Goal: To understand gravity Objectives: 1)To understand who discovered what about gravity. 2)To learn about the Universal nature of gravity 3)To explore the Gravitational Constant 4)To understand how gravity is responsible for Tides 5)To understand how gravity changes when you are inside of the earth 6)To understand how gravity can lead to Black Holes! Next hour we will look at orbits

Who discovered gravity? Discuss with a neighbor

Newton Discovers Newton realized that gravity extended far beyond the surface of the earth. Gravity extends to the moon, and even to the other side of the universe. Gravity is truly universal. However, it does fall off with distance.

Inverse Square Law Is just how it sounds. As you get further away from an object, the force of gravity drops as the distance squared. The moon is about 60 times further from the center of the earth than we are. If the gravitational force on me is 950 N on the surface of the earth then what is the force of Earth’s gravity on me from the orbit of the moon?

Putting it together Obviously, the more mass you have the greater the gravitational force is on you. Also, the more mass the other thing has, the greater the pull. So, that means the gravitational force is proportional to mass 1 * mass 2 / distance squared

Gravitational Constant The only thing left out is a constant value which gets everything exactly right. This constant is noted as G (not to be confused with g). G = 6.67 * N m 2 / kg 2 So, the equation is: Force = G * mass1 * mass 2 / (radius * radius) Where radius is the distance between the CENTERS of the two objects

Tides What causes the tides?

Tidal forces Tidal forces are the result of a net difference in the gravitational force on 2 sides of an object. So, the part of the earth facing the moon feels a greater tug than the part away from it. This creates a net force for the parts of the earth near to and far away (near to towards the moon, and far away is away from the moon). At the parts of the earth in the middle, there is no net force. So, material (water mostly) goes towards the two points of greatest force. Thus the high tide!

Basic tidal facts For most places on the earth, there are 2 high tides and 2 low tides a day. Since the earth rotates the position of the tides is about 10 degrees in front of the moon, and on the opposite side of the earth from that. Due to local coastlines, the sizes of the tides vary, but average to be about 1-2 m in height. The moon also affects land! The land tide is about 6 inches, but is so gradual we don’t feel it. Finally, since the moon orbits the earth, the time of the tides changes by about 50 minutes each day – the same as the rise/set times of the moon.

ect/time/tides.html Tide from the sun is 10% that of the moon, but enough to affect the Magnitude of the tides.

Tidally locked! The moon is tidally locked. That means that the position of the “high tide” for the ground on the moon is locked roughly into place.

But wait, there’s MORE! Since the bulge is pulled forward (due to tidal friction), that bulge will tug on the moon, and the moon on the bulge. This will result in a force which slows down the earth’s rotation ( our days increase by 2 milliseconds per day per century). Since energy must be conserved, the moon gains orbital energy, and gets 4 cm further from the earth each year!

How do we know? Sorry hoax enthusiasts, but we know this by shining laser light onto mirrors we placed on the moon (i.e. we had to be there to do this, sorry). By finding the time it takes to come back, they can measure the distance to the moon accurate to a few millimeters.

Gravity inside an object. If you were to drill a hole to the center of the earth, would the gravitational force increase or decrease as you fell down the hole?

Only to the inside Only the mass inside of you counts (assuming symmetry) The mass inside of you falls a lot faster than the radius squared law. So, the gravitational force on you goes DOWN. In fact, in the center, the force is ZERO!

Black Hole A black hole is an object that is either so massive or so dense that the escape velocity on its surface is greater than the speed of light. As Einstein discovered nothing can travel faster than the speed of light. Therefore NOTHING, not even light can escape from a black hole!

No escape! The radius at which the escape velocity is exactly the speed of light is called the Schwarzschild radius. The Schwarzschild radius is an event horizon. An event horizon is a surface where if something were to pass through it, it is gone (event horizon = goodbye forever).

But there’s more! Mass warps space. Time is relative to space. Therefore masses warp time also! Tobject = Tuniversal / (1 – r s / r) 1/2 Where r s is the Schwarzschild radius (the radius of the event horizon of a black hole) r s = 1.5 km * Mass of object / Mass of our sun

Black hole astrophysics What would happen if we swapped our sun for a black hole of exact equal mass? A) The earth would be sucked into the black hole B) Time on the earth would slow down C) The earth would be slingshot out of the solar system D) Nothing would happen to the orbit of the earth or the clocks on earth.

Black hole astrophysics What would happen if we swapped our sun for a black hole of exact equal mass? D) Nothing would happen to the orbit of the earth or the clocks on earth. Black holes are not vacuum cleaners. They obey gravity just like everything else. In fact it is harder to run into a black hole because it is so frikkn small (diameter of 3 km for one the mass of out sun).

Can we “see” black holes? Nope, light can’t escape. However, we do see them indirectly by watching stars or accretion disks in orbit around them. In fact we find lots of them out there. In the center of every galaxy there seems to be one. Ours has a 2.6 million solar mass black hole (which is small, many galaxies have a black hole which is over a billion solar masses)

Death of black holes? Turns out that black holes can die! This is because of Hawking radiation. What is this? Well… Long winded answer coming up that won’t be on the test but is kinda cool!

Conclusion We have examined the universal nature of gravity. We have also seen how gravity causes tides as well as black holes.