NASA\'s OSIRIS-REx mission will travel to asteroid Bennu to study and collect a

Question

NASA's OSIRIS-REx mission will travel to asteroid Bennu to study and collect a sample which will be returned to Earth.

(a) Bennu has a period of 436.65 days. What is the length a of the semi major axis of its orbit?

(b) Bennu has an orbital eccentricity of e= 0.20375. What is the closest distance that the asteroid can be to the Sun? Should we be worried about this asteroid intersecting the orbit of Earth? (NOTE: see the formulas below. I'm not sure how to tell if the asteroid can intersect the orbit of earth. The eccentricity of the Earth is e=0.0167, but I'm not sure if I have to use that and compare Bennu to Earth to be able to tell if the asteroid can intersect the orbit of Earth)

(c) Bennu is thought to have a mass of approximately 7.0 x 1010kg. The mass of OSIRIS-REx (without rocket fuel) is 880kg. Using the conservation of linear momentum and the equation for escape velocity, vesc=(2GM/r)1/2 show whether it is possible for OSIRIS-REx to crash into Bennu and eject it from the solar system.

Other formulas to consider:

For part (a):

For part (b)

rp =at perihelion, closest to the Sun=a(1-e) where a=length of semimajor axis measured in AU (should have been found in part a), e=eccentricity, which was given as 0.20375

ra=at aphelion, farthest from Sun= a(1+a)

Explanation / Answer

  a) semi major axis = a

    p^2 = a^3 in AU

(436.65/365)^2= a^3

1.1963^(2/3) = a

a =1.127 AU

B) Closest approach to sun = 1.127*(1-0.20375)

= 0.897 AU

C) For this part you will require velocity of OSIRIS

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