Newton's Law of Gravitation

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AP Physics 1: Universal Gravitation Review

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Key Questions

  • Answer:

    The Sun's gravitational force pulls on the planets which move perpendicular to this force at all times creating a elliptical (ideally circular) path around the Sun.

    Explanation:

    Let's use the Earth as an example:
    As the Sun pulls the Earth towards it, the Earth moves very quickly (velocity around 30km/s) perpendicular to the force of gravity. These two forces create a resultant force pointed between the Sun and the Earth's path (let's just say this 30 degrees). Therefore, at all points around the Sun, the Earth will move at a 30 degree angle, creating a circle with radius r (r=93 million miles).

  • In a stronger gravitational field a given mass will have a larger weight.


    An object's weight is given by this equation: #w=mg#

    Gravitational field strength at a distance, r, from a centre of mass is given by this equation:
    #g=(GM)/r^2#

    If an object is nearer a centre of mass then r will be smaller so g will be larger. In that case the weight of the object will be larger. If an object is moved from a distance R away from one centre of mass and placed a distance R away from the centre of a smaller mass then g will be smaller. In that case the weight of the object will be smaller.

    A practical example: if an astronaut on earth has a weight of 833 N, on the moon he/she will have a weight of 136 N.

    Using #m=w/g# the mass of the astronaut is #833/9.8=85 kg#.

    So the weight on the moon (#g_M=1.6 Nkg^-1#) is: #w_M=mg_M=85×1.6=136 N#

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