Newton s Law of Gravity

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1 Newton s Law of Gravity Example 4: What is this persons weight on Earth? Earth s mass = kg Mar s mass = kg Mar s radius = 3400 km Earth s radius = 6378 km

2 Newton s Form of Kepler s Third Law P 2 = 4π 2 G m + m 1 2 ( ) a 3 P = sidereal period of orbit, in seconds a = semimajor axis of orbit, in meters m 1 = mass of first object, in kilograms m 2 = mass of second object, in kilograms G = universal constant of gravitation = newton m 2 /kg 2

3 Newton s Form of Kepler s Third Law According to Newton s third law, just as the Sun exerts a force on the Earth, the Earth exerts a force on the Sun. However, since the Sun is so much more massive, it doesn t move much. But if the Earth were more massive, the Sun would move. In fact, both the Sun and the Earth circle a common center of mass.

4 Newton s Form of Kepler s Third Law Q4.47 Figure 4-21 shows the lunar module Eagle in orbit around the Moon after Completing the first successful lunar landing in July (The photograph was taken from the command module Columbia, in which the astronauts returned to Earth.) The spacecraft orbited 111 km above the surface of the Moon. Calculate the period of the spacecraft s orbit. R moon = 1738km M moon = kg G = N m 2 /kg 2

5 Conical Sections Circle: e = 0 ellipse: 0 < e < 1 Parabola: e =1 Hyperbola: e > 1 e = a2 b 2 a 2 e = eccentricity a = semimajor axis b = semiminor axis

6 Sample questions: Why does a person orbiting Earth in the Space Shuttle feel weightless? A feather and a boulder are left to fall under the influence of gravity in a vacuum. Compare their accelerations. You throw a ball straight up in the air. At its highest point what are the ball's acceleration and velocity. Suppose that a planet of the same mass as Earth were orbiting the Sun at a distance of 10 AU. By how much would the gravitational force on this planet due to the Sun change. Astro 129: Chapter 1a

7 Newtonian Mechanics Newtonian mechanics can describe the orbits of planets, satellites, asteroids and comets very accurately. Neptune was predicted to exist and later observed through a telescope.

8 Astro 129: Chapter 1a

9 Astro 129: Chapter 1a

10 Astro 129: Chapter 1a

11 The Post and Courier Tuesday, September 15, 2009 Persistent onshore winds and astronomical factors made for higher-than-normal tides Monday afternoon. The tides began to cover Sol Legare Road on James Island, while a number of downtown streets also experienced flooding. Astro 129: Chapter 1a

12 Tidal Forces

13 Tides The Moon exerts a force on the Earth, but since the Earth has a finite size, this force is different from one side of the Earth to the other. The side of the Earth near the Moon gets pulled most, the center of the Earth less, and the backside least of all. Since most of the Earth is solid, it doesn t move much, but water reacts to this difference. So we have tides. Note that due to the Earth s rotation, there are 2 high tides and 2 low tides per day.

14 Tides The Moon exerts a force on the Earth, but since the Earth has a finite size, this force is different from one side of the Earth to the other. The side of the Earth near the Moon gets pulled most, the center of the Earth less, and the backside least of all. Since most of the Earth is solid, it doesn t move much, but water reacts to this difference. So we have tides. Note that due to the Earth s rotation, there are 2 high tides and 2 low tides per day.

15 The Sun also produces tides on the Earth, but due to its much larger distance, the solar tides are only half as strong as the lunar tides. When the Sun, Earth, and Moon are aligned (full or new moon), you get spring or extra-strong tides. When the Sun, Earth, and Moon are at right angles, the solar tide partially cancels the lunar tide.this produces neap tides. Tides

16 Tides In reality, the times of high and low tides are usually an hour or so off the simple prediction, due to the rotation of the Earth. The water wants to align itself with the Moon, but the rotation of the Earth moves it away.

17 Moon s Synchronous Orbit Earth also produces a tidal bulge in the Moon. The Moon's much larger tidal deformation caused it to evolve into a synchronous orbit long ago, and the Moon is said to have become tidally locked to Earth. Most of the moons in the solar system are similarly locked by the tidal fields of their parent planets.

18 Tidal Forces on a Galaxy NGC 2207 and IC 2163 are respectively 143,000 light-years and 101,000 light-years in diameter. Both galaxies are 114 million light-years away in the constellation Canis Major.

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship).

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