The NEAR spacecraft flew by the asteroid Eros in 1997 (Fig. P6.98). The fly by allowed the craft to measure the asteroid’s density at 2.7 g/cm3. Assume most asteroids have similar composition and you personally can jump 1.0 m high on the Earth.
(a) What is the radius of the largest spherical asteroid you could literally jump off (in other words, that you could jump from with an initial speed equal to the escape speed of the asteroid)?
(b) Eros has a mass of 6.7 × 1015 kg. Could you jump off Eros? If not, how far from the surface would you go before descending back to the asteroid? For simplicity, assume Eros is spherical.
Figure P6.98
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