There is an asteroid 3AU away from the sun that is orbiting in a circle. a) Find
ID: 284222 • Letter: T
Question
There is an asteroid 3AU away from the sun that is orbiting in a circle.
a) Find the velocity of the asteroid.
b) If the asteroid collides with something and its velocity is reduced by a factor of 2^(1/2), what shape would its orbit be now? (think it is an ellipse but not sure how to find this)
c) Find the closest distance to the sun the asteroid reaches on its new orbit.
d) What is its velocity at that location?
e) How long does it take for the asteroid to reach the closest distance to the sun on its new orbit (rc) after the collision?
Table N12.1 Table of useful equations for solving orbit problems Symbols Item Equation (s) r distance from the primary Formula for a conic section. b scale constant Formula fora cos 8 E eccentricity angle from the axis between Definitions of E and L 2E 2GM and the primary and the orbit's closest point E total system energy Formulas for Eand b and b 1 (GM) GM Im L system's angular momentum G gravitational constant satellite's mass M primary's mass Elliptical Case Hyperbolic Case Item satellite's speed at an instant 2E GM 2E GM angle between and Connection between a and E a semimajor axis (for ellipse, half the widest diameter) a (1 re distance from primary to the Location of extremes closest point on the orbit (-1/E) rs- distance from primary to the farthest point on the orbit tan v E T orbital period GM Other useful relations epler's third law L. /2E 0,s value that 0 approaches as r oo in a hyperbolaExplanation / Answer
Answer:a
The velocity of the asteroid can be calculated as follows;
Velocity = (Distance)/(time)
Where, distance= 3AU, time= time period
Answer:b
The eccentricity is equal to 0, but when the speed becomes square root of 2 its orbital shape changes and become ellipse.
Answer:c
The closest distance can be calculated as follows:
D= a(1-e)
D= closest distance, a= semi-major axis, e= eccentricity
Answer:d
The velocity at instant can be calculated as follows:
V2 = (2E/m)+(2GM/r)
Where, V= velocity, E= total system energy, m=satellite mass, G= gravitational constant, r= distance between the objects.
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