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

Answer:

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

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;

$v = \sqrt{{\dfrac{G \times M}{r} } }$

Where;

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

Substituting the known values gives;

$v = \sqrt{{\dfrac{6.67408 \times 10^{-11} \times 4 \times 10^{16}}{16,000} } } \approx 12.917$

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