Gravity by Newton
Sir Isaac Newton’s second law of motion states: The acceleration of an object is equal to the net force applied to it, divided by its mass. Mathematically this can be represented more simply as:
F = ma.
In 1665 Newton went on to develop the law of universal gravitation, which is given by the following equation:
F_{g}= GM_{1}M_{2}/R^{2}
This shows that the gravitational force between two masses is found by product of their masses, times the gravitational constant – G, and divided by the square of distance between them. The value of G was originally determined experimentally by Henry Cavendish and has a value of 6.67×10^{-11} N (m^{3}/kg-s^{2})
By using these two equations, one can derive another equation that shows the acceleration due to gravity at the surface of a planet.
g = GM/R^{2},
Where M is the mass of the planet and R is its radius.
A Tour Of The Planets
The surface gravity of the planets, as determined by the equation above and shown relative to Earth’s gravity can be seen below in the first column. In the second and third columns the value of the acceleration (g), felt at the surface is shown in Metric and English units:
Object…………..g/g-earth……Acceleration at the surface
- Mercury:……….0.378………. g = 3.78 m/s^{2}…..(12.1 ft/s2)
- Venus:………… 0.903………. g = 8.8 m/s^{2}…….(29.1 ft/s2)
- Earth:……………1.0……………g = 9.78 m/s^{2}…..(32.1 ft/s2)
- Mars:……………..0.377………..g = 3.72 m/s^{2}…..(12.1 ft/s2)
- Jupiter:………….2.36………….g = 23.1 m/s^{2}…..(75.9 ft/s2)
- Saturn:………….1.07………….g = 9.05 m/s^{2}…..(29.4 ft/s2)
- Uranus:…………0.889………..g = 8.69 m/s^{2}…..(28.5 ft/s2)
- Neptune:……….1.12………….g = 11.0 m/s^{2}…..(36.0 ft/s2)
- Pluto:……………0.06………….g = .6 m/s^{2}………(1.90 ft/s2)
- Sun:……………28.0……………g = 274 m/s^{2}……(899 ft/s2)
- Moon:…………..0.165…………g = 1.63 m/s^{2}…..(5.30 ft/s2)
- Ganymede:…..0.145………….g = 1.42 m/s^{2}…..(4.66 ft/s2)
Points of Interest
Some interesting observations can be made from this data:
- Even though Ganymede, a moon of Jupiter, is the largest moon in the Solar System, (in fact it’s larger than Mercury) its surface gravity is less than half of Mercury’s, and it’s even less than our Moon’s. This is an indication that the density of Ganymede is less than these other objects, and it is most likely composed of ice and rocky materials, whereas our Moon and Mercury are all rock and therefore denser.
- These values vary depending on the density of the planet and its radius. Saturn is much larger than the Earth but its density is much less than the Earth’s, (it’s about 1/8 as dense) and therefore its surface gravity is much smaller than you might expect.
- You may see some variation on the values for surface gravity, especially for the gas giants. This is partly because they do not have a solid surface, and selecting a value for the radius – R is subject to some debate. Also, the mass of these planets is constantly being refined as we track probes that pass by them and measure the gravitational effects on the known mass of the probes.
To calculate your weight as you hop about the Solar System all you need to know is your mass (m) in kilograms for the metric system (slugs in the English system) and multiply it by the appropriate value of “g" for the planet of your choice.
F = mg
Note that your weight will be the units of Newtons in the metric system and pounds in the English system.
References
https://hyperphysics.phy-astr.gsu.edu/hbase/solar/soldata2.html#c4
https://nssdc.gsfc.nasa.gov/planetary/factsheet/
https://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html