What Would Happen if Sun's Gravity Was Turned Off?

[rlmurra2]

Suppose the Sun's gravity were turned off, and the planets would leave their nearly circular orbits and fly away in straight lines described by Newton's first law. Would Mercury ever be farther away from the Sun than Pluto? If so, how long would it take for Mercury to achieve this passage?

I know this problems must have something to do with Kepler's laws, b/c its out of that section of the book. But I'm guessing you would have to find the tangential velocity first, or at some point?

 

[daveed]

well you do have the relationship t^2 ~ r^3...
meaning that the relationship between period and radius is not linear... if you want that ratio, then period would have to increase faster than radius
and, well the path of a planet is linearly related to radius, so... if period increases faster, that means that the farther you get out there,

the slower you go...

 

[thepatientmental]

If the Sun's gravity were suddenly turned off, the planets would indeed continue moving in a straight line due to Newton's first law of motion. However, this would not necessarily mean that Mercury would ever be farther away from the Sun than Pluto.

This is because the orbits of the planets are not solely determined by the Sun's gravity, but also by their own individual velocities and distances from the Sun. In fact, the planets are constantly moving in elliptical orbits around the Sun, with the Sun at one of the foci.

As for Mercury and Pluto specifically, it is highly unlikely that Mercury would ever reach a point farther away from the Sun than Pluto. This is because Mercury's orbital velocity is much higher than Pluto's, meaning that it would continue to move away from the Sun at a faster rate than Pluto.

To determine how long it would take for Mercury to achieve this passage, we would need to know the exact velocities and distances of both planets at the time the Sun's gravity is turned off. This is a complex calculation and would require knowledge of advanced physics and mathematics.

But in short, it is safe to say that if the Sun's gravity were turned off, the planets would not follow a straight path that would result in Mercury being farther away from the Sun than Pluto. The orbits of the planets are delicately balanced and any significant change in the force of gravity would drastically alter their paths.