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Task 1 – Deep Impact

Task 1 – Deep Impact. So far the only impact demonstration was done by the Deep Impact mission. A 350 kg projectile hit the comet with 10.2 km/s. The comet has a size of about 8 x 5 x 5 km 3 . What are reasonable assumptions for the momentum transfer coefficient b ?

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Task 1 – Deep Impact

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  1. Task 1 – Deep Impact • So far the only impact demonstration was done by the Deep Impact mission. A 350 kg projectile hit the comet with 10.2 km/s. The comet has a size of about 8 x 5 x 5 km3. • What are reasonable assumptions for the momentum transfer coefficient b? • What is the velocity change (assume a reasonable b)? • Assume the comet is hit in apocenter– how much later does it arrive atpericenter compared to without hit?What distance does that correspondto? • a = 3.12404524 AU • e = 0.516946

  2. Task 1 – Deep Impact • Reminder: • From Kepler 1 • Kepler 3 • Vis-Viva • Gravitational constant: 6.67300.10-11 m3kg-1s-2 • Mass of the Sun: 1.98892.1030 kg •  = GM

  3. Task 2 - Apophis flyby • Apophis will have a close encounter on 13 Apr 2029, flyby distance is 0.0002547 AU. • (a) What is the expected brightest magnitude of the object? (Albedo = 0.33, diameter 0.27 km) • (b) What will be the relative flyby velocity? (a = 0.922296 AU, e = 0.19109) • (c) How long will it roughly take to cross half the sky (90 deg)? And the diameter of the Moon (0.5 deg)? • (d) If it did hit – what’s the released energy in comparison to the Hiroshima bomb? • Impact energies are often given in ‘kilotons TNT’ or ‘megatons TNT’ • 1 kt TNT = 4.184 * 1012 J • The ‘little boy’ Hiroshima bomb had an explosive yield of 15 kt TNT

  4. Task 2 – Apophis flyby – p. 2 • Reminder for (a): MSun = -26.7

  5. Task 3 – Apophis deflection • Rosetta (~2 t) was sent away from the Earth with 3.5 km/s – let’s assume we use it to deflect Apophis, when Apophis is at r = 1 AU. Assume b = 2 and 20 % loss because of different velocity vector directions. • Approximation: ds = 3 * dv * t (Chesley 2005)

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