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I have an doubts in the gravitation law.

  1. Apr 22, 2012 #1
    Dear Sir,
    My name is Ashish R. Sai Im from India.I just appeared for 11th std.A few days ago I went through Gravitation.I completed my assignment.After completing assignments,I tried to find the gravitation between the moon and earth. During this i got a few doubts in this gravitation law.
    1> My class sir told me that while dealing with planets we can consider planets as a point mass He told me that we can consider that that earth as an sphere because it got an imaginary boundary. My question is how can we consider the earth as an sphere when sphere got uniform density at each point But when we talk about earth itdont have same density at every point (I think so ).So how can we consider it as an sphere.
    2>After this first I tried to find the force req for the motion of earth I thought it must be F=ma ,I found that mass is 5.9742 × 1024 and then i tried to find the 'a' of earth I found it in this way.
    F=ma with the Newtonian law of gravity and the centripetal acceleration a = v2/r,
    mv2r = −GMmr2.
    This gives v = GM/r√, which is v = 29.5km/s or v = 2.95×104m/s, for the mass of the sun and r = 1.5×108km. The acceleration is then 5.8m/s2
    Is it right if yes then the force req to move earth is f=ma which is equal to 3.48 × 1025

    After this i found the force of gravitation between earth and moon which come as 1.9848 × 10^56 N ( By using ,)
    How can be the gravitation between earth and moon be grater the force req to move earth so should earth move towards moon or moon should move towards earth.
    3>Then I thought that not only moon is extracting force on earth other planets must be extracting some gravitational force on earth so somehow it must be balancing both forces.Am I right?
    4> If yes then how can it be possible ? The number of planet is an constant so I think that the gravitational force extracted on earth and the gravitational force of moon.Both of them will not have an huge difference because even if we think that there is an planet out side of galaxy which have an huge size but in the formula of gravitation we know that there is distance so i mean to say when the size of plant is too large and it is located so far away from us and the distance comes in upon in this formula so it nullify the mass so the net force acting on earth and the net fore acting on moon will not have an huge difference .
    5>If yes then why moon moves towards the huge gravitational force extracting plant so i think on moon earth must be the planet which extracting max gravitational force.So why moon is not moving towards earth.
  2. jcsd
  3. Apr 22, 2012 #2
    You are right. Earth is not sphere, but we do that kind of approximation so we can easily do calculation. When we consider Earth as a sphere, we can show that we can replace that problem with a point mass problem. If you know how to integrate, you can investigate what difference in force would be if you had a bit different shape of Earth.

    I did not check you calculation, but this conclusion is correct. Earth is moving towards the Moon and vice versa, but in the (quasi)circular motion sense.

    This is true. You can calculate it. Small effect, but it's there.
  4. Apr 22, 2012 #3
    Thank you for your reply but can you please explain me how its possible when earth got the attraction force between earth and moon is this much so why its not moving towards moon??
  5. Apr 22, 2012 #4
    Huh, this can be explained in couple ways. I don't know did you do derivation of Kepler laws - when you do that, you can see that objects have elliptic (or almost circular) orbits because they had a initial velocity, and therefore angular momentum and in the combination with gravitational law, you will get that kind of motion.

    But there is an old thread with the same question:
  6. Apr 22, 2012 #5
    I asked same qun to the mit walter lewin and he told me that its an centripetal force so its dosnt move earth towards moon It keeps earth in its path ..
  7. Apr 22, 2012 #6
    How can we know its an centripetal force or its an centrifugal force??
  8. Apr 22, 2012 #7


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    First, let me note that you say "how can we consider the earth as an sphere when sphere got uniform density at each point". Being a sphere is a purely geometric property and has nothing at all to do with density.

    Second, the earth does move toward the moon and the moon moves toward the. More accurately, the earth and moon both move toward their center of gravity which, because the earth is so much bigger than the moonl, lies well within the earth. But they also have a "sideways" motion so they keep missing each other!
  9. Apr 22, 2012 #8
    It got to do with density, bcz density is = mass per unit volume so when we talk about an sphere it got an uniform density at each point bcz its mass is distributed in an uniform manner but when we talk about earth its didn't got same mass at each point so it's density is not uniform in this way we can relate sphere to the density
  10. Apr 22, 2012 #9
    Your calculations seem messy. You calculated the speed of earth around the sun, then the centripetal acceleration and force in the case of earth going round the sun. Then you calculated the gravitational force between the moon and the earth, which I think you got the wrong number for. It should be 10^20 not 10^56.

    Then you compare these numbers and ask how can they be different. One is for earth orbiting the sun, the other is for the moon orbiting the earth.
  11. Apr 22, 2012 #10
    yaa you are right ,,Back to the original question, the amount of force required depends on how long one plans to take accelerating or decelerating. Earth masses ~6E+24 kg and there's roughly ~3E+7 seconds in a year. Braking by 30 km/s over 1 year requires deceleration at 3E+4/3E+7 = 0.001 m/s2 which is a force of...

    F = m.a = 6E+24 kg * 0.001 m/s2 = 6E+21 N

    ...which is an immense amount of force. Earth is about 1.3E+14 m2 in cross-sectional area, so spreading out the force means an average of ~46 GPa pressure applied over the whole surface pointing in that direction. Just a bit high at ~460,000 bars.

    To avoid the need to apply such forces directly one can use a so-called "Gravity Tractor", in which a smaller mass is pushed directly and its gravitational attraction of the Earth pulls the Earth along with it. Using the Moon, for example. But the force applied needs to be less than the force that would cause the tractor object to break up.

    Of course the usual reason for moving Earth is the need to avoid the Sun's rising luminosity. The Sun has 5.5 billion years left on the Main Sequence and will rise to ~2 times its present output by the end of that phase. This means Earth needs to recede to a distance of sqrt(2) ~1.4 AU from the Sun. To do that requires an impulse amounting to a speed change of ~16 km/s. Spread over 5.5 billion years that's an average acceleration of ~1E-13 m/s2 and thus a force of ~5.8E+11 N, which averaged over the whole cross-section of the Earth is ~0.0044 Pa. Much better.

    For such a "low" pressure we could use sunlight, which exerts a force of ~1E-5 N per square metre of perfect reflector at the Earth-Sun distance. Thus Earth would need to be towed by a solar-sail that's about ~500 times bigger in area. Alternatively a matter conversion drive annihilating ~2,000 kg/s would supply sufficient force, though finding a suitable place for it could be tricky.
  12. Apr 22, 2012 #11
    but how can it affect the gravitational force bcz what ever caln mistake you told they dosnt affect the it .See the gravitation formula it dosnt depend on centripetal acceleration nor on speed of earth.And I have caled again F= m.a = 6E+24 kg * 0.001 m/s2 = 6E+21 N
    Its again aroung 10^21N Now what??
  13. Apr 22, 2012 #12


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    Just as a side note, part of the earth moving towards the moon is what causes tides in the ocean.
  14. Apr 22, 2012 #13


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    Gravity acts on every particle on earth, it is a force applied in the whole volume.
    And you are right, as surface force it would be extremely high.

    For moving the earth, I think asteroids are the way to go. The system is chaotic and thousands of years would be no issue, therefore a good description of the objects and enough computing time would reduce the required momentum changes a lot.

    The gravitational force between earth and sun is ~3.5*10^22 N, while the force between earth and moon is only 1.8*10^20 N.
    The forces between the earth and other planets are some orders of magnitude smaller.
  15. Apr 22, 2012 #14
    Can you please tell me how you got the gravitation of moon as 10^20
  16. Apr 22, 2012 #15

    D H

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    He used Newton's law of gravitation, [itex]F=GMm/r^2[/itex]. Click on mfb's 1.8*10^20 N. It's a hyperlink.

    Note: This is using the current distance between the Earth and the Moon. A couple of weeks from now and the answer will be around 2.2×10^20 N. The average value, 1.98×10^20 N may be obtained replacing "distance between earth and moon" with the "moon semimajor axis".
  17. Apr 22, 2012 #16
    Centripetal is a real force which means it have some origin due to some interactions like the gravitational force, Electrostatic force, and one can derive CPF as acting towards and the centre; in conclusion, if one wants an object to be revolving in circular path there must be CPF, which maintains the circular path of the body.

    Whereas Centrifugal force is a fictitious force (i would say an imaginary idea) just to make Newtons law applicable in a non-inertial frame of reference as you might be knowing NEwton's law are applicable in an inertial frame of reference (a frame of reference moving with no acceleration).
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