Astronomy: Early The Greeks
Pythagoras (560-480 BC): Earth was spherical, based on mysticism (spheres are perfect, shapes and the gods are perfect) Aristotle (384-322 BC): Argued spherical Earth based on naked-eye observations, earth surface appears curved during lunar eclipse Aristarchus (310-230 BC): First to propose a suncentered solar system
Size of the Earth
Eratosthenes (276-195 BC): First to measure the size of the Earth How did Eratosthenes do it? Sun at noon directly overhead at noon at Syene, but was at ~70 angle with the ground at Alexandria. Sun's rays are parallel 3600 around a whole circle
Size of the Earth
Syene and Alexandria 5000 stadia (~500 miles) apart Circumference of earth is thus (360/7) x 500 miles or ~ 25,000 miles
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Motion of the Planets
Eudoxus (400-347 BC): Geocentric (earth-centered) solar system, each body mounted on its own transparent sphere, could not explain retrograde motion (planet movement across the sky changing direction) Ptolemy (90-168 AD): Geocentric, each planet moved on one small circle (epicycle), which moved on a larger circle (deferent). Prevalent theory until 16th century Courtesy of Dr. S.J. Daunt, U. of Tenn.
The Renaissance
Copernicus (1473-1543): Could not reconcile Ptolemy's geocentric model with observations Reconsidered Aristarchus's idea of a heliocentric solar system Retrograde motion explained by one planet on a smaller orbit overtaking another planet Can also calculate distances from sun to planets (relative to earthsun distance)
Courtesy of Dr. S.J. Daunt, U. of Tenn.
Tycho and Kepler
Tycho Brahe (1546-1601): Stubbornly disagreed with Copernicus, believed the sun orbited the Earth and all other planets orbited the sun. Died of mercury poisoning, some say given to him by his assistant Johannes Kepler. Kepler (1571-1630): Inherited all of Brahe's observational data Determined that planets did not follow circular orbits, but ellipses
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Kepler's Laws
1. Planets move in elliptical orbits with the Sun at one focus of the ellipse. 2. The orbital period of a planet varies such that a line joining the Sun and the planet will sweep equal areas in equal time intervals.
Earth R = 1 AU = 150,000,000 km Orbital period T: 1 yr 365.25 days
Sun
Orbital Speed of Earth around Sun:
Earth
VEarth !
Total Dist. Time
=
2# "150,000,000 km 2#R ! Time 365.25 " 24 " 60 " 60 sec
= 30 km/s
Mars R = 1.52 AU Orbital period T: 1.88 yrs
Sun
Mars
Kepler's 3rd Law T2 $R3 or T $ R3/2
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Mars R = 1.52 AU Orbital period T: 1.88 yrs
Sun
Mars
V $ 1/R1/2
VMars !
Total Dist. Time
!
2# "1.52 "150,000,000 km 1.88 " 365.25 " 24 " 60 " 60 sec
= 24 km/s
Kepler's Law Applied to the Planets Planet Mercury Venus Earth Mars Jupiter Saturn T (yr) 0.24 0.62 1 1.88 11.9 29.5 R (AU) 0.39 0.72 1 1.52 5.2 9.54 T2 0.06 0.39 1 3.53 142 870 R3 0.06 0.37 1 3.51 141 868 Speed (km/s) 61 30 38 24 13 10
Kepler's Laws
III. The amount of time a planet takes to orbit the Sun is related to its orbit's size such that the period P, squared, is proportional to the semi-major axis, a, cubed
P2 = a3
or
P = a3/2
where P is in years and a is in astronomical units (AU).
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Critical Speeds to Remember Speed of Solar Wind: Orbital Speed of Earth around Sun: Orbital Speed of Mars around Sun: Speed of Satellite in Low Earth Orbit: Car moving Down the Freeway: 400 km/s 30 km/s 24 km/s 8 km/s 100 km/hr
or 1.67 km/min or 0.03 km/s
How to Get to Mars? Place the planets ready for a mission from Earth to Mars Chose a speed at which you wish to travel to Mars Does the Configuration work?
Earth Mars
Possible Solution (1) Start Earth Behind Mars
Mars
Earth
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Possible Solution (1) 3 Months Later Requires 7km/s acceleration plus deceleration at Mars Mars at arrival Earth at arrival Mars at launch Earth at launch
Stay On Mars (2) 1 Month Stay on Mars
Mars at departure Mars at arrival Earth at departure Earth at arrival Mars at launch Earth at launch
Departure from Mars Have to decelerate to fall into closer orbit Earth pulls away from Mars Almost impossible to catch up with Earth and requires stay on Mars to allow planetary alignment
Mars at departure Mars at arrival Earth at departure Earth at arrival Mars at launch Earth at launch
Return planetary trips is very difficult
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Orbital Transfer (a) To move outwards into the solar system, spacecraft has to increase speed relative to the planet
Mars at arrival Earth at arrival Mars at launch Earth at launch Increase Orbital speed
(b) Faster you travel from Earth means more braking required at arrival at the planet
e.g. Earth 30 km/s, spacecraft + 7 km/s; Mars is ...