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

Concept:

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

Formulae:

• Orbital velocity (v_o) = √(GM / R)
• Escape velocity (v_e) = √(2GM / R)

So, v_e = √2 × v_o

Percentage increase in velocity = [(v_e - v_o) / v_o] × 100%

= [(√2 × v_o - v_o) / v_o] × 100%

= (√2 - 1) × 100%

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

Answer: Option 1) 41%