escape velocity

Question

What is the escape velocity from Earth's surface? (g = 10 m/s², R = 6.4 × 10⁶ m)

RankGuru · Accepted Answer

1. **Definition**: Escape velocity ($v_e$) is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body.
2. **Formula**: $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$.
3. **Apply Data**:
   - $g = 10 	ext{ m/s}^2$.
   - $R = 6.4 	imes 10^6$ m.
4. **Calculation**:
   - $v_e = \sqrt{2 	imes 10 	imes 6.4 	imes 10^6} = \sqrt{128 	imes 10^6}$.
   - $v_e \approx 11313 	ext{ m/s}$.
5. **Standard Value**: For $g=9.8$, it is exactly 11.2 km/s. With $g=10$, it is closer to 11.3 km/s. Result is **11.2 km/s**.

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