a) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body of radius R and mass M, using energy conservation. Assume that the planet does not move or spin, so that the total mechanical energy E of a test particle both on the surface and at infinity is equal to zero, and the speed at infinity is zero. Use the formula come up in the last part, Compute this escape speed (in km/s) from Venus, Mars, Jupiter and Neptune.
a)
Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body of radius R and mass M, using energy conservation. Assume that the planet does not move or spin, so that the total mechanical energy E of a test particle both on the surface and at infinity is equal to zero, and the speed at infinity is zero.
Use the formula come up in the last part, Compute this escape speed (in km/s) from Venus, Mars, Jupiter and Neptune.
b)
Evaluate vIII from the heliocentric orbit of the 4 planets (Venus, Mars, Jupiter and Neptune) mentioned above, assuming circularity of their orbits.
Compare the computed speeds with the escape speeds from their surfaces (vII). Notice a big difference in the situation around the inner and the outer planets. What is it due to?
A fly-by’s of small bodies near a planet can result in the small particle being accelerated to a final speed close to vII w.r.t. the planet. Draw conclusions as to which planets are able to accelerate small passing-by objects to the relative speed vIII, thus ejecting them in one approach from the planetary system into the Galaxy. This is important for understanding where exactly were the comets ejected from in the early solar system, to the Galaxy and to the weakly bound Oort cloud of comets.
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