the escape speed

Question

The escape speed from an object is v² = 2GM/R, where M is the mass of the object, R is the object's starting radius, and G is the gravitational constant 6.67 × 10^-11 m³ kg^-1 s^-2. What is the approximate escape speed, in km/s, from the Solar System starting from an orbit at 1.1 AU? In this case, the mass of the Sun, 1.9e+30 kg, can be used as the mass of the Solar system.

Answer 1

V² = (2GM)/R

G= 6.67*10^-11 m^-3 (Kg)^-1 s^-2 , M _{Solar System} ≅ M _sun= 1.9*10³⁰ Kg

R = (1.1 AU) * (93*10⁶ miles)/(1 AU) = 102.3 * 10⁶ miles (1609 m/ 1 mile) = 164.6 * 10⁹ meters

Units of G and M _Sun are set in metric system. Then, unit of R also must be in metric system.

V² = (2*6.67*10^-11)(1.9*10³⁰) / (164.6*10⁹) , V = 39240.9 m/sec = 39.24 Km/sec