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 1.0 AU? In this case, the mass of the Sun, 2.3e+30 kg, can be used as the mass of the Solar system

Answer 1

Approximate escape speed = 45.3 km/s

Step-by-step explanation:

Escape speed

`v=\sqrt{(2GM)/(R)}`

Here we have

Gravitational constant = G = 6.67 × 10⁻¹¹ m³ kg⁻¹ s⁻²

R = 1 AU = 1.496 × 10¹¹ m

M = 2.3 × 10³⁰ kg

Substituting

`v=\sqrt{(2* 6.67* 10^(-11)* 2.3* 10^(30))/(1.496* 10^(11))}=4.53* 10^4m/s=45.3km/s`

Approximate escape speed = 45.3 km/s