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Thread: Mass and gravity

  1. #1 Mass and gravity 
    The Doctor Quantime's Avatar
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    If Mars is 1 tenth as massive as earth, why does it have 0.3g gravity?

    Likewise if The Moon has 1/100th as much mass, why does it have 0.15g gravity?

    If gravity is due to the curvature of spacetime, then why is gravity apparently stronger than it should be? If after all mass causes gravitational fields, then should not the amount of mass be directly proportional to the gravity?


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  3. #2  
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    The reason is that the radius is less, so that a mass on the surface is closer to the center of mass.
    Surface gravity - Wikipedia, the free encyclopedia
    These proportionalities may be expressed by the formula g = m/r2, where g is the surface gravity of an object, expressed as a multiple of the Earth's, m is its mass, expressed as a multiple of the Earth's mass (5.9761024 kg) and r its radius, expressed as a multiple of the Earth's (mean) radius (6,371 km).[8] For instance, Mars has a mass of 6.41851023 kg = 0.107 Earth masses and a mean radius of 3,390 km = 0.532 Earth radii.[9] The surface gravity of Mars is therefore approximately
    times that of Earth.


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    Quagma SpeedFreek's Avatar
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    Or to put it another way, it is a question of density (mass v radius) rather than just mass on its own.
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  5. #4  
    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by SpeedFreek View Post
    Or to put it another way, it is a question of density (mass v radius) rather than just mass on its own.
    Yes and no, While Mars is slightly less dense than the Earth, this is not the major contributor to its lower surface gravity.( For example, Jupiter is less dense than the Earth but has a higher surface gravity.) Even if it had the same density as the Earth and the same radius it would have 1/6.6 the mass and just a little under 1/2 the gravity. For bodies of equal density the volume and thus the mass increases by the cube of the radius, while gravity decreases by the square.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  6. #5  
    Quagma SpeedFreek's Avatar
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    Good point, well made! Thank you, Janus.
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