The correct answer is B because:

List the known quantities:
- Volume of asteroid 1, V₁ = 113 km³ = 113 × 10⁹ m³
- Surface area of asteroid 2, S₂ = 18.1 km² = 18.2 × 10⁶ m²
- Density of asteroid 1, ρ₁ = 600 kg m⁻³
- Density of asteroid 2, ρ₂ = 1300 kg m⁻³
- Gravitational force, F = 73 MN = 73 × 10⁶ N
- Gravitational constant, G = 6.67 × 10⁻¹¹ N m² kg⁻²
Determine the radius of asteroid 1:
- Recall the equation for spherical volume: $V_{1} = \frac{4}{3} π {r_{1}}^{3}$
- Rearrange for radius: $r_{1} = \sqrt[3]{\frac{3 V_{1}}{4 π}} = \sqrt[3]{\frac{3 \times (113 \times 10^{9})}{4 π}} = 2999 m$

Determine the radius of asteroid 2:
- Recall the equation for spherical surface area: $S_{2} = 4 π {r_{2}}^{2}$
- Rearrange for radius: $r_{2} = \sqrt{\frac{S_{2}}{4 π}} = \sqrt{\frac{18.2 \times 10^{6}}{4 π}} = 1203 m$

Determine the mass of asteroid 1:
- Recall the density equation: $ρ_{1} = \frac{m_{1}}{V_{1}}$
- Rearrange for the mass of A₁: $m_{1} = ρ_{1} V_{1} = 600 \times (113 \times 10^{9}) = 6.78 \times 10^{13} kg$

Determine the mass of asteroid 2:
- Determine the volume of asteroid 2 using its radius: $V_{2} = \frac{4}{3} π \times {(1203)}^{3} = 7.293 \times 10^{9} m^{3}$
- Determine the mass of A₂: $m_{2} = ρ_{2} V_{2} = 1300 \times (7.293 \times 10^{9}) = 9.48 \times 10^{12} kg$
Determine the separation of the centres of mass:
- Use Newton's law of gravitation: $F = \frac{G m_{1} m_{2}}{r^{2}}$
- Rearrange for separation: $r = \sqrt{\frac{G m_{1} m_{2}}{F}}$
- Substitute the known quantities: $r = \sqrt{\frac{(6.67 \times 10^{- 11}) \times (6.78 \times 10^{13}) \times (9.48 \times 10^{12})}{73 \times 10^{6}}}$
- Separation of the centres of mass: $r = 24 230 m$

Determine the separation d :
- $r = r_{1} + r_{2} + d$
- $d = (24 230 - 2999 - 1203) = 20 028 m = 20 km$

Gravitational Fields (SL IB Physics)

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