# An artificial satellite revolves around the Earth at a distance of 3400 km. Calculate its orbital velocity and period of revolution. Radius of the Earth = 6400 km; g = 9.8 m/s²

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by Ishi262

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by Ishi262

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v = orbital velocity we know g = G M / R²

d = 3400 + 6400 km = 10000 km

gravitational force = centripetal force

G M m / d² = m v² / d

v² = G M / d = g R² / d

v = R √(g/d)

ω = angular velocity = v / R = √(g/d)

T = time period = 2π/ ω = 2 π √(g/d)

substitute the values to get answers.

d = 3400 + 6400 km = 10000 km

gravitational force = centripetal force

G M m / d² = m v² / d

v² = G M / d = g R² / d

v = R √(g/d)

ω = angular velocity = v / R = √(g/d)

T = time period = 2π/ ω = 2 π √(g/d)

substitute the values to get answers.

Radius of earth(R) = 6400 km = 6.4×10⁶ m

Radius of orbit(r) = R+d = 10,000 km = 10⁷ m

g = 9.8 m/s²

Orbital velocity,

Period of revolution, T = ?

(i) Orbital velocity

(ii) Time period