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# Determination of asteroid parameters

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Remember that in answering questions involving calculations you should show all working and that answers should be given to appropriate numbers of significant figures.

Asteroid 2008 TC3 was determined from observations to have a semi-major axis of 1.296 AU and eccentricity of 0.303. It has a diameter of 50 m, measured to one significant figure.

(i) Calculate 2008 TC3s orbital period in years, and its furthest and closest distance to the Sun.

(ii) Calculate 2008 TC3s mass, assuming that it is spherical and that it is a dense rocky body of density around 3000 kg m-3. Give your answer in scientific notation.

(iii) Hence, if it has a velocity relative to the Earth of 30 km s-1, calculate the kinetic energy of the asteroid in joules and in megatonnes of TNT. Answers should be given in scientific notation.

Remember that in answering questions involving calculations you should show all working and that answers should be given to appropriate numbers of significant figures.

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https://brainmass.com/physics/asteroids/determination-asteroid-parameters-381977

## SOLUTION This solution is FREE courtesy of BrainMass!

See the attached file.

To work out the orbital period of the asteroid use Kepler's 3rd law

Period T^2=a^3 where a is the semi-major axis of the defined orbit

To work out the closest approach to the Sun use

R(min) = p/(1+e) where e is eccentricity of the orbit and p is the semi-latus rectum given by p=a(1-e^2)

To work out furthest approach in orbit from the Sun use

R(min) = p/(1-e^2)

To work out Mass of asteriod assume it is psherical and work out the volume of the sphere defined by its radius r = 25m by

V = (4/3)*pi*r^3

Multiply be the density given rho so Mass is given by

M = rho*V

Work out the KE that the Asteriod possesses using

KE = 0.5M*v^2 where the velocity is given as v = 30 km/s = 3 x 10^4 m/s

Work out the equivalent KE in terms of Megatonne of TNT using the fact that 1 MT of TNT represents 4.2 x 10^15 J of energy

See attachment for full treatise.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Â© BrainMass Inc. brainmass.com December 24, 2021, 9:28 pm ad1c9bdddf>
https://brainmass.com/physics/asteroids/determination-asteroid-parameters-381977