8.3 Universal Gravitation and Orbital Motion 1

Chapter 8 Objectives Calculate angular speed in radians per second. Calculate linear speed from angular speed and vice-versa. Describe and calculate centripetal forces and accelerations. Describe the relationship between the force of gravity and the masses and distance between objects. Calculate the force of gravity when given masses and distance between two objects. Describe why satellites remain in orbit around a planet. 2

Chapter 8 Vocabulary linear speed orbit radian revolve rotate satellite angular displacement angular speed axis centrifugal force centripetal acceleration centripetal force circumference ellipse gravitational constant law of universal gravitation

Inv 8.3 Universal Gravitation and Orbital Motion Investigation Key Question: How strong is gravity in other places in the universe? 4

8.3 Universal Gravitation and Orbital Motion Sir Isaac Newton first deduced that the force responsible for making objects fall on Earth is the same force that keeps the moon in orbit. This idea is known as the law of universal gravitation. Gravitational force exists between all objects that have mass. The strength of the gravitational force depends on the mass of the objects and the distance between them.

8.3 Law of Universal Gravitation Mass 1 Mass 2 Force (N) F = m1m2 r2 Distance between masses (m)

Calculating the weight of a person on the moon The mass of the Moon is 7.36 × 1022 kg. The radius of the moon is 1.74 × 106 m. Use the equation of universal gravitation to calculate the weight of a 90-kg astronaut on the Moon’s surface. You are asked to find a person’s weight on the Moon. You are given the radius and the masses. Use: Fg = Gm1m2 ÷ r 2 Solve:

8.3 Orbital Motion A satellite is an object that is bound by gravity to another object such as a planet or star. An orbit is the path followed by a satellite. The orbits of many natural and man-made satellites are circular, or nearly circular.

8.3 Orbital Motion The motion of a satellite is closely related to projectile motion. If an object is launched above Earth’s surface at a slow speed, it will follow a parabolic path and fall back to Earth. At a launch speed of about 8 kilometers per second, the curve of a projectile’s path matches the curvature of the planet.

8.3 Satellite Motion The first artificial satellite, Sputnik I, which translates as “traveling companion,” was launched by the former Soviet Union on October 4, 1957. For a satellite in a circular orbit, the force of Earth’s gravity pulling on the satellite equals the centripetal force required to keep it in its orbit.

8.3 Orbit Equation The relationship between a satellite’s orbital radius, r, and its orbital velocity, v is found by combining the equations for centripetal and gravitational force.

8.3 Geostationary orbits To keep up with Earth’s rotation, a geostationary satellite must travel the entire circumference of its orbit (2π r) in 24 hours, or 86,400 seconds. To stay in orbit, the satellite’s radius and velocity must also satisfy the orbit equation.

Use of HEO All geostationary satellites must orbit directly above the equator. This means that the geostationary “belt” is the prime real estate of the satellite world. There have been international disputes over the right to the prime geostationary slots, and there have even been cases where satellites in adjacent slots have interfered with each other.