At the turn of the 17th and 18th centuries, there lived in Britain a scientist, Isaac Newton, who was distinguished by great powers of observation. It so happened that the view of the garden, where apples fell from branches to the ground, helped him discover the law of universal gravitation. What force makes the fetus move faster and faster towards the surface of the planet, according to what laws does this movement occur? Let's try to answer these questions.
And if these apple trees, as Soviet propaganda once promised, grew on Mars, what would that fall be like then? Acceleration of free fall on Mars, on our planet, on other bodies of the solar system… What does it depend on, what values does it reach?
Free fall acceleration
What is remarkable about the famous Leaning Tower of Pisa? Tilt, architecture? Yes. And it’s also convenient to throw down various objects from it, which was what the famous Italian explorer Galileo Galilei did at the beginning of the 17th century. Throwing down all sorts of gizmos, he noticed that the heavy ball in the first moments of the fall moves slowly, then its speed increases. The researcher was interested in the mathematical law according to whichspeed change occurs.
Measurements made later, including by other researchers, showed that the speed of the falling body:
- for 1 second of fall becomes equal to 9.8 m/s;
- in 2 seconds - 19.6 m/s;
- 3 – 29.4 m/s;
- …
- n seconds – n∙9.8 m/s.
This value of 9.8 m/s∙s is called "free fall acceleration". On Mars (Red Planet) or another planet, is the acceleration the same or not?
Why is it different on Mars
Isaac Newton, who told the world what universal gravitation is, was able to formulate the law of free fall acceleration.
With advances in technology that have raised the accuracy of laboratory measurements to a new level, scientists have been able to confirm that the acceleration of gravity on planet Earth is not such a constant value. So, at the poles it is greater, at the equator it is less.
The answer to this riddle lies in the above equation. The fact is that the globe, strictly speaking, is not quite a sphere. It is an ellipsoid, slightly flattened at the poles. The distance to the center of the planet at the poles is less. And how Mars differs in mass and size from the globe… The acceleration of free fall on it will also be different.
Using Newton's equation and common knowledge:
- mass of the planet Mars − 6, 4171 1023 kg;
- average diameter − 3389500 m;
- gravitational constant − 6, 67∙10-11m3∙s-2∙kg-1.
It will not be difficult to find the acceleration of free fall on Mars.
g Mars=G∙M Mars / RMars 2.
g Mars=6, 67∙10-11∙6, 4171 1023 / 33895002=3.71 m/s2.
To check the received value, you can look into any reference book. It coincides with the table, which means that the calculation was made correctly.
How acceleration due to gravity is related to weight
Weight is the force with which any body with mass presses on the surface of the planet. It is measured in newtons and is equal to the product of the mass and the acceleration of free fall. On Mars and any other planet, of course, it will be different from the earth. So, on the Moon, gravity is six times less than on the surface of our planet. This even created certain difficulties for the astronauts who landed on a natural satellite. It turned out to be more convenient to move around, imitating a kangaroo.
So, as it was calculated, the free fall acceleration on Mars is 3.7 m/s2, or 3.7 / 9.8=0.38 of Earth.
And this means that the weight of any object on the surface of the Red Planet will be only 38% of the weight of the same object on Earth.
How and where it works
Let's travel mentally through the Universe and find the acceleration of free fall on planets and other space bodies. NASA astronauts plan to land on one of the asteroids within the next decades. Let's take Vesta, the largest asteroid in the solar system (Ceres was bigger, but it was recently transferred to the category of dwarf planets, “promoted in rank”).
g Vesta=0.22 m/s2.
All massive bodies will become 45 times lighter. With such a small gravity, any work on the surface will become a problem. A careless jerk or jump will immediately throw the astronaut several tens of meters up. What can we say about plans for the extraction of minerals on asteroids. An excavator or drilling rig will literally have to be tied to these space rocks.
And now the other extreme. Imagine yourself on the surface of a neutron star (a body with the mass of the sun, while having a diameter of about 15 km). So, if in some incomprehensible way the astronaut does not die from the off-scale radiation of all possible ranges, then the following picture will appear before his eyes:
g n.stars=6, 67∙10-11∙1, 9885 1030 / 75002=2 357 919 111 111 m/s2.
A coin weighing 1 gram would weigh 240 thousand tons on the surface of this unique space object.
