Escape Velocity And Newton’s Laws of Gravity

Leaving Earth -CLc. -CLc We have gotten to the point where we do not take much notice of space ships blasting off.

Newton’s Brain Neil deGrasse Tyson on Isaac Newton. on/yt/watch?videoId=7S3uAgyNyrs on/yt/watch?videoId=7S3uAgyNyrs

Newton and His Laws Starting with the works of Galileo and Kepler (then adding his own), Newton deduced three laws of motion which: – describe any moving object (from automobiles to galaxies colliding). – were the underpinnings for Newton’s understanding of gravity. Published in “Mathematical Principles of Natural Philosophy” – 1687.

Newton’s First Law

Newton’s Second Law The acceleration of a body is inversely proportional to its mass, directly proportional to the force, and in the same direction as the force. This law establishes cause and effect. Objects do not just move, they accelerate due to the action of a force. F=MA (F is measured in Newtons * )

A Newton The amount of force needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared. F = 1kg(m/s 2 )

Question How does Newton’s 2 nd law account for your weight?

Newton’s Third Law

Universal Mutual Gravitation From his laws, Newton derived the law of universal gravitation. Law of Universal Gravitation – Gravity is an attractive force between all pairs of massive objects – Gravitational force is proportional to the masses, and inversely proportional to the square of the distance between them.

Universal Mutual Gravitation (Con.) Newton’s law led him to conclude that: 1.Gravity is an Attractive force: It draws massive objects closer together 2.Gravity is a Universal force: It operates everywhere in the Universe. 3.Gravity is a Mutual force: It works between pairs of massive objects.

Question Think about the gravitational force of Jupiter. How would Jupiter’s gravitational effect on Mars differ from its effect on Earth?

G – The Gravitational Constant From his calculations, Newton derived the constant G, which is the gravitational constant. G is the constant that connects mass to gravity – and a term in our formula to figure escape velocity (from Earth or any other planet/star in the universe).

Escape Velocity If you launch a rocket upward, it will consume its fuel in a few moments – reaching its maximum speed. The rocket will then coast upward, leaving us to ask how fast must a rocket “coast” in order to coast away from Earth and its gravity?

Escape Velocity We can calculate the speed needed to escape from the Earth’s gravity and from that of any other astronomical body. Escape velocity is that speed and it has a simple formula. In essence, the escape velocity is directly proportional to the objects mass (the Earth in our case) times the gravitational constant/the radius of the object. The square root of the resulting number is then taken.

Escape Velocity Formula

Escape Velocity Once the calculations are done, we find that the escape velocity for Earth is 11.2 km/s or approximately 24,600 mph. Notice that the escape velocity formula depends on both its mass and radius. – Therefore, a large body could have a low escape velocity if it has a very large radius (examples are giant stars). – Conversely, a small body could have a very large escape velocity if it has a small radius (example – a black hole).

Escape Velocity for Other Planets on MercuryMercury's gravity:4.3 km/s on VenusVenus's gravity:10.3 km/s on Earththe Earth's gravity:11.2 km/s on the Moonthe Moon's gravity:2.4 km/s on MarsMars' gravity:5.0 km/s on JupiterJupiter's gravity:59.5 km/s on GanymedeGanymede's gravity:2.7 km/s on SaturnSaturn's gravity:35.6 km/s on UranusUranus' gravity:21.2 km/s on NeptuneNeptune's gravity:23.6 km/s on PlutoPluto's gravity:1.2 km/s on the event horizona black hole's gravity: = 299,792 km/s (Speed of light)Speed of light

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