# Why do inner planets orbit the sun faster than the outer planets?

Let me begin by thanking you of your question. I had never realised that it was so. Hence, I simply went to Wikipedia and checked the facts.

Yes, you are right. Planets revolve at decreasing orbital velocities as they get further away from . Mercury turns at approximately 47 km per second, Earth at 30 km per second and Pluto, the last one of the throng, at slightly less than 5 km per second.

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Their distance from the Sun is a condition for such behaviour: the further they are from it, the weaker the gravitational attraction, the lesser the centripetal force necessary to keep them in orbit and, therefore, the slower their orbital velocity. Gravity provides the centripetal force. There is no such thing as centrifugal force (i.e. a force acting outwards).

However, such condition is not sufficient to justify the facts you pointed out. Gravity attraction depends on the product of the masses and the inverse square of the distance.

As I did not know, I went meticulously through Wikipedia and, again, checked out the figures.To my astonishment, that is the case.

As one could expect, Jupiter has the largest mass of the solar planets with a value of ##2*10^27## kg . But Mercury, the smallest and closest planet to the Sun, has a mass of ##3*10^23## kg , which is only one in ten thousand times the mass of Jupiter that has more than a million times its volume.

In fact the masses of all the other solar planets are included between ##10^24## and ##10^26## kg . A spread of only two orders of magnitude between the larger and the smaller ones. I was flabbergasted.

I did not do the math (nor do I intend to) to quantify this mass/velocity observation of yours and check it out against the actual orbital distances. People have been doing such computations since Ptolemy and I am certain that you will find comforting figures somewhere around the Web.

##(mv^2)/r=(GMm)/r^2##

where the term on the left is centripetal force and the term on the right is Newton’s law of gravitation.

##m## = mass of the planet and ##M## = mass of the Sun

##v^2=(GM)/r ## as ##m## cancels out

##v =sqrt((GM)/r)##

Therefore, the orbital speed, ##v##, is independent of the mass of the planet and depends only on the orbital radius, ##r##, as ##M## and ##G## are constants.

Isn’t it fantastic that, at my grandfatherly age, I can still learn something important from the young student you probably are?This is what Socrates was, and Socratic is, all about. Thanks goodness his spirit is still around.

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