Intercepting Bennu

101955 Bennu is a 500 meter diameter Near Earth Asteroid, likely to crash into the Earth sometime in the next 20,000 years, and possibly sooner than 200 years from now. The impact energy would be equivalent to a 100 megaton bomb, or 4 times the explosive energy of the Mount Saint Helens eruption. That won't be a global catastrophe, but it could kill millions of people if it impacted in the wrong place.

Bennu is an Apollo asteroid, with a semimajor axis of 1.1264 AU and an eccentricity of 0.20375. It will make a close approach of 750,000 km on 23 September 2060, and another of 300,000 ± 200,000 km on 25 September 2125. The uncertainty results from small variations of arrival distance creating larger variations in the scattering angle after the 2060 encounter.

I am unable to calculate an accurate model of Bennu's orbit, nor whether it will arrive "inbound" or "outbound", or which side of the Earth the miss will occur. However, I have enough information to calculate the relative velocity (5 km/s) and the angle from the Sun ( 13 degrees ). How?

The 2060 and 2135 encounters both are about 100 days before Earth's perihelion in around January 4th. That lets us calculate Earth's radial distance from the Sun (1.0029 AU), hence the radius of Bennu at that close approach. Given the radius and Bennu's orbit, we can compute Bennu's angle from perihelion, 1.1858 radians ( 67.94 degrees ). At that angle, the radial velocity (sunwards or outwards?) is ±5.143 km/s, and the circumferential velocity is 30.860 km/s, relative to the Earth's radial velocity of -0.490 km/s (sunwards) and circumferential velocity of 29.703 km/s. So, the radial velocity difference is -0.490∓5.143 km/s, either