Calculate Surface Gravity Activity

The table below gives the mass, radius and surface gravity for many of the larger bodies in the Solar System.

Body	Mass (kg)	[Earth =1]	Radius (km)	[Earth =1]	Surface Gravity (m/s²)
Sun	1.99 x 10³⁰	[330,000]	696000	[110]	274
Mercury	3.30 x 10²³	[0.06]	2439	[0.38]	3.7
Venus	4.87 x 10²⁴	[0.81]	6051	[0.95]	8.9
Earth	5.98 x 10²⁴	[1.00]	6378	[1.00]	9.8
Moon	7.35 x 10²²	[0.01]	1738	[0.27]	1.6
Mars	6.42 x 10²³	[0.11]	3393	[0.53]	3.7
Phobos	1.08 x 10¹⁶	[0.00]	11	[0.002]	0.006
Deimos	1.8 x 10¹⁵	[0.00]	6	[0.001]	0.003
Ceres	8.7 x 10²⁰	[0.0001]	467	[0.07]	0.3
Vesta	3.0 x 10²⁰	[0.00005]	265	[0.04]	0.3
Pallas	3.18 x 10²⁰	[0.00005]	261	[0.04]	0.3
Jupiter	1.90 x 10²⁷	[318]	71492	[11.2]	24.8
Io	8.93 x 10²²	[0.01]	1815	[0.28]	1.8
Europa	4.80 x 10²²	[0.01]	1569	[0.25]	1.3
Ganymede	1.48 x 10²³	[0.02]	2631	[0.41]	1.4
Callisto	1.08 x 10²³	[0.02]	2400	[0.38]	1.3
Saturn	5.69 x 10²⁶	[95]	60268	[9.45]	10.4
Titan	1.35 x 10²³	[0.02]	2575	[0.40]	1.4
Uranus	8.68 x 10²⁵	[15]	25559	[4.01]	8.9
Neptune	1.02 x 10²⁶	[17]	24764	[3.88]	11.1
Pluto	1.29 x 10²²	[0.002]	1150	[0.18]	0.7
Charon	1.90 x 10²¹	[0.0003]	564	[0.09]	0.4

You can claculate the comparitive surface gravity of each body approximately by dividing the value in the last column by 10. So the surface gravity on jupiter can be said to be about 2.5g or two and a half times as strong as on Earth. On the Sun it is about 27 times as strong as on Earth and on Mars it is about a third.

Note that the Gas Giant planets (Jupiter, Saturn, Uranus and Neptune) do not have solid surfaces. The radius of these planets is specified as the point where the pressure in their atmosphere is approximately equal to that at the surface of the Earth. Phobos and Deimos (the moons of Mars) are oddly shaped and the radius given is an average. Ceres, Pallas and Vesta are the three largest asteroids that orbit between Mars and Jupiter. In 1802 Ceres and Pallas were considered to be planets, but were downgraded to asteroids when it was realised there were many such things orbiting between Mars and Jupiter (see this US Naval Observatory page for more details).

Calculate it for yourself...

The surface gravity (g) of a body depends on the mass (M) and the radius (r) of the given body. The formula which relates these quantities is:

When calculating the surface gravity using this formula it is best to stick to the MKS system where the units for distance are meters, the units for mass are kilograms, and the units for time are seconds. In this system, the gravitational constant has the value:

As an example, the mass M of the Earth is 5.98 x 10²⁴ kilograms. The radius r of the Earth is 6378 kilometers, which is equal to 6.378 x 10⁶ meters. The surface gravity on Earth can therefore be calculated by:

So, a simple formula from the science of Physics can be used to calculate the surface gravity for a body (in this case the Earth) if you know the mass of the body and its radius! The assumption in using this formula is that the body is spherical, but this is a pretty good assumption. If the radii of a body at its equator and pole are very different, then the surface gravity is different at those places and should be calculated separately.

The surface gravity for the Earth is therefore 9.81 meters per second², or 9.81 meters per second per second. This is the acceleration due to gravity that an object feels near the surface of the Earth. For example, if an object were dropped from rest near the Earth's surface, it would accelerate to a velocity of 9.81 meters per second after one second, and the velocity would increase by another 9.81 meters per second for every additional second that the object was falling (in the vicinity of the Earth's surface).

g	=	*G M / r²**
	=	*(6.67 x 10^-11) (5.98 x 10²⁴) / (6.378 x 10⁶)²**
	=	9.81 meters/second²