Astronomy 101 The Solar System Tuesday, Thursday Tom Burbine

Course Course Website: – Textbook: –Pathways to Astronomy (2nd Edition) by Stephen Schneider and Thomas Arny. You also will need a calculator.

HWs #1, 2, 3, 4, and 5 HWs on Spark: If you can’t get on Spark, the HWs are also on the website: Due Date: February 2, :00 PM

Exam #1 Next Thursday Covers all material from January 19-28

A hypothesis is an educated guess, based on observation. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven, but not proven to be true. A scientific theory summarizes a hypothesis or group of hypotheses that have been supported with repeated testing. A theory is valid as long as there is no evidence to dispute it. Therefore, theories can be disproven. A law generalizes a body of observations. At the time it is made, no exceptions have been found to a law.

Kepler’s Three Laws http://brunelleschi.imss.fi.it/museum/esim.asp?c=

Orbits all the planets orbit the Sun in a counterclockwise direction (but they do not orbit it at the same rate). The Earth rotates counterclockwise The Sun, the Moon, the planets, and the stars all rise in the east and set in the west

Arguments against the Sun being the center of the solar system 1) If the Earth was moving, objects such as birds and clouds would be left behind as the Earth moved 2) The heavens must be perfect and unchanging. Noncircular orbits do not fit this model 3) Stellar parallax would be observable

Galileo Galilei ( ) He was able to figure out answers to these arguments 1) Things in motion tend to remain in motion. 2) He used a telescope to see sunspots on the Sun and features on the Moon. 3) Galileo found that stars were more numerous and more distant than imagined

He also He discovered the moons of Jupiter and saw that they were orbiting Jupiter –Io –Europa –Ganymede –Callisto Proving that bodies could orbit other bodies besides the Earth

Galileo also found that Venus orbited the Sun

Acceleration Acceleration is when your velocity is changing Velocity not changing, no acceleration

Acceleration a = ∆v/∆t Car is travelling at 10 m/s Increases its speed to 30 m/s over 5 seconds a = (30 m/s – 10 m/s)/5 seconds a = 4 m/s 2

Difference between mass and weight Mass is the amount of matter in your body Weight is the amount of force acting on your body So on the Moon, you would have the same mass as on Earth but weigh less on the Moon since the Moon is less massive than Earth

Supposedly saw an apple fall to the ground He then understood that gravity was universal, meaning it affected both the planets and us on Earth Came up with 3 Laws of Motion Isaac Newton ( )

Force Force – anything that can cause a body to change velocity

Gravity Gravity is a natural phenomenon by which objects with mass attract one another.

Newton’s 1 st Law In the absence of a net (overall) force acting upon it, an object moves with a constant velocity An object at rest remains at rest An object in motion tends to remain in motion unless a force is acting upon it

Why do things on Earth not remain in motion?

Friction

Newton’s 2 nd Law Force = mass x acceleration Units of Force kg  m/s 2 = newton

Newton A Newton is equal to the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second per second

How much do you weigh? So much do you weigh Say your mass is 100 kg F = 100 kg x 9.8 m/s 2 F = 980 Newtons 9.8 m/s 2 is the acceleration of gravity on Earth This is the acceleration due to the Earth’s gravitational field

Newton’s 3 rd Law For any force, there is an equal and opposite reaction force Gravity is holding you on the ground The ground is also pushing back up on you with the same amount of force

Newton’s Universal Law of Gravitation Every mass attracts every other mass through the force called gravity Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses

Formula Newton came up with this formula Force is proportional to M 1 M 2 r 2 M 1, M 2 are the masses of the two objects r is the distance between the objects

If you want to calculate actual forces F = G M 1 M 2 r 2 M 1, M 2 are the masses of the two objects r is the distance between the objects G = constant = 6.67 x m 3 /(kg  s 2 )

So what should you know about this formula F = G M 1 M 2 r 2 The force of attraction between any two objects is directly proportional to the product of their masses The force of attraction between two objects decreases with the square of the distance between their centers G is a very small number

assume all mass is concentrated in the center of a body r r

What is the attraction of two people in this room? F = G M 1 M 2 r 2 Say their masses are both 100 kg Their distances are 10 meters apart F = 6.67 x m 3 /(kg  s 2 ) * 100*100 kg 2 /(10*10 m 2 ) F = 6.67 x N = N Remember the person weighs 980 N

F = G M 1 M 2 r 2 The value of G was determined by Henry Cavendish between G = 6.67 x m 3 /(kg  s 2 ) calculate-the-gravitational-constant-like-cavendish- did/ calculate-the-gravitational-constant-like-cavendish- did/

F = G M 1 M 2 r 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

F = G M 1 M 2 = G M 1 M 2 = 4 G M 1 M 2 (r/2) 2 r 2 /4 r 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

Acceleration of gravity (g) M is the Earth’s mass F = ma = G Mm r is the Earth’s radius r 2 m is the mass of an object F is the force a is the acceleration a = G M r 2 g = a = G M r 2

Acceleration of gravity (g) M is the Earth’s mass g = G M r is the Earth’s radius r 2 g = 6.67 x m 3 /(kg  s 2 ) * (6.0 x kg) (6.4 x 10 6 m) * (6.4 x 10 6 m) g = 9.8 m/s 2

Gravitational acceleration Gravitational acceleration is different on different planets because they have different sizes and masses Gravitational acceleration (on Moon) = 1.6 m/s² (0.165 g) Gravitational acceleration (on Jupiter) = 24.8 m/s² (2.53 g)

Experiment on the Moon

How things fall Heavy and light objects fall at the same rate The heavy object does not fall faster (as long as there is no air resistance) g = G M (does not depend on mass of object) r 2

How does gravity work? Gravity distort space-time einsteins-messengershttp:// einsteins-messengers

Escape velocity Velocity above this will allow an object to escape a planet’s gravity For Earth: v = square root[(2 x 6.67 x m 3 /(kg  s 2 ) x (6.0 x kg)] (6.4 x 10 6 m) v = square root [1.25 x 10 8 m 2 /s 2 ] v = 11.2 x 10 3 m/s = 11.2 km/s v

Escape velocity Escape velocity is different on different planets because they have different sizes and masses Escape velocity (on Moon) = 2.4 km/s Escape velocity (on Jupiter) = 59.5 km/s

What causes tides on earth? Moon pulls on different parts of the Earth with different strengths khttp:// k

Forces on Water Average Force on 1 kg water on Earth from Moon F = G M m = 6.67 x m 3 /(kg  s 2 ) * (7.35 x kg) * (1 kg) r 2 (3.84 x 10 8 m) 2 F = 3.33 x N Force of 1 kg on water on near-side of Earth from Sun F = G M m = 6.67 x m 3 /(kg  s 2 ) * (7.35 x kg) * (1 kg) r 2 (3.84 x 10 8 m x 10 6 m) 2 F = 3.44 x N Difference in forces is 1.1 x N Called Tidal Force

Tidal force arises because the gravitational force exerted on one body by a second body is not constant across its diameter Water flows so this tidal force causes the tides that are seen on Earth

Effects on tides due to Sun Sun exerts a stronger gravitational force on the Earth But since farther away, the differential force from one side of the Earth to the other is smaller Sun’s tidal effect is about one-half that of the Moon

Forces on Water Average Force on 1 kg water on Earth from Sun F = G M m = 6.67 x m 3 /(kg  s 2 ) * (2 x kg) * (1 kg) r 2 (1.5 x m) 2 F = x N Force of 1 kg on water on near-side of Earth from Sun F = G M m = 6.67 x m 3 /(kg  s 2 ) * (2 x kg) * (1 kg) r 2 (1.5 x m x 10 6 m) 2 F = x N Difference in forces is 5.0 x N due to Sun Difference in forces is 1.1 x N due to Moon

Remember Force downwards is 9 Newtons on 1 kg of water Water won’t be pulled off Earth Water can flow

Shoemaker-Levy 9 Comet that hit Jupiter Jupiter-orbiting comet Broken apart by tidal forces Discovered in 1993 Hit Jupiter in 1994

Roche Limit The smallest distance at which a natural satellite can orbit a celestial body without being torn apart by the larger body's gravitational force (tidal forces). The distance depends on the densities of the two bodies and the orbit of the satellite. If a planet and a satellite have identical densities, then the Roche limit is times the radius of the planet. Jupiter's moon Metis and Saturn's moon Pan are examples of natural satellites that survive despite being within their Roche limits

Why is the Roche Limit important? Comet Shoemaker-Levy 9's decaying orbit around Jupiter passed within its Roche limit in July, 1992, causing it to break into a number of smaller pieces. All known planetary rings are located within the Roche limit

Impact of Shoemaker-Levy 9 The first impact occurred at 20:15 UTC on July 16, 1994 Fragment A of the nucleus slammed into Jupiter's southern hemisphere at a speed of about 60 km/s. Instruments on Galileo detected a fireball which reached a peak temperature of about 24,000 K, compared to the typical Jovian cloudtop temperature of about 130 K, before expanding and cooling rapidly to about 1500 K after 40 s.

Has this happened before? Ganymede

Any Questions?