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October 24, 2014

Posted by **sana** on Tuesday, March 6, 2012 at 9:44am.

- physics -
**drwls**, Tuesday, March 6, 2012 at 11:14amThis is a very clever problem. Here is how to do it.

The cross product of the V and R vectors is the rate at which area is swept out by the asteroid, which (according to Kepler's second law) is a constant related to the angular momentum. Compute its value using the experimental measurements.

C1 = |R|*Vtheta

= [(3.1)(8.4) - (6.3)(1.8)]*10^11

= 14.7*10^11 m^2/s

Vtheta is the velocity component perpendicular to the position vector, R

Another constant of motion is the total energy, which is (1/2)mV^2 -GMm/R.

Since m (the asteroid mass) is constant,

V^2/2 - GM/R = C2 , another constant. Compute this constant using G, M(solar) and the observed values of the magnitudes of R and V.

At perihelion, the C1 constant is the product of the velocity Vmax and closest approach distance, Rmin

Vmax*Rmin = C1

Vmax^2/2 - G*M/Rmin = C2

You now have two equations for the two unknowns, Vmax and Rmin. You will need to use the other known constants, M and G

- physics -
**Sana**, Tuesday, March 6, 2012 at 12:16pmCould u rewrite the eqn that you used for C2

- physics -
**drwls**, Tuesday, March 6, 2012 at 12:37pm(V^2/2) - (GM/R) = C2

(Vmax^2/2) - (G*M/Rmin) = C2

It is the sum of kinetic and potential energy per unit mass. Using the first equation and the |V| and |R| magnitudes of the observation, you can compute the value of C2.

- physics -
**please**, Tuesday, March 6, 2012 at 3:50pmi am unable to get the right answer..please help

- physics -
**drwls**, Tuesday, March 6, 2012 at 4:36pmSorry. You'll have to fill in the blanks. I have explained how to do it. Make sure you are using the correct values of G and M, and that your equations are dimensionally consistent.

- physics -
**Anonymous**, Thursday, March 15, 2012 at 4:55pmwhat drwls did makes no sense..

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