Comets travel around the sun in elliptical orbits with large eccentricities. If
ID: 1518848 • Letter: C
Question
Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.4×104 m/s when at a distance of 2.1×1011 m from the center of the sun, what is its speed when at a distance of 5.1×1010 m . Express your answer using two significant figures. Use this link in order to make sure you follow the methodology and get the correct answer: https://www.chegg.com/homework-help/questions-and-answers/comets-travel-around-sun-elliptical-orbits-large-eccentricities-comet-speed-24-104-m-s-dis-q9704589 The answers are NOT 9.9 104 m/s, or 6.23 x 104 m/s.
Explanation / Answer
v = 24000 m/s
r = 2.1e11 meters
v = ?
r = 5.1e10 meters
The solar gravitational parameter.
GM = 1.32712440018e20 m³ sec²
The Vis Viva equation.
v = [GM(2/r 1/a)]
Find the semimajor axis of the comet's orbit.
a = [2/r v²/GM]¹
a = 1.8357e11 meters
Find the heliocentric relative speed v.
v = [GM(2/r 1/a)]
v = 72866 m/s