Orbital Motion

1
Orbital Motion
Phobos is one of two small moons that orbit Mars.
Phobos is a very small moon, and has
correspondingly small gravityit varies, but a
typical value is about 6 mm/s2. Phobos isnt
quite round, but it has an average radius of
about 11 km. What would be the orbital speed
around Phobos, assuming it was round with gravity
and radius as noted?
Slide 6-30
2
Orbital Motion
Phobos is one of two small moons that orbit Mars.
Phobos is a very small moon, and has
correspondingly small gravityit varies, but a
typical value is about 6 mm/s2. Phobos isnt
quite round, but it has an average radius of
about 11 km. What would be the orbital speed
around Phobos, assuming it was round with gravity
and radius as noted?
The weight of an object (M) will be the only
force that can play the role of centripetal
force. So, near the surface, Mg Mv2/r or v
gr1/2
Slide 6-30
3
Orbital Motion
Phobos is one of two small moons that orbit Mars.
Phobos is a very small moon, and has
correspondingly small gravityit varies, but a
typical value is about 6 mm/s2. Phobos isnt
quite round, but it has an average radius of
about 11 km. What would be the orbital speed
around Phobos, assuming it was round with gravity
and radius as noted?
The weight of an object (M) will be the only
force that can play the role of centripetal
force. So, near the surface, Mg Mv2/r or v
gr1/2 (.006 m/s2)(11,000 m1/2 So that v
8.12 m/s.
Slide 6-30
4
Orbital Motion
Phobos is one of two small moons that orbit Mars.
Phobos is a very small moon, and has
correspondingly small gravityit varies, but a
typical value is about 6 mm/s2. Phobos isnt
quite round, but it has an average radius of
about 11 km. What would be the orbital speed
around Phobos, assuming it was round with gravity
and radius as noted?
The weight of an object (M) will be the only
force that can play the role of centripetal
force. So, near the surface, Mg Mv2/r or v
gr1/2 (.006 m/s2)(11,000 m1/2 So that v
8.12 m/s. Note It would take 8512 s or 142
minutes for one orbit.
Slide 6-30
5
The Force of Gravity
Slide 6-31
6
Example
A typical bowling ball is spherical, weighs 16
pounds, and has a diameter of 8.5 in. Suppose two
bowling balls are right next to each other in the
rack. What is the gravitational force between the
twomagnitude and direction? What is the
magnitude and direction of the force of gravity
on a 60 kg person?
Slide 6-32
7
Example
71.2 N?7.27 kg
A typical bowling ball is spherical, weighs 16
pounds, and has a diameter of 8.5 in. Suppose two
bowling balls are right next to each other in the
rack. What is the gravitational force between the
twomagnitude and direction? What is the
magnitude and direction of the force of gravity
on a 60 kg person?
FBB1 on BB2 (6.6710-11 Nm2/kg2)(7.27 kg)(7.27
kg)/r2 (4.010-9 Nm2)/(0.216 m)2
8.610-8 N
Slide 6-32
8
Example
71.2 N?7.27 kg
A typical bowling ball is spherical, weighs 16
pounds, and has a diameter of 8.5 in. Suppose two
bowling balls are right next to each other in the
rack. What is the gravitational force between the
twomagnitude and direction? What is the
magnitude and direction of the force of gravity
on a 60 kg person?
FBB1 on BB2 (6.6710-11 Nm2/kg2)(7.27 kg)(7.27
kg)/r2 (4.010-9 Nm2)/(0.432 m)2
2.110-8 N (directed toward BB1) FBB1 on 60 kg
(6.6710-11 Nm2/kg2)(7.27 kg)(60 kg)/r2
1.610-7 N (directed toward BB1) If we assume the
same r holding the BB against your chest, say.
Slide 6-32
9
Example
71.2 N?7.27 kg
A typical bowling ball is spherical, weighs 16
pounds, and has a diameter of 8.5 in. Suppose two
bowling balls are right next to each other in the
rack. What is the gravitational force between the
twomagnitude and direction? What is the
magnitude and direction of the force of gravity
on a 60 kg person?
FBB1 on BB2 (6.6710-11 Nm2/kg2)(7.27 kg)(7.27
kg)/r2 (4.010-9 Nm2)/(0.432 m)2
2.110-8 N (directed toward BB1) FBB1 on 60 kg
(6.6710-11 Nm2/kg2)(7.27 kg)(60 kg)/r2
1.610-7 N (directed toward BB1) If we assume the
same r holding the BB against your chest, say.
Compare W60 kg 588 N. The Earths pull is more
than 1 billion times greater.
Slide 6-32
10
Gravity on Other Worlds
A 60 kg person stands on each of the following
planets. Rank order her weight on the three
bodies, from highest to lowest.
Slide 6-33
11
Answer
A 60 kg person stands on each of the following
planets. Rank order her weight on the three
bodies, from highest to lowest.
Lowest
Highest
Slide 6-34
12
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
v
Slide 6-35
13
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
v
Fc
Rorbit RMoon
Slide 6-35
14
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
Slide 6-35
15
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
Slide 6-35
16
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
Slide 6-35
17
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
MMoon 7.361022 kg rMoon 1.74106 m
vsc 1680 m/s
Slide 6-35
18
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
MMoon 7.361022 kg rMoon 1.74106 m
vsc 1.680 km/s
Slide 6-35
19
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
Fc Msc(vsc)2/rMoon (toward center) But, Fgrav
provides Fc here Fgrav (to center) Fc (to
center)
vsc
Fc
Rorbit RMoon
MMoon 7.361022 kg rMoon 1.74106 m
vsc 3,763 mph
Slide 6-35
20
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
vsc
Circumference of orbit 2prorbit 10.9106 m.
Rorbit RMoon
vsc 1680 m/s
Slide 6-35
21
Gravity and Orbits
A spacecraft is orbiting the moon in an orbit
very close to the surfacepossible because of the
moons lack of atmosphere. What is the crafts
speed? The period of its orbit?
vsc
Circumference of orbit 2prorbit 10.9106
m. Orbital period (10.9106 m.)/(1680 m/s)
6506 s 108.5 minutes 1.81 hours
Rorbit RMoon
vsc 1680 m/s
Slide 6-35
22

• Would the orbital period increase or decrease if
  the spacecraft orbited farther from the Moon?
• Increase
• Decrease
• No change

23

• Would the orbital period increase or decrease if
  the spacecraft orbited farther from the Moon?
• Increase

Period of orbit
24

• Would the orbital period increase or decrease if
  the spacecraft orbited farther from the Moon?
• Increase

Period of orbit
Quadruple the orbital radius and you increase the
orbital period by a factor of 8.
25
Why do we feel weightless in orbit?
Earth
vsc
26
Why do we feel weightless in orbit?
rorbit
Fc Fgrav
Earth
vsc
27
vsc vyou
FEarth on sc
28
you
vsc vyou
FEarth on sc
29
you
vsc vyou
Newton 2 for SC, aSC (FEarth on SC )/MSC
(GMEarth)/(rorbit)2 Doesnt depend on MSC
FEarth on SC
30
ayou aSC (just like in an elevatoryou
accelerate together)
you
vsc vyou
Newton 2 for SC, aSC (FEarth on SC )/MSC
(GMEarth)/(rorbit)2 Doesnt depend on MSC
FEarth on SC
31
FBDyou
n
ayou
you
FEarth on you
ayou (GMEarth)/(rorbit)2
32
Newton 2 for you
y
FBDyou
n
ayou
you
FEarth on you
ayou (GMEarth)/(rorbit)2
33
Newton 2 for you
y
FBDyou
n
ayou
n must equal 0.
you
FEarth on you
ayou (GMEarth)/(rorbit)2
34
Newton 2 for you
y
FBDyou
n
ayou
If n 0 then by Newton 3, Fyou on floor must
also equal 0. Your apparent weight is zero.
you
FEarth on you
ayou (GMEarth)/(rorbit)2
35
Phobos is the closer of Mars two small moons,
orbiting at 9400 km from the center of Mars, a
planet of mass 6.4 ? 1023 kg. What is Phobos
orbital period? How does this compare to the
length of the Martian day, which is just shy of
25 hours?
36
Phobos is the closer of Mars two small moons,
orbiting at 9400 km from the center of Mars, a
planet of mass 6.4 ? 1023 kg. What is Phobos
orbital period? How does this compare to the
length of the Martian day, which is just shy of
25 hours?
37
Question

• A coin sits on a rotating turntable.
• At the time shown in the figure, which arrow
  gives the direction of the coins velocity?

Slide 6-38
38
Answer

• A coin sits on a rotating turntable.
• At the time shown in the figure, which arrow
  gives the direction of the coins velocity?

Slide 6-39
39
Question

• A coin sits on a rotating turntable.
• At the time shown in the figure, which arrow
  gives the direction of the frictional force on
  the coin?

Slide 6-40
40
Answer

• A coin sits on a rotating turntable.
• At the time shown in the figure, which arrow
  gives the direction of the frictional force on
  the coin?

Slide 6-41
41
Question

• A coin sits on a rotating turntable.
• At the instant shown, suppose the frictional
  force disappeared. In what direction would the
  coin move?

Slide 6-42
42
Answer

• A coin sits on a rotating turntable.
• At the instant shown, suppose the frictional
  force disappeared. In what direction would the
  coin move?

Slide 6-43
43
Additional Example
The Globe of Death is a spherical cagein which
motorcyclists ride in circularpaths at high
speeds. One outfit claimsthat riders achieve a
speed of 60 mphin a 16 ft diameter sphere. What
would be the period for this motion? What would
be the apparent weight of a 60 kg rider at the
bottom of the sphere? Given these two pieces of
information, does this high speed in this small
sphere seem possible?
Slide 6-44
44
Additional Example
The Globe of Death is a spherical cagein which
motorcyclists ride in circularpaths at high
speeds. One outfit claimsthat riders achieve a
speed of 26.8 m/sin a 4.26 m diameter sphere.
What would be the period for this motion? What
would be the apparent weight of a 60 kg rider at
the bottom of the sphere? Given these two pieces
of information, does this high speed in this
small sphere seem possible?
Slide 6-44
45
Additional Example
The Globe of Death is a spherical cagein which
motorcyclists ride in circularpaths at high
speeds. One outfit claimsthat riders achieve a
speed of 26.8 m/sin a 4.26 m diameter sphere.
What would be the period for this motion? (13.4
m)/(26.8 m/s) 0.5 s! What would be the apparent
weight of a 60 kg rider at the bottom of the
sphere? Given these two pieces of information,
does this high speed in this small sphere seem
possible?
Slide 6-44
46
Additional Example
The Globe of Death is a spherical cagein which
motorcyclists ride in circularpaths at high
speeds. One outfit claimsthat riders achieve a
speed of 26.8 m/sin a 4.26 m diameter sphere.
What would be the period for this motion? (13.4
m)/(26.8 m/s) 0.5 s! What would be the apparent
weight of a 60 kg rider at the bottom of the
sphere? W Mg(v2/r) M9.8 m/s2 337 m/s2
(35 gs) Given these two pieces of information,
does this high speed in this small sphere seem
possible?
Slide 6-44
47
Additional Example
The Globe of Death is a spherical cagein which
motorcyclists ride in circularpaths at high
speeds. One outfit claimsthat riders achieve a
speed of 26.8 m/sin a 4.26 m diameter sphere.
What would be the period for this motion? (13.4
m)/(26.8 m/s) 0.5 s! What would be the apparent
weight of a 60 kg rider at the bottom of the
sphere? W Mg(v2/r) M9.8 m/s2 337 m/s2
(35 gs) Given these two pieces of information,
does this high speed in this small sphere seem
possible? NO!!!
Slide 6-44
48
Example problem 19 (page 203). The passengers
in a roller coaster car feel 50 heavier than
their true weight as the car goes through a dip
with a 30 m radius of curvature. What is the
cars speed at the bottom of the dip?
30 m
v
49
Example problem 19 (page 203). The passengers
in a roller coaster car feel 50 heavier than
their true weight as the car goes through a dip
with a 30 m radius of curvature. What is the
cars speed at the bottom of the dip?
FBD
passenger
30 m
v
50
Example problem 19 (page 203). The passengers
in a roller coaster car feel 50 heavier than
their true weight as the car goes through a dip
with a 30 m radius of curvature. What is the
cars speed at the bottom of the dip?
y
FBD
n
passenger
30 m
Mg
v
51
Example problem 19 (page 203). The passengers
in a roller coaster car feel 50 heavier than
their true weight as the car goes through a dip
with a 30 m radius of curvature. What is the
cars speed at the bottom of the dip?
y
FBD
ac v2/r v2/(30 m)
n
passenger
30 m
Mg
v
52
Example problem 19 (page 203). The passengers
in a roller coaster car feel 50 heavier than
their true weight as the car goes through a dip
with a 30 m radius of curvature. What is the
cars speed at the bottom of the dip?
y
FBD
ac v2/r v2/(30 m)
n
passenger
30 m
Now lets write Newton 2 for the passenger.
Mg
v
53
But Wapparent (1.5)Mg. This means (by Newton
3) that n (1.5)Mg in magnitude.
54
But Wapparent (1.5)Mg. This means (by Newton
3) that n (1.5)Mg in magnitude.
55
But Wapparent (1.5)Mg. This means (by Newton
3) that n (1.5)Mg in magnitude.
(27.2 mph)