Solar System Orbits

1
Module 4 The Wanderers
Activity 1 Solar System Orbits
2
Summary
In this Activity, we will investigate (a) motion
under gravity, and (b) circular orbits in the
Solar System and Keplers First and Third
Laws.
3
(a) Motion under Gravity

• In the last Activity we saw that the length of
  planetary years increases and the orbital speed
  decreases as one moves out from the neighbourhood
  of the Sun.

To understand these trends we need to know a
little about how objects move under gravity.
4
When Newton was studyinghow objects move under
gravity, he found it helpfulto imagine throwing
a ball from the top of a gigantic mythical
mountain on Earth.
5
As the ball falls towards Earth, aphysicist
would say that it gainsenergy of motion
(kinetic energy) at the expense of its
potential energy (which depends on how far it
is from the Earths centre).
This is a formal way of saying that the lower it
gets, the faster it falls! (... until it enters
the atmosphere and air resistance sets in.)
6

• Depending on how much total energy (kinetic plus
  potential) the projectile has, it might ...

7

• take one of a number of possible orbital paths

The projectile never manages to escape the
Earth alongthese paths -these are bound
elliptical orbits..
8
Remember that circles are special cases of
ellipses.
In particular, Keplers First Law states that all
orbits of planets in our Solar System are
ellipses with the Sun at one focus.
But lets get back to our ball thrown off a
mythical mountain
9

• If it were thrown just hard enough, the ball
  could conceivably keep going until it escapes the
  Earths gravity entirely!

(The path it takesthis time is called a
parabola.)
10

• The minimum launch speed from the Earths surface
  for a projectile to escape the Earth entirely is
  11.2 km/s.

This is called the escape velocity from Earth -
the velocity an object needs to be moving at to
escape the Earths gravitational attraction.
The more massive planets (e.g. Jupiter, Saturn,
Uranus) have higher escape velocities.
11
The escape velocity, ve, is proportional to the
square-root of the planets mass, M
A graph of escape velocity versus mass would look
like this
more massive planetshave higher escape
velocities
12

• Escape velocity doesnt just depend on the
  planets mass - it also depends on the distance
  between the planet and the escaping object.

13
A graph of escape velocity versus distance from a
planet looks like
The further away theplanet is, the smalleris
the velocity needed toescape it
14

• this will become important when we talk about
  the escape velocity from very small, extremely
  dense objects like white dwarfs and neutron stars
  (and even black holes) in the Stars and the Milky
  Way unit.

15

• The full equation for the escape velocity ve from
  the surface of a planet depends on the planets
  mass M and its radius rp and is given by

ve
rp
where G Gravitational Constant
6.67 x 10-11 N m2/kg2
As the object moves away from the surface of the
planet, we can replace the planet radius rp with
the distance d from the (centre of the) planet.
16

• We can compare escape velocities from each of the
  planets

(where the escape velocities for the giant gas
planets, Jupiter, Saturn Uranus, are calculated
at cloud tops,as these planets have no distinct
solid surfaces).
Planet Escape Velocity (km/sec)
Mercury 4.3 Venus 10.3 Earth
11.2 Mars 5.0 Jupiter 61 Saturn
35.6 Uranus 22 Neptune
25 Pluto 1.2
17
(b) Circular orbits in the Solar System

• Nearly all Solar System orbits are good
  approximations to circles.

M
r
m
v
18
When objects do travel in circles, the time they
take to do a complete orbit - the period -
depends on the radius of the orbit (r) and the
mass they are orbiting (M), but not on the
objects mass (m).
(This isnt always strictly true,but it works
well when the object
M
- e.g. the Earth
r
- is much less massive than whatits orbiting
m
- in this case, the Sun!)
v
19
The period of an orbit increases with its
radiuslike this

• So for planets orbiting the same object - the Sun

Distant planets have much longer years than
do planets near the Sun
20

• which explains the increase we saw in the last
  Activity in planetary orbital period for the
  planets as we move out from the Sun

21
Orbital periods of the planets

Planet (Sidereal) Year
planetary orbital period
Mercury 0.241 Venus 0.615 Earth 1.00 Mars 1
.88 Jupiter 11.9 Saturn 29.5 Uranus 84.0 Neptu
ne 165 Pluto 249

• (measured in multiples of Earth years)

22

• The relationship between orbital period and
  orbital radius is worth writing down

For objects orbiting a common central body (e.g.
the Sun)on near circular orbits, the
orbital period squared is proportional to the
orbital radius cubed.
This is Keplers Third Law, applied to circular
orbits.
( yes, we have skipped the Second Law - back to
it later!)
23
It essentially means that, as you look at larger
and larger orbits, the orbital period (the
year for each planet)increases even faster
than does the orbital radius.
24

• For example, planets with very large orbital
  radii such as Neptune and Pluto have such long
  periods that we havent observed them go through
  an entire year yet.

25
In this Activity we looked mainly at circular
orbits.
In the next Activity we will focus on the more
generalcase of elliptical orbits.
26
Image Credits
NASA Pluto Charon http//pds.jpl.nasa.gov/plane
ts/welcome/thumb/plutoch.gif NASA View of
Australia http//nssdc.gsfc.nasa.gov/image/planeta
ry/earth/gal_australia.jpg
27

• Now return to the Module home page, and read more
  about Solar System orbits in the Textbook
  Readings.

Hit the Esc key (escape) to return to the Module
4 Home Page
28
(No Transcript)