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Total Velocity Required to Place Satellite in Orbit Formula

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The Total Velocity of Rocket is defined as the total velocity required to place a satellite in the fixed circular orbit of earth. Check FAQs

V T = \sqrt{\frac{[G.] \cdot M E \cdot (R E + 2 \cdot h)}{R E \cdot (R E + h)}}

V_T - Total Velocity of Rocket?M_E - Mass Of Earth?R_E - Radius of Earth?h - Height of Satellite?[G.] - Gravitational constant?

Total Velocity Required to Place Satellite in Orbit Example

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Here is how the Total Velocity Required to Place Satellite in Orbit equation looks like with Values.

Here is how the Total Velocity Required to Place Satellite in Orbit equation looks like with Units.

Here is how the Total Velocity Required to Place Satellite in Orbit equation looks like.

10509.5796 = \sqrt{\frac{6.7E-11 \cdot 1E+25 \cdot (6.4E+6 + 2 \cdot 375000)}{6.4E+6 \cdot (6.4E+6 + 375000)}}

10509.5796m/s = \sqrt{\frac{6.7E-11 \cdot 1E+25kg \cdot (6.4E+6m + 2 \cdot 375000m)}{6.4E+6m \cdot (6.4E+6m + 375000m)}}

10509.5796 = \sqrt{\frac{6.7E-11 \cdot 1E+25 \cdot (6.4E+6 + 2 \cdot 375000)}{6.4E+6 \cdot (6.4E+6 + 375000)}}

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Total Velocity Required to Place Satellite in Orbit Solution

Follow our step by step solution on how to calculate Total Velocity Required to Place Satellite in Orbit?

FIRST Step Consider the formula

V T = \sqrt{\frac{[G.] \cdot M E \cdot (R E + 2 \cdot h)}{R E \cdot (R E + h)}}

Next Step Substitute values of Variables

∴

V T = \sqrt{\frac{[G.] \cdot 1E+25kg \cdot (6.4E+6m + 2 \cdot 375000m)}{6.4E+6m \cdot (6.4E+6m + 375000m)}}

Next Step Substitute values of Constants

∴

V T = \sqrt{\frac{6.7E-11 \cdot 1E+25kg \cdot (6.4E+6m + 2 \cdot 375000m)}{6.4E+6m \cdot (6.4E+6m + 375000m)}}

Next Step Prepare to Evaluate

∴

V T = \sqrt{\frac{6.7E-11 \cdot 1E+25 \cdot (6.4E+6 + 2 \cdot 375000)}{6.4E+6 \cdot (6.4E+6 + 375000)}}

Next Step Evaluate

∴

V T = 10509.5795897818m/s

LAST Step Rounding Answer

∴

V T = 10509.5796m/s

Total Velocity Required to Place Satellite in Orbit Formula Elements

Variables

Constants

Functions

Total Velocity of Rocket

The Total Velocity of Rocket is defined as the total velocity required to place a satellite in the fixed circular orbit of earth.

Symbol: V_T

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Total Velocity of Rocket

Mass Of Earth

Mass Of Earth is equal to 5.972×10^24 kg.

Symbol: M_E

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass Of Earth

Radius of Earth

Radius Of earth is equal to 6378.1 km.

Symbol: R_E

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Earth

Height of Satellite

Height of Satellite is the distance of launch vehicle from the surface of earth.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Satellite

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Theory Of Rockets category

Go Velocity Increment of Rocket

ΔV = V e \cdot \ln (\frac{m i}{m final})

Go Rocket Exhaust Gas Velocity

V e = \sqrt{(\frac{2 \cdot γ}{γ - 1}) \cdot [R] \cdot T 1 \cdot (1 - {(\frac{p 2}{p 1})}^{\frac{γ - 1}{γ}})}

Go Structural Mass Fraction

σ = \frac{m s}{m p + m s}

Go Payload Mass Fraction

λ = \frac{m d}{m p + m s}

How to Evaluate Total Velocity Required to Place Satellite in Orbit?

Total Velocity Required to Place Satellite in Orbit evaluator uses Total Velocity of Rocket = sqrt(([G.]*Mass Of Earth*(Radius of Earth+2*Height of Satellite))/(Radius of Earth*(Radius of Earth+Height of Satellite))) to evaluate the Total Velocity of Rocket, Total Velocity Required to Place Satellite in Orbit formula is defined as the necessary speed a satellite must achieve to maintain a stable orbit around a celestial body, balancing gravitational forces and orbital mechanics. Total Velocity of Rocket is denoted by V_T symbol.

How to evaluate Total Velocity Required to Place Satellite in Orbit using this online evaluator? To use this online evaluator for Total Velocity Required to Place Satellite in Orbit, enter Mass Of Earth (M_E), Radius of Earth (R_E) & Height of Satellite (h) and hit the calculate button.

FAQs on Total Velocity Required to Place Satellite in Orbit

What is the formula to find Total Velocity Required to Place Satellite in Orbit?

The formula of Total Velocity Required to Place Satellite in Orbit is expressed as Total Velocity of Rocket = sqrt(([G.]*Mass Of Earth*(Radius of Earth+2*Height of Satellite))/(Radius of Earth*(Radius of Earth+Height of Satellite))). Here is an example- 10509.58 = sqrt(([G.]*1E+25*(6378100+2*375000))/(6378100*(6378100+375000))).

How to calculate Total Velocity Required to Place Satellite in Orbit?

With Mass Of Earth (M_E), Radius of Earth (R_E) & Height of Satellite (h) we can find Total Velocity Required to Place Satellite in Orbit using the formula - Total Velocity of Rocket = sqrt(([G.]*Mass Of Earth*(Radius of Earth+2*Height of Satellite))/(Radius of Earth*(Radius of Earth+Height of Satellite))). This formula also uses Gravitational constant and Square Root (sqrt) function(s).

Can the Total Velocity Required to Place Satellite in Orbit be negative?

No, the Total Velocity Required to Place Satellite in Orbit, measured in Speed cannot be negative.

Which unit is used to measure Total Velocity Required to Place Satellite in Orbit?

Total Velocity Required to Place Satellite in Orbit is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Total Velocity Required to Place Satellite in Orbit can be measured.

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Total Velocity Required to Place Satellite in Orbit Formula

Total Velocity Required to Place Satellite in Orbit Example

Total Velocity Required to Place Satellite in Orbit Solution

Total Velocity Required to Place Satellite in Orbit Formula Elements

Other formulas in Theory Of Rockets category

How to Evaluate Total Velocity Required to Place Satellite in Orbit?

FAQs on Total Velocity Required to Place Satellite in Orbit

Variable Name