Escape Velocity

Enter Newton(Newton’s Laws of Gravity)

Newton’s Brain

• Neil deGrasse Tyson on Isaac Newton. • http://www.cleanvideosearch.com/media/acti

on/yt/watch?videoId=7S3uAgyNyrs

Leaving Earth

• https://www.youtube.com/watch?v=OnoNITE-CLc.

• We have gotten to the point where we do not take much notice of space ships blasting off.

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.

For a constant mass, force equals mass times acceleration: F=ma

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 (or F=mg – where g is the strength of a constant gravitational field)

Question

• How does Newton’s 2nd 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 States:1. Gravity is an Attractive force between all pairs of massive

objects - drawing them closer together2. Gravity is a Universal force: It operates everywhere in the

Universe.3. Gravity is a Mutual force: It works between pairs of massive

objects.4. Gravitational force is proportional to the masses, and inversely

proportional to the square of the distance between them.

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

The lowest velocity that a body must attain in order to escape the gravitational attraction of a particular planet or other object.

Earth’s escape velocity is 11.2 km/s or 24,600 mph.

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. – 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 large radius and a low density (example - Mars). – Conversely, a small body could have a very large escape

velocity if it has a small radius and very high density (example – a black hole).

Escape Velocity for Other Planetson Mercury Mercury's gravity: 4.3 km/s

on Venus Venus's gravity: 10.3 km/s

on Earth the Earth's gravity: 11.2 km/s

on the Moon the Moon's gravity: 2.4 km/s

on Mars Mars' gravity: 5.0 km/s

on Jupiter Jupiter's gravity: 59.5 km/s

on Ganymede Ganymede's gravity: 2.7 km/s

on Saturn Saturn's gravity: 35.6 km/s

on Uranus Uranus' gravity: 21.2 km/s

on Neptune Neptune's gravity: 23.6 km/s

on Pluto Pluto's gravity: 1.2 km/s

on the event horizon a black hole's gravity: = 299,792 km/s (Speed of light)

Escape Velocity

• Last Words