Due to our enormous scientific-technological advances, we have discovered a large number of celestial bodies in the universe, therefore, these advances make us think that in the future we could inhabit some of these celestial bodies, especially those with similar conditions to our planet Earth.
Exercise
Assuming that we have colonized a new planet whose geometric shape is circular or spherical, with a radius of 2,200 km, and a gravity of 4.8 m/s2, in relation to the above, answer the following questions:
a.- What would be the escape velocity of such a planet that would allow us to send any body or object to orbit around this new planet?
b.- What would be the mass of that new planet?
Data:
Solution
a.- To answer our first question, we must mention an example, i.e., the minimum initial velocity that allows us to send a given satellite orbiting around the Earth is the so-called escape velocity, therefore, we need to know the escape velocity for the planet Earth by applying the following formula:
This is the escape velocity for the Earth, therefore, we can do the same to find the escape velocity of our new planet, so we can proceed in the following way:
In this way we obtain the minimum initial velocity necessary for a given body or object (such as an artificial satellite) to escape from the gravitational field of our new planet, that is, the escape velocity on that planet.
b.- Now with that escape velocity, we can answer our other question and find the mass (MNP) of our new planet to inhabit, therefore, we have to clear mass from our first formula:
Thus we were able to find the mass of our new planet with the help of the magnitude of the escape velocity.
Conclusion
One of the greatest dreams made true by man through science, is to have managed to take a large number of bodies or objects out of our Earth, this thanks to the understanding of the physical magnitude of the escape velocity, therefore, it allows us to escape or make escape any body or object from the gravitational pull of a particular celestial body, as is the case of our planet Earth and, thus, to apply it to other bodies, if necessary, and thus to know these values of great value.
On this occasion we managed to know important physical magnitudes related to astrophysics, and we know that this branch of science has allowed us to go to the conquest of our outer universe, and thus, to the conquest of our possible change of habitat if necessary later, all this, we did by implementing mathematical formulas and that will be our intention in other deliveries.
Until another opportunity my dear friends.
Note: The images were created by the author using Power Point.
Recommended Bibliographic Reference
[1] Gravitational Forces. Link.
[2] Centripetal Force. Link.
[3] Universal Gravitational Constant. Link.
[4] Escape Velocity. Link.