LESSON 10: Gravity and Orbits

Modified from http://www.psci.unt.edu/~roberts/Pics/Fall/Chapter

%2005.ppt#295,6,Isaac Newton (1643 - 1727)

http://www.csub.edu/Physics/phys110/Ch3.ppt#257,2,Section 3.1 Inertia

The Universal Law of Gravity

• Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance:

F = - G Mm

r2

(G is the Universal constant of gravity.)

Understanding Orbital MotionThe universal law of gravity allows us to understand orbital motion of planets and moons:

• Earth and moon attract each other through gravitation.

Example:

Earth

Moon

• Since Earth is much more massive than the moon, the moon’s effect on Earth is small.

• Earth’s gravitational force constantly accelerates the moon towards Earth.

• This acceleration is constantly changing the moon’s direction of motion, holding it on its almost circular orbit.

Orbital Motion and Gravity

• A force is any kind of push or pull exerted by one object on another.

• Besides contact, friction, electric, magnetic, elastic, pressure, etc. forces, Newton said that objects also exert a gravitational force on each other.

• The force of gravity causes all bodies to attract all other bodies.

• Gravity, coupled with laws of motion, enabled Newton to explain exactly how orbits work.

The Moon and the Earth• the Earth will exert a

gravitational forces on the Moon pulling the Moon towards the Earth.

• So, what holds the Moon up?

• Why doesn’t it fall down like if you drop a rock?

Earth

Moon

GravitationalForce

The Moon and the Earth• If the Moon was just sitting up

there, it would fall straight down onto the Earth.

• But the Moon is moving, “sideways” at a pretty high speed.

• The Moon does fall down, but it is moving sideways at the same time.

• Just like if I throw a baseball, it moves across the room while falling downwards.

Earth

Moon

GravitationalForce

Moon’s velocity

The Moon and the Earth (3)• Without gravity, the Moon would

move in a straight line, flying away from the Earth.

• The orbit is a balance between the natural straight-line motion and the attractive pull towards the Earth.

• The Moon is always falling towards the Earth but it is also always shooting away from the Earth.

Earth

Moon

GravitationalForce

Moon’s velocity

Path followed by the Moon

The Sun and Planets• Orbits of planets around the Sun work just

like the Moon’s orbit around the Earth.• If the gravitational force and orbital speed are

exactly balanced, a planet will orbit in a perfect circle.

• If the planet’s speed is a little faster or slower, a non-circular orbit results.

• If the planet’s speed is much too fast or slow it may escape the Sun altogether or fall into the Sun.

Orbital MotionIn order to stay on a closed orbit, an object has to be within a certain range of velocities:

Too slow => Object falls back down to Earth

Too fast => Object escapes Earth’s gravity