (R₁/0.001)*(M₁/M₂)^(2/5) --> (14000000000/0.001)*(5E+24/1E+30)^(2/5)

Evaluating ... ...

R₂ = 106100159655.728

STEP 3: Convert Result to Output's Unit

106100159655.728 Meter -->106100159.655728 Kilometer (Check conversion here)

FINAL ANSWER

106100159.655728 ≈ 1.1E+8 Kilometer <-- Planet 2 radius

(Calculation completed in 00.018 seconds)

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Created by Kaki Varun Krishna

Mahatma Gandhi Institute of Technology (MGIT), Hyderabad

Kaki Varun Krishna has created this Calculator and 25+ more calculators!

Verified by Abhishek Dharmendra Bansile

Vishwakarma Institute of Information Technology, Pune (VIIT Pune), Pune

Abhishek Dharmendra Bansile has verified this Calculator and 10+ more calculators!

< 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 Formula

Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5)
R₂ = (R₁/0.001)*(M₁/M₂)^(2/5)

What is Sphere of Influence(Black Hole)

The sphere of influence is a region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy

How to Calculate Radius of Sphere of Influence?

Radius of Sphere of Influence calculator uses Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5) to calculate the Planet 2 radius, Radius of Sphere of Influence in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body. Planet 2 radius is denoted by R₂ symbol.

How to calculate Radius of Sphere of Influence using this online calculator? To use this online calculator for Radius of Sphere of Influence, enter Planet 1 radius (R₁), Planet 1 Mass (M₁) & Planet 2 Mass (M₂) and hit the calculate button. Here is how the Radius of Sphere of Influence calculation can be explained with given input values -> 106100.2 = (14000000000/0.001)*(5E+24/1E+30)^(2/5).

FAQ

What is Radius of Sphere of Influence?

Radius of Sphere of Influence in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body and is represented as R₂ = (R₁/0.001)*(M₁/M₂)^(2/5) or Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5). Planet 1 radius is the radius of the first considered planetary body, Planet 1 Mass is the mass of the first planetary body & Planet 2 Mass is the mass of the second planetary body.

How to calculate Radius of Sphere of Influence?

Radius of Sphere of Influence in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body is calculated using Planet 2 radius = (Planet 1 radius/0.001)*(Planet 1 Mass/Planet 2 Mass)^(2/5). To calculate Radius of Sphere of Influence, you need Planet 1 radius (R₁), Planet 1 Mass (M₁) & Planet 2 Mass (M₂). With our tool, you need to enter the respective value for Planet 1 radius, Planet 1 Mass & Planet 2 Mass 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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