The orbits of the planets can be modeled easily by assuming i). that the sun is a perfect sphere and ii). that each planet is influenced only by the gravitational field of the sun (that is, each planet is unperturbed by gravitational forces from other planets, distant stars, etc.). According to Newton's (classical) theory of gravity, these assumptions result in elliptical planetary orbits with the sun at one focus. That is, the orbit can be described by the polar equation . However, according to Einstein's (relativistic) theory of gravitation, the orbits are more accurately described by , where is a constant such that . Describe how the inclusion of the factor affects the orbit. That is, compare the classical orbit to the relativistic orbit. How do they differ? Draw figures that summarize the differences in the classical and relativistic orbits.

Question

The orbits of the planets can be modeled easily by assuming i). that the sun is a perfect sphere and ii). that each planet is influenced only by the gravitational field of the sun (that is, each planet is unperturbed by gravitational forces from other planets, distant stars, etc.). According to Newton's (classical) theory of gravity, these assumptions result in elliptical planetary orbits with the sun at one focus. That is, the orbit can be described by the polar equation  . However, according to Einstein's (relativistic) theory of gravitation, the orbits are more accurately described by  , where  is a constant such that  . Describe how the inclusion of the factor  affects the orbit. That is, compare the classical orbit to the relativistic orbit. How do they differ? Draw figures that summarize the differences in the classical and relativistic orbits.

Quizplus · Accepted Answer

The Answer of The orbits of the planets can be modeled easily by assuming i). that the sun is a perfect sphere and ii). that each planet is influenced only by the gravitational field of the sun (that is, each planet is unperturbed by gravitational forces from other planets, distant stars, etc.). According to Newton's (classical) theory of gravity, these assumptions result in elliptical planetary orbits with the sun at one focus. That is, the orbit can be described by the polar equation  . However, according to Einstein's (relativistic) theory of gravitation, the orbits are more accurately described by  , where  is a constant such that  . Describe how the inclusion of the factor  affects the orbit. That is, compare the classical orbit to the relativistic orbit. How do they differ? Draw figures that summarize the differences in the classical and relativistic orbits.

The Orbits of the Planets Can Be Modeled Easily by Assuming