A rocket (with mass m = 3000 kilograms) orbits around a fictious planet named "Kerbin" with the periapsis of the orbit at 100 kilometers above the surface of Kerbin and apoapsis at 11,400 kilometers above the surface. The planet Kerbin has a radius of 600 kilometers and a mass of 5.29 x 10²² kilograms. The force of gravity on the rocket in its orbital plane is given by the 2D vector field F (7) = GMm i %3D 72 Irl where G = 6.67x10 is the universal gravitational constant, M is the mass of Kerbin and m is the mass of the rocket. The vector i = xî + yj is the position vector for the rocket.

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A rocket (with mass m = 3000 kilograms) orbits around a fictious planet named "Kerbin" with the
periapsis of the orbit at 100 kilometers above the surface of Kerbin and apoapsis at 11,400 kilometers
above the surface. The planet Kerbin has a radius of 600 kilometers and a mass of 5.29 x 1022 kilograms.
The force of gravity on the rocket in its orbital plane is given by the 2D vector field F (*) = GMm
r2 lr||
where G= 6.67x101" is the universal gravitational constant, M is the mass of Kerbin and m is the mass of
the rocket. The vector i = xî + yj is the position vector for the rocket.
Use the fundamental theorem of line integrals to compute the work done by gravity as the
rocket orbits from periapsis to apoapsis.
Given the rocket's speed at periapsis is 3087 meters/second and 180 meters/second at
apoapsis, check the answer in question 1 by computing the change in kinetic energy of the
rocket.
Transcribed Image Text:A rocket (with mass m = 3000 kilograms) orbits around a fictious planet named "Kerbin" with the periapsis of the orbit at 100 kilometers above the surface of Kerbin and apoapsis at 11,400 kilometers above the surface. The planet Kerbin has a radius of 600 kilometers and a mass of 5.29 x 1022 kilograms. The force of gravity on the rocket in its orbital plane is given by the 2D vector field F (*) = GMm r2 lr|| where G= 6.67x101" is the universal gravitational constant, M is the mass of Kerbin and m is the mass of the rocket. The vector i = xî + yj is the position vector for the rocket. Use the fundamental theorem of line integrals to compute the work done by gravity as the rocket orbits from periapsis to apoapsis. Given the rocket's speed at periapsis is 3087 meters/second and 180 meters/second at apoapsis, check the answer in question 1 by computing the change in kinetic energy of the rocket.
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