The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v₀. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

Calculation:

Orbital velocity (v) of a satellite at distance r from the center of the Earth is given by:

v = √(GM / r)

Let v₀ be the orbital velocity just above the Earth's surface. Then:

v₀ = √(GM / R)

Now consider a satellite at an altitude of half the Earth's radius. So, total distance from Earth's center = R + R/2 = (3/2)R

New orbital velocity (v') = √(GM / (3R/2)) = √((2/3) × GM / R)

= √(2/3) × √(GM / R)

= √(2/3) × v₀

Answer: Option 1) √(2/3) × v₀