From initial calculations:
The instantaneous velocity of Apophis at 1 A.U. is about 28.50213 km/sec.
The algorithm used to calculate that value is shown below. It is based on two separate equations for Specific Orbital Energy. I ran it against some known values and I think it works. There are rem statements showing the equations on which it is based as well as the value for the heliocentric gravitational parameter that was used.
I used the orbital data on Apophis found at the below link as input data.
http://newton.dm.unipi.it/cgi-bin/neodys/neoibo?objects:Apophis;main
I used earth mean velocity to calculate the relative velocity of Apophis assuming that the inclination of Apophis Orbit (3.331 degrees) was small enough to ignore for rough estimation.
The Earth/Apophis relative velocity is roughly calculated to be 1.28256 Km/sec and was calculated as Earth Mean Velocity – Apophis Velocity at 1 A.U. This relative velocity is so low because the semi-major axis of Apophis is so close to that of earth, it orbits on nearly the same plane, and assuming the heliocentric flight path angle is small enough to ignore for roughly estimating relative velocity. I used .922281 A.U. as the value of Apophis semi-major axis.
I calculated the minimum passing radius without capture to be roughly 490593.3 km from barycenter.
This was calculated from the equation V=√ 2u/r where r= 2u/v2. I used the sum of the gravitational parameters of earth and moon for the gravitational parameter of the earth/moon system for the calculation.
It appears that orbital capture will occur if the passing radius is less than 490593.3 km from barycenter. Intuition tells me that if the radius of passing is less than this and if the geocentric flight path angle at that range lies outside minimum parameters; then rebound or delayed impact will occur subsequent to capture; with either the moon or earth taking the hit.
If this is the case then I think we should pay Apophis a visit as soon as possible, hopefully unifying or efforts with other nations. We all have a stake in this and 5 or more cowboys trying to rope the same calf could well make matters worse. I don't think the long term bond markets should be our overriding concern here. The effects on those markets will be mitigated if there is seen to be a dedicated effort in the approach.
It appears that this object is not a planet killer but impact, if it were to occur, would probably be the most energetic event in recorded human history.
I want to trust the experts enough to believe that there must be something fundamentally wrong with my assumptions. I am ready to continue to learn.
MJ
10 PRINT"This program solves for instantaneous V of an elliptical heliocentric orbit"
20 PRINT"where the semi-major axis and instantaneous r is known"
40 PRINT"by - Mark J. Carter"
50 PRINT:PRINT
60 PRINT"Input the semi-major axis."
70 INPUT A
80 U=132712440018#:REM Gravitational Parameter - Sun
90 E=U/(2*A):REM Specific Orbital Energy
100 PRINT"Input the instantanious orbital radius."
110 INPUT R
120 NUM1=(2*(E-(U/R)))
121 NUM2=ABS(NUM1): Rem convert a negative number so the square root of V can be found.
125 V=SQR(NUM2)
130 PRINT:PRINT:PRINT
140 PRINT V
150 STOP
If anyone would like a copy of the BASIC interpreter send me a private message with your email addresss.
Apophis Capture in 2029?
Re: Apophis Capture in 2029?
