Formula for escape velocity

The escape velocity from the surface of a planet is $v_e = \sqrt{\frac{2GM}{R}}$ where:

• $G$ = gravitational constant
• $M$ = mass of the planet
• $R$ = radius of the planet

Dependence on the mass of the body

In this formula, there is no dependence on the mass $m$ of the escaping body.

So, $v_e \propto m^0$

Check the options

• A: $m^0$ ✅
• B: $m^1$ ❌
• C: $m^2$ ❌
• D: $m^3$ ❌

Conclusion

The escape velocity is independent of the mass of the body.

Hence, the correct answer is: $\boxed{A}$