| Planet | Density, d | Radius, r | Est. Gravity, ge*d*r^3 /de*re^3 | Gravity, g |
|---|---|---|---|---|
| Earth | 5515 | 6378.1 | - | 9.798 |
| Mercury | 5427 | 2439.7 | 0.5396187681 | 3.7 |
| Venus | 5243 | 6051.8 | 7.9570393314 | 8.87 |
| Mars | 3933 | 3396.2 | 1.0549251963 | 3.71 |
| Moon | 3350 | 1738.1 | 0.1204445163 | 1.62 |
| Pluto | 1750 | 1195 | 170.3312091696 | 11.15 |
| Sun | 1408 | 695500 | 3243485.82145521 | 274 |
| Jupiter | 1326 | 71492 | 3317.6747704011 | 24.92 |
| Uranus | 1270 | 25559 | 145.1955281771 | 8.87 |
| Saturn | 687 | 60268 | 1029.7576378577 | 10.44 |
The 4th column is an estimate of gravity based on
gravity = \(\frac{d*r^3}{de*re^3}\).\({g}_{e}\)
Because gravity is directly proportional to density and radius3
For the case of Mars,
\({g}_{m}\) = (3933*(3396.2)^3) / (5515*(6378.1)^3) * 9.798 = 1.0549 ms-2.
The published data are not consistent.
The estimation using
\({G}_{o}.density.\frac{4}{3}\pi{(r1)}^3m. \frac{1}{(r1+x)^2}\) is wrong, because after the estimation, the estimated value is applicable only to the original formula involving the factor \(\frac{1}{(r1+x)^2}\) not a new formula with a factor of \(\frac{1}{(r2+x)^2}\), where r2 radius of the body for which surface gravity is to be estimated. In all cases, x must be set to zero for the estimation to be valid, ie. x = 0. Furthermore both the formulas are for point mass and does not apply to values x < r1 nor can r1 < x < r2, if both formulas are to be considered together. The following graph illustrate the point that 5/(1+x)^2 and 125/(5+x)^2 are simply different.
The graphs plotted are:
blue curve 1/((1+x)^2)
red curve 125/((5+x)^2)
green curve 5/((1+x)^2)
grey curve 5/((5+x)^2)
Notice the intersection at x = 0 between the green and red curve, that's what the approximation is about. But for values other than x = 0, they are simply two different curves. The grey curve is often used after the calculation to estimate gravity, which is clearly wrong.
