The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km from the asteroid's center. Eros is roughly box-shaped, with dimensions 40 km 6 km 6 km. Assume Eros has a density (mass/volume) of about 2.3 103 kg/m3.

Question

The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km from the asteroid's center. Eros is roughly box-shaped, with dimensions 40 km  6 km  6 km. Assume Eros has a density (mass/volume) of about 2.3  103 kg/m3.
(a) What will be the period of NEAR as it orbits Eros?
(b) If Eros were a sphere with the same mass and density, what would its radius be?
(c) What would g be at the surface of this spherical Eros?

bobpursley · Answer

a. find the volume of the box, then knowing density, find the mass.
So now, the period.

centripetal force= gravitational force
massNear*v^2/15E3=GMassEros*massNEAR*/(15E3)^2

you have all that , solve for V. then,
V= 15E3*2PI/Period
solve for period.

Millie · Answer

what is 15E3 and how do you know the mass of Near?

bobpursley · Answer

15E3 meters = 15km= 15*10^3 meters Mass Near= volume*density=XxYxZ*density you are given those dimensions.

billy · Answer

billy millie I would say m=v2-Fc So, r2xFc3=M2g