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Saturn has a mass that is approximately 100 times greater than Earth\'s distance

ID: 804451 • Letter: S

Question

Saturn has a mass that is approximately 100 times greater than Earth's distance from the Sun. How much stronger is the gravitational force between the Sun and Saturn as compared to the gravitational force between the Sun and Earth? How much longer is Saturn's orbital compared to Earth's orbital period? Imagine that we move Earth to 10au, but we let Earth maintain the velocity that it had on a circular orbit at 1 au. What is the ratio of Earth's orbital velocity in this scenario to the escape velocity at 10au? What type of orbit would the Earth have in this scenario?

Explanation / Answer

The gravitational force between the Sun and Saturn is the same as than the gravitational force between the Sun and Earth. Earth may be closer to the Sun than Saturn, but Saturn's mass exactly makes up for it's severe distance.

Saturn is the sixth planet from the Sun and the second-largest in the Solar System. It is a gas giant with an average radius about nine times that of Earth. Earth takes 24 hours to complete a day, while Saturn takes 10 hours and 32 minutes. A year on Earth is, well, 1 year, while a year on Saturn lasts 30 years.

Given escape velocity perpendicular to a massive body, the object will move away from the body, slowing forever and approaching but never reaching zero speed. Once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body.The fact that gravity decreases with distance means that at some distance, it will be negligible; an object sufficiently distant from Earth may be considered to have "escaped" Earth's gravity. In reality, the force of gravity has no distance limit; two objects would have to be at infinite distance from each other to have no gravitational interaction, but for practical purposes, one can think of finite distances where gravitational forces become small enough to ignore.

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