Download Mars at arrival

Prograde motion (west-to-east)
Leo
Retrograde motion (east-to-west)
Cancer
Mars
Jupiter
Mercury
Sun
Venus
Earth
Moon
Saturn
Visual Parallax
Nicholas Copernicus (15th century)
•universe is heliocentric
•planets orbit Sun in perfect circles
Tycho Brahe (16th century)
• Naked-eye astronomer
• Documented planet motions to within 4
minutes of arc.
• Could not detect stellar parallax
Johannes Kepler (1573-1631)
• Succeeded Tycho
• Used Tycho’s data tables to fit planetary
motions to Copernican model
Kepler’s first law:
Planetary orbits are ellipses, with Sun at one focus
Kepler’s second law:
A line drawn from the planet to the Sun sweeps out equal areas in
equal time intervals
Kepler’s third law:
The square of a planet’s orbital period is proportional to the cube
of its average distance from the sun
p2
= constant
3
a
Earth:
( 1.00 year)2
2/au3
=
1.00
yr
(1.00 AU) 3
Kepler’s third law:
The square of a planet’s orbital period is proportional to the cube
of its average distance from the sun
p2
= constant
3
a
Mars:
( 1.88 year)2
2/au3
=
1.00
yr
(1.52 AU) 3
Kepler’s third law:
The square of a planet’s orbital period is proportional to the cube
of its average distance from the sun
p2
= constant
3
a
Jupiter: (11.87 year)2
2/au3
=
1.00
yr
(5.20 AU) 3
Hohmann transit orbital
Earth
1.00 AU
2.52 AU
1.52 AU
Mars
Hohmann transit orbital
Earth at launch
(spacecraft perihelion)
0.98 AU
2.50 AU
1.52 AU
1.20 AU
Mars at arrival
(spacecraft aphelion)
Hohmann transit orbital
(1.25 au)3
= 1.95 yr2
1.00 au3/yr2
Earth at launch
(spacecraft perihelion)
Mars at arrival
(spacecraft aphelion)
Hohmann transit orbital
(1.25 au)3
= 1.95 yr2
1.00 au3/yr2
Earth at launch
(spacecraft perihelion)
= 1.40 years
Mars at arrival
(spacecraft aphelion)
Hohmann transit orbital
(1.25 au)3
= 1.950 yr2
1.00 au3/yr2
Earth at launch
(spacecraft perihelion)
= 1.40 years
= 510 days (full orbit)
= 255 days (half orbit)
Mars at arrival
(spacecraft aphelion)
Hohmann transit orbital
(1.25 au)3
= 1.95 yr2
1.00 au3/yr2
Mars at launch
Earth at launch: Nov. 26,2011
(spacecraft perihelion)
= 1.40 years
= 510 days (full orbit)
Earth at arrival
= 255 days (half orbit)
Mars at arrival: August 06, 2012
(spacecraft aphelion)
Galileo Galilei (1564 - 1642)
• “Father of modern science”
• First to use telescope for astronomy
• Observations supported a Heliocentric
solar system
• Experiments with gravity, inertia
Galileo Galilei (1564 - 1642)
• “Father of modern science”
• First to use telescope for astronomy
• Observations supported a Heliocentric
solar system
• Experiments with gravity, inertia
Galileo Galilei (1564 - 1642)
• “Father of modern science”
• First to use telescope for astronomy
• Observations supported a Heliocentric
solar system
• Experiments with gravity, inertia
Galileo Galilei (1564 - 1642)
• “Father of modern science”
• First to use telescope for astronomy
• Observations supported a Heliocentric
solar system
• Experiments with gravity, inertia
Galileo’s Moon
Appenine Mountains
described sunspots and their
movement, showing that the Sun
rotates.
described the phases of Venus
Ptolemaic system couldn’t explain full phases
Galileo was the first to observe the moons of
Jupiter and record their motion
Up to this point it was assumed that the motion
of a planet around the Sun would leave a moon
behind
Total distance covered by ball is proportional to time squared
For any steepness or starting height the ball always approaches
the same elevation on the opposite ramp (ignoring friction)…
…if we remove the opposite ramp the ball can never reach the
same elevation and so should continue to roll forever in a straight
line (again ignoring friction).
Inertia: a body at rest remains at rest while a body in motion
remains in motion at a constant velocity, unless acted upon by an
outside force (such as gravity or friction).
Issac Newton (1642-1727)
• Universal Law of Gravitation
• Calculus
• Wave nature of light
Issac Newton (1642-1727)
• Universal Law of Gravitation
• Calculus
• Wave nature of light
Speed:
distance/time
Issac Newton (1642-1727)
• Universal Law of Gravitation
• Calculus
• Wave nature of light
Speed:
distance/time
Velocity:
distance/time in a specific direction
Issac Newton (1642-1727)
• Universal Law of Gravitation
• Calculus
• Wave nature of light
Speed:
distance/time
Velocity:
distance/time in a specific direction
Acceleration: any change in velocity with time (requires an
outside force)
Issac Newton (1642-1727)
• Universal Law of Gravitation
• Calculus
• Wave nature of light
Speed:
distance/time
Velocity:
distance/time in a specific direction
Acceleration: any change in velocity with time (requires an
outside force)
Force:
Mass x Acceleration (weight is an example)
Newton’s Law of Universal Gravitation: The force of
attraction between two bodies is proportional to the
product of their masses and inversely proportional to the
square of the distance between them.
T 0
1
2
3
4
5
T
0
1
2
3
4
5
T 0
0
1
2
3
4
5
1
2
3
4
5
Horizontal velocity (v) is constant
V3
V2
V1
Acceleration (g) is constant
projectile falls to the ground in exactly the
same time.
CM
Ve = √2GM/r
Where:
Ve = escape velocity
G = gravitational constant
M = mass of planet or other body
r = radius of planet or other body
Geocentric or
Geostationary
orbit
EARTH SATELLITES
GPS SATELLITES
Space Elevator
Lagrange Points
Gravity according to Einstein
Gravity according to Einstein
Gravity according to Einstein
Gravity according to Einstein
In a “flat” universe, light travels in a straight line
Earth
Sun
Distant star
In Einstein’s universe, light follows
curvature created by massive objects
Sun
Distant star
Earth
Light sources located behind massive objects
will appear in different positions in the sky
Sun
Distant star
(apparent position)
Distant star (actual position)
Earth
Actual position of star
Apparent position of star
Einstein Cross
Distant galaxy
Multiple images of the same
(more distant) quasar
Einstein Ring
Distant blue galaxy,
distorted into ring
LRG 3-757 (foreground galaxy)