Question

Calculate the speed with which you would have to throw a rock to put it into orbit around the asteroid 234 Ida near its surface, assuming 234 Ida is spherical. Ida’s mass is 4 × 1016 kg and its radius is 16 km.

Answer 1

The speed with which a rock would have to be thrown to put it in 234 Ida's orbit, near its surface is approximately 12.917 m/s

Step-by-step explanation:

The given parameters are;

The mass of Ida, M = 4 × 10¹⁶ kg

The radius of 234 Ida, r = 16 km = 16,000 m

The speed, v, required to put a rock in 234 Ida's orbit near its surface is given by the orbital velocity equation as follows;

`v = \sqrt{{(G * M)/(r) } }`

Where;

G = The universal gravitational constant = 6.67408 × 10⁻¹¹ m³·kg⁻¹·s⁻²

Substituting the known values gives;

`v = \sqrt{{(6.67408 * 10^(-11) * 4 * 10^(16))/(16,000) } } \approx 12.917`

Therefore, the speed required to put a rock in 234 Ida's orbit near its surface = v ≈ 12.917 m.