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Stable Orbits Kepler’s Laws Newton’s Gravity Stable Orbits, Kepler’s Laws and Newton’s Law of Gravity I. Stable Orbits A. A satellite with no horizontal velocity will __________________. B. A satellite with some horizontal velocity will follow a ___________. C. A satellite with sufficient horizontal velocity will fall at the same rate that the Earth is curving away from it, maintaining a constant height above the ground. This satellite will be in a _______________ orbit. D. Essentially all satellites, moons and planets move in __________ orbits. I. Stable Orbits A. A satellite with no horizontal velocity will __fall straight down__. B. A satellite with some horizontal velocity will follow a ___________. C. A satellite with sufficient horizontal velocity will fall at the same rate that the Earth is curving away from it, maintaining a constant height above the ground. This satellite will be in a _______________ orbit. D. Essentially all satellites, moons and planets move in __________ orbits. I. Stable Orbits A. A satellite with no horizontal velocity will __fall straight down__. B. A satellite with some horizontal velocity will follow a _curved path_. C. A satellite with sufficient horizontal velocity will fall at the same rate that the Earth is curving away from it, maintaining a constant height above the ground. This satellite will be in a _______________ orbit. D. Essentially all satellites, moons and planets move in __________ orbits. I. Stable Orbits A. A satellite with no horizontal velocity will __fall straight down__. B. A satellite with some horizontal velocity will follow a _curved path_. C. A satellite with sufficient horizontal velocity will fall at the same rate that the Earth is curving away from it, maintaining a constant height above the ground. This satellite will be in a __stable circular__ orbit. D. Essentially all satellites, moons and planets move in __________ orbits. I. Stable Orbits A. A satellite with no horizontal velocity will __fall straight down__. B. A satellite with some horizontal velocity will follow a _curved path_. C. A satellite with sufficient horizontal velocity will fall at the same rate that the Earth is curving away from it, maintaining a constant height above the ground. This satellite will be in a __stable circular__ orbit. D. Essentially all satellites, moons and planets move in _elliptical__ orbits. F. Speeds vary for a planet as it moves around the Sun in an elliptical orbit. Speed Distance From Sun E. Planets near the Sun will orbit with a _______ speed. Planets far from the Sun will orbit with a _________ speed. F. Speeds vary for a planet as it moves around the Sun in an elliptical orbit. faster Speed slower Distance From Sun E. Planets near the Sun will orbit with a _______ speed. Planets far from the Sun will orbit with a _________ speed. F. Speeds vary for a planet as it moves around the Sun in an elliptical orbit. faster Speed slower Distance From Sun E. Planets near the Sun will orbit with a _faster_ speed. Planets far from the Sun will orbit with a _________ speed. Sun F. Speeds vary for a planet as it moves around the Sun in an elliptical orbit. faster Speed slower Distance From Sun E. Planets near the Sun will orbit with a _faster_ speed. Planets far from the Sun will orbit with a __slower__ speed. Sun F. Speeds vary for a planet as it moves around the Sun in an elliptical orbit. faster Speed slower Distance From Sun E. Planets near the Sun will orbit with a _faster_ speed. Planets far from the Sun will orbit with a __slower__ speed. faster slower II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _______ with the Sun at one _______. Sun 2. A line joining the Sun and the planet sweep out equal ______ in equal _______. 3. The square of the planet’s orbital _______ is directly proportional to the cube of the ______________ of the planet’s orbit. II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. Sun 2. A line joining the Sun and the planet sweep out equal ______ in equal _______. 3. The square of the planet’s orbital _______ is directly proportional to the cube of the ______________ of the planet’s orbit. focus II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. focus Sun elliptical orbit 2. A line joining the Sun and the planet sweep out equal ______ in equal _______. 3. The square of the planet’s orbital _______ is directly proportional to the cube of the ______________ of the planet’s orbit. focus II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. focus Sun elliptical orbit 2. A line joining the Sun and the planet sweep out equal _areas_ in equal _times_. 3. The square of the planet’s orbital _______ is directly proportional to the cube of the ______________ of the planet’s orbit. focus II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. focus Sun elliptical orbit A2 A1 A3 A1 = A2 = A3 3. The square of the planet’s orbital _______ is directly proportional to the cube of the ______________ of the planet’s orbit. 1 month 2. A line joining the Sun and the planet sweep 1 month out equal _areas_ in equal _times_. focus II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. focus Sun elliptical orbit A2 A1 A3 A1 = A2 = A3 3. The square of the planet’s orbital _period_ is directly proportional to the cube of the _semimajor axis_ of the planet’s orbit. 1 month 2. A line joining the Sun and the planet sweep 1 month out equal _areas_ in equal _times_. focus II. Kepler’s 3 Laws 1. The orbit of a planet around the Sun is an _ellipse_ with the Sun at one _focus_. focus Sun elliptical orbit A2 A1 A3 A1 = A2 = A3 3. The square of the planet’s orbital _period_ is directly proportional to the cube of the _semimajor axis_ of the planet’s orbit. T (period) = time it takes for the planet to make one orbit a (semimajor axis) = average distance between the planet and the Sun T2 ~ a3 1 month 2. A line joining the Sun and the planet sweep 1 month out equal _areas_ in equal _times_. III. Newton’s Law of Gravity 1. All masses ________ one another and never ______. 2. The gravitational force between two masses, m1 and m2, is proportional to the ________ of the two masses. 3. The gravitational force between two masses is also _____________________ to the distance between to the two masses squared. m2 m1 r III. Newton’s Law of Gravity 1. All masses _attract_ one another and never _repel_. 2. The gravitational force between two masses, m1 and m2, is proportional to the ________ of the two masses. 3. The gravitational force between two masses is also _____________________ to the distance between to the two masses squared. m2 m1 r III. Newton’s Law of Gravity 1. All masses _attract_ one another and never _repel_. 2. The gravitational force between two masses, m1 and m2, is proportional to the _product_ of the two masses. 3. The gravitational force between two masses is also _____________________ to the distance between to the two masses squared. m2 m1 r III. Newton’s Law of Gravity 1. All masses _attract_ one another and never _repel_. 2. The gravitational force between two masses, m1 and m2, is proportional to the _product_ of the two masses. 3. The gravitational force between two masses is also _inversely_proportional_ to the distance between to the two masses squared. m2 m1 r III. Newton’s Law of Gravity 1. All masses _attract_ one another and never _repel_. 2. The gravitational force between two masses, m1 and m2, is proportional to the _product_ of the two masses. 3. The gravitational force between two masses is also _inversely_proportional_ to the distance between to the two masses squared. m2 m1 r F G Newton’s gravitational constant m1m2 r2
