Expert: Philip Stahl - 8/27/2010

Question
How is it that gravity supposedly holds the 8 known planets in orbit around our sun when they are so far away ?

Answer
Hello,

It really is no problem at all! You can actually compute the magnitude of the force of gravitational attraction, and it will be found to quite significant for each of the planets! Don't forget that while F (force of attraction) falls off as the inverse square of the distance, you are *also* reckoning in a product of the masses which can be quite considerable.

Let's take the force of attraction of the Sun on the Earth, and we employ the standard Newtonian equation:

F = G Mm/ r^2

where r = 1.5 x 10^11 m

G = 6.7 x 10^-11 N-m^2/kg^2

M = 2 x 10^30 kg,    m = 6 x 10^24 kg

Then F = 3.5 x 10^22 N

which is no measly amount! (Note the '22' exponent)

While it is true the 1/r^2 is on the order of 10^-22

this is more than compensated for by a mammoth mass product yielding an exponent of 54!

Using a table of masses, you can use the same formula as given above to work out the forces of attraction for each of the planets and all will be fond to be considerable!

Even little Pluto - estimated mass ~  6 x 10^21 kg - will experience a force of attraction to the Sun of:

F ~  2.2 x 10^16 N

The peculiar aspect of gravitation is that while a putatively "weak" force for normal distances and masses, it becomes quite significant when one factors in and multiplies the products of typical planet masses with the Sun's.

So, once more - don't be fooled or misled by the distances, without also factoring in the magnitudes of the masses! (And be sure when you do these sort of calculations your units are consistent!)