Orbital Speed, Escape Velocity and Satellites
Orbital speed vo = √(GM/r); escape speed ve = √(2GM/R) = 11.2 km/s for Earth; total orbital energy is negative.
What is Orbital Speed, Escape Velocity and Satellites?
Orbital speed vo = √(GM/r); escape speed ve = √(2GM/R) = 11.2 km/s for Earth; total orbital energy is negative.
Key formula / rule: ve = √(2) × vo at the same radius.
Key points
- Derive orbital and escape speeds from energy considerations.
- Evaluate whether a given launch speed produces a bound orbit.
Common exam trap
Assuming escape velocity depends on the mass of the escaping body.
Definitions
- Term
Orbital Speed, Escape Velocity and Satellites
- Meaning
Orbital speed vo = √(GM/r); escape speed ve = √(2GM/R) = 11.2 km/s for Earth; total orbital energy is negative.
- Term
Orbital Speed, Escape Velocity and Satellites — explanation
- Meaning
A bound satellite has negative total energy, and the escape condition is precisely total energy reaching zero. Geostationary satellites need a 24-hour period, which fixes their altitude at about 36000 km.
Learning objectives
Derive orbital and escape speeds from energy considerations.
Evaluate whether a given launch speed produces a bound orbit.
Formulae
- Key point
ve = √(2) × vo at the same radius.
- Key point
Total orbital energy E = -GMm/2r, negative for bound orbits.
- Key point
Escape speed is independent of the mass and direction of the projectile.
Prerequisites
PHY-U2-GRAV-T2-S1-C1
PHY-U2-GRAV-T1-S1-C2
Common mistakes
Assuming escape velocity depends on the mass of the escaping body.
Using R instead of the orbital radius r in orbital speed.
Keywords
Orbital
Speed
Escape
Velocity
Satellites
Practice preview
A satellite of mass 'm' orbits a planet of mass 'M' in a circular orbit of radius 'r'. Which of the following statements about its energy is INCORRECT?…
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Which of the following statements is true regarding a geostationary satellite?…
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A satellite is orbiting Earth at a height of 3600 km above the surface. Given Earth's radius R = 6400 km and acceleration due to gravity g = 9.8 m/s^2, what is its orbital speed? (Assume G = 6.67 x 10^-11 Nm^2/kg^2 and M…
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