A comet orbits the sun with an apogee of 124 AU and a perigee of 34.50 AU. The c

Question

A comet orbits the sun with an apogee of 124 AU and a perigee of 34.50 AU. The comet's mass is estimated at 4.36e+13 kg. Note that an AU (astronomical unit) is the distance from the Earth to the sun; 1.0 AU = 1.49E11 m. The sun's mass is 1.98E30 kg and its Kepler constant is 3.35E18 m3/s2. A. What is the semimajor axis of this comet? B. What is the total mechanical energy of this comet C. What is the gravitational potential energy at apogee? D. What is the kinetic energy at apogee? E. What is the velocity of the comet at apogee? F. What is the gravitational potential energy at perigee? G. What is the kinetic energy at perigee? H. What is the velocity of the comet at perigee? I. What is the eccentricity of the comet's orbit? J. What is the period of the comet's orbit?

Explanation / Answer

Rmax=124AU

Rmin=34.50AU

A) a= (Rmax+Rmin)/2=(124+34.50)/2=79.25AU

C) energy= G*M*m/a = (6.67*10^-11*4.36*10^13*1.98*20^30)/(79.25*1.49*10^11) = 0.4876*10^21 J

F) b=Rmax*Armin=124*34.50=65.41AU

energy= = G*M*m/b = (6.67*10^-11*4.36*10^13*1.98*20^30)/(65.41*1.49*10^11) = 0.5908*10^21 J

I) eccentricity = (Rmax-Rmin)/(Rmax+Rmin)= (124-34.50)/(124+34.50)=0.5647

J)as we know that T^2=kepler constant*a^3

T=kepler constant*a^3 =3.35*10^18*79.25*1.49*10^11 = 62.8945*10^14 second

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