A satellite is projected from a point P at distance r₀ from the Earth's centre with speed v₀ = √(GM/r₀), making an angle α = 37° with the local horizontal. It enters an elliptical orbit. If e is its eccentricity, find 5e.

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G1 Physics · Accepted Answer

Step 1: v₀²=GM/r₀, so specific energy ε=v₀²/2-GM/r₀=-GM/(2r₀); hence the semi-major axis is a=r₀. Step 2: Specific angular momentum h=r₀v₀cos37°=√(GMr₀)(4/5). For an ellipse h²=GMa(1-e²). Step 3: (16/25)=1-e² givₑ e=3/5, hence 5e=3.