For a satellite orbiting in an orbit, close to the surface of earth, to escape, the percentage increase in the velocity is ________.

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  1. 41%
  2. 61% 
  3. 81%
  4. 98%

Answer (Detailed Solution Below)

Option 1 : 41%
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Concept:

To escape Earth's gravity, a satellite in low Earth orbit must increase its velocity from orbital velocity (vo) to escape velocity (ve).

Formulae:

  • Orbital velocity (vo) = √(GM / R)
  • Escape velocity (ve) = √(2GM / R)

So, ve = √2 × vo

Percentage increase in velocity = [(ve - vo) / vo] × 100%

= [(√2 × vo - vo) / vo] × 100%

= (√2 - 1) × 100%

≈ (1.414 - 1) × 100% = 0.414 × 100% = 41.4%

Answer: Option 1) 41%

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