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Determination of asteroid parameters

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.

Solution Preview

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) = ...

Solution Summary

The solution calculates the orbital period, mass and kinetic energy for asteroid 2008 TC3 given basic orbital parameters.

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