Chapter 4
how does the moons orbital period increase oper century
0.014 seconds per century
lowest to strongest gravity
1 MEarth/2 MSolar/2 AU = (1 × 2)/2^2 = 1/2 4 MEarth/2 MSolar/3 AU = (4 × 2)/3^2 = 8/9
smallest to largest circular velocities
1. 10kg object orbiting earth just above earth surface 2. 5kg orbiting earth halfway to moon 3. 15kg object orbiting earth at same distance as the moon
force due to gravity has the following properties
1. attractive fofrce acting along a straight line between two objects 2. it is proportiional to the product of the masses of the objects 3. it is inversely proportional to the square of teh distance r between the centers of the two objects
Jupiter's moon Callisto orbits Jupiter at a distance of 1.883×109 m and completes one orbit every 16.69 days. What is the mass of Jupiter?
1.89x10^27 (M=4π^2/G x a^3/P2)
If earth were 6 times farther away from the sun than it is now, how many times weaker would the gravitaitonal force between the sun and earth be
36 times weaker decrease by a factor of 6.02
If the Moon were 2 times closer to Earth than it is now, the gravitational force between Earth and the Moon would be
4 times stronger
A star and a planet orbit about the center of mass for their system. The star is 50 times more massive than the planet. What is the ratio of the planet's distance from the center of mass compared to the star's distance from the center of mass?
50 𝑀𝑠𝑡𝑎𝑟𝑅𝑠𝑡𝑎𝑟=𝑚𝑝𝑙𝑎𝑛𝑒𝑡𝑟𝑝𝑙𝑎𝑛𝑒𝑡 (50×mplanet)𝑅𝑠𝑡𝑎𝑟=𝑚𝑝𝑙𝑎𝑛𝑒𝑡𝑟𝑝𝑙𝑎𝑛𝑒𝑡
Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.38 times that on Earth.Assume your mass is 67.00 kg. Then your weight on Earth is 656.60 newtons (656.60 N = m × g = 67.00 kg × 9.8 m/s2). mass on mars? weiught on mars?
67 (mass stays the same) 249.5 (multiple mass tiemes graviational acceleration)
What is the velocity of the Hubble Space Telescope if it has a circular orbit around Earth at an altitude of roughly 6×10^5meter s? G = 6.67×10^−11 m^3 / (kg s2) MEarth = 5.98×10^24 kgrEarth = 6.4×10^6m
7549 m/s (M will be the mass of Earth, which is 5.98×10^24 kg. The distance, r, is the distance from the center of Earth to the telescope. This is the radius of Earth, 6.4×10^6, plus the altitude at which the telescope is orbiting. So the distance for our problem is 7×10^6m.The circular velocity of an object is given by √GM/r.
Force equation
F = G((m1m2)/r^2) G is graviation constant R is distance between the center of the objects
Newtons 2nd law
F=ma
Astronauts in a space shuttle can float while orbiting Earth. Why are these astronauts weightless?
They are falling around Earth at the same rate as the shuttle.
weakest to strongest tides
Third quarter moon in january First quarter moon in july New moon in july Full moon in january
how to calculate radius of spherically symmetric body
add the radius of the body plus the height above the surface
For a pair of objects, the center of mass is located
along the line between the two objects, closer to the more massive object.
because of moons orbit and tidal forces, what will happen to earths day
become longer over time
An object in a(n) __________ orbit in the Solar System will remain in its orbit forever. An object in a(n) __________ orbit will escape from the Solar System.
boud; unbound
what parts of earth does moon pull harder on
closest parts of earth => producing tides
how does gravitational forces affect a planets orbit
direction and speed
whcih tidal effect is the greatest
earth on moon
Tides on Earth occur only in the oceans.
false
speherically symmetric bodies
force from a spherically symmetric body is the same as from a point mass at the center
strongest to weakest rtides
full moon in january new moon in july first quarter moon in july third quarter moon in january
newtons universal law of graviation
gravity is a force between any two objects having mass
if earth shrank to a smaller radius but kep the same mass, everyones weight on earth would
increase
Suppose you are transported to a planet with twice the mass of Earth, but the same radius of Earth. Your weight would __________ by a factor of __________.
increase by 2
what would happen to the graviation force between sun and earth if earth mass doubled
increase by a factor of 2
if distance between earth and sun were cut in half, gravitational force between two objects would
increase by a factor of 4
what would happen to graviational force between sun and earth if mass of sub doubled
increased bvy factor of 2
for a smaller satellite, the center of mass is located where
inside the mroe massive body
what is gravity governed by
inverse square law
what is gravity determined byt
mass and distance between objects
If an object crosses from farther to closer than the Roche limit, it
may be torn apart
mass
measzure of the amount of material in an object
newton and kepler
newton derived keplers laws from his law of gravity
do objects have to be in contact to feel bgravity
no
neap tides
occur when moon, earth, and sun are at right angles (quarter phases) the sun an moonb fill in opposing directions and partially cancel each other
spring tides
occur when sun an moon are aligned are more extreme than normal
Subsequent semi-diurnal (twice daily) tides happen precisely once every 12 hours and 25 minutes. Given what you know of the motions of the Earth and Moon, where is this extra 25 minutes likely coming from?
orbit of moon around the earth
Rank the parts of the Earth on the figure in order of decreasing gravitational force felt from the Moon.
point closest to earth:1 point to the left of closest to earth: 2 middle of earth: 3 side of earth: 4 opposite side: 5
self-gravity
produces internal forces, whcih holds planets together
what would happen to everyones mass if earths radius doubled, but mjass stayed the same
remain the same
what is the less massive object in orbit to a more massive object
satellite
the more massive an object in regards to acceleration
smaller acceleration with bigger the object
a greater r ( distance between center of objects) is equal to
smaller force
which phases spring tide vs neap tide
spring: full moon, new moon neap: 1st and 3rd quarter
if earth shrank to a smaller radius but kep the same mass, graviational force between earth and moon would
stay the same
weight
the graviational foce acting on an object attracted by a planet
why is there a high tide on the side of earth farthest away from the moon
the moon pulls earth closer to it than it pulls the water on the far side
tidal locking
the moons rotation period equals its orbial period
gravity
the mutually attractive force between objects that have mass
is the moon to earth or earth to moon graviational force stronger
they are equal, ACCELERATIONS ARE DIFFERENT
moon always keeps same face toward earth because of
tidal locking
why is earth not a perfect sphere
tides
Why are physicists still measuring G, centuries after Newton described this constant?
to determine if it changes as a function of time
T/F the moon use to be closer to earth than it is now
tru
what force provides the centripetal force that holds a satellite in orbit
vgravity
The "second" high tide is caused by
weaker gravity pulling on Earth on the side opposite the Moon.
does gravity cause acceleration
yes
does gravity impact tides
yes
Compute the ratio of the tidal influence of the doctor delivering a baby (mass = 80.00 kg, distance = 1 m) to the tidal influence of Venus (mass = 4.87×10^24 kg, distance = 4.1×10^10 m). For this calculation, we are assuming that the planet is at its closest point to Earth.
𝐹𝑡𝑖𝑑𝑎𝑙, 𝑑𝑜𝑐𝑡𝑜𝑟/𝐹𝑡𝑖𝑑𝑎𝑙, 𝑝𝑙𝑎𝑛𝑒𝑡=(𝑚𝑑𝑜𝑐𝑡𝑜𝑟/𝑑^3𝑑𝑜𝑐𝑡𝑜𝑟)/(𝑚𝑝𝑙𝑎𝑛𝑒𝑡/𝑑^3𝑝𝑙𝑎𝑛𝑒𝑡)=80.00/1.0^3/(4.87×10^24 /4.1×10^10)^3)=1.13×10^9
