What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)

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Q: What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)

Solution: Escape velocity = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s

Steps: 8

Step 1: Identify the formula for escape velocity, which is Escape velocity = √(2GM/R).
Step 2: Identify the values needed for the formula: G = 6.67 × 10^-11 N m²/kg², M = 6 × 10^24 kg, and R = 4,000 km (which needs to be converted to meters).
Step 3: Convert the radius from kilometers to meters: 4,000 km = 4 × 10^6 m.
Step 4: Substitute the values into the formula: Escape velocity = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6).
Step 5: Calculate the numerator: 2 * 6.67 × 10^-11 * 6 × 10^24 = 8.004 × 10^{14}.
Step 6: Divide the result by the radius: 8.004 × 10^{14} / 4 × 10^6 = 2.001 × 10^{8}.
Step 7: Take the square root of the result: √(2.001 × 10^{8}) = 11,200 m/s.
Step 8: Conclude that the escape velocity from the surface of the planet is 11,200 m/s.