How do you find the gravitation force of a planet?

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science_man

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Lets say we discovered a new planet. We know many characteristics about the planet, such as: mass, surface area, density, etc. How do you find the gravitation force (pull) of that planet with those information.
 
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agnau

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F=MA or F=GMm/r^2 --- either way, M matters and acceleration or distance matters (little m can be taken as a point mass for something as large as a planet). You can calculate several of these from the remaining values you specified if you are careful.
 
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science_man

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ok, then lets say the planet it 4,000,000,000 newtons. What is the force of gravity in the planet. <br />How would you get the accleration? And, what is the acceleration refering to? Accleration of gravity?? Accleration of what? <br /><br /><br />
 
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doubletruncation

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As agnau mentioned the mass of the planet basically comes from f=ma and g=GmM/r^2. In practice, for most planets around other stars, the mass is found by measuring the velocity shifts of the host star from the spectra (you can work out from those equations above what the velocity shift might be for different orbital semi-major axes, eccentricities and inclinations and planet/star masses). For planets in our own solar system the masses are determined by looking at how long it takes moons to orbit those planets. If it doesn't have a moon (like for some of the far away kuiper belt objects, or many asteroids) the mass is estimated based on the observed brightness/distance to the thing (and radius if you can measure it independently) using models or empirical correlations. To get the radius of a planet you wouldn't use the law of gravitation. For planets in our own solar system we can get the radius by just taking a picture of the thing and knowing how far away it is, or for many objects we actually know it best by occultation timing (seeing how long it takes for a star to appear to move behind the object). For the extra-solar planets, the radius can actually be measured if the planet appears to move across the disk of the star from our vantage point, in that case the star will become dimmer (usually for a few hours). These so-called transiting planets allow you to measure the radius since the depth of the transit is basically proportional to fraction of the star that the planet blocks, which is (radius_planet)^2/(radius_star)^2. If you know the radius of the star, you can get the radius of the planet from the transit (the stellar radii come from comparing the observed spectrum of the star with stellar models. The models themselves are confirmed with eclipsing binaries where you can see the eclipses from both stars and also the radial velocities of both stars from their spectra). If you can measure both the mass and the radius of a planet, then the average densit <div class="Discussion_UserSignature"> </div>
 
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kmarinas86

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<font color="yellow">ok, then lets say the planet it 4,000,000,000 newtons.</font><br /><br />It can't be measured in newtons, because the acceleration due to gravity varies within it. You must decide on the mass.<br /><br /><font color="yellow">What is the force of gravity in the planet.</font><br /><br />Depends on a few things, the mass of the object that is not the planet, this object's radius from earth's center of mass, the mass of earth within the sphere of that radial distance.<br /><br /><font color="yellow">How would you get the acceleration?</font><br /><br />You would get acceleration due to gravity by dividing the gravitational force by the mass of the small object. The gravitational force is proportional to the mass of the small object, in the equation:<br /><br />gravitational force=Gravitational Constant * Mass of Earth within the Radial Distance * Mass of the smaller object / Radial Distance^2<br /><br />Which can be written simply as:<br /><br />gravitational force=(G*M*m)/(r^2)=m*a<br /><br /><font color="yellow">And, what is the acceleration refering to? Accleration of gravity?? Accleration of what?</font><br /><br />The acceleration that would occur in freefall. Since something inside the earth is not likely to be in freefall, you would have to consider all the forces involved.
 
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doubletruncation

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You measure the change in velocity of something that's orbiting with the planet. For extrasolar planets, you observe the change in velocity of the host star itself by measuring the doppler shift of its absorption lines over time. Note that the planet and host star are both orbiting around the center of mass (which is very close to the center of the star), so the planet causes the star to wobble a little. <div class="Discussion_UserSignature"> </div>
 
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siarad

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4,000,000,000 newtons is it's weight but wrt what? it's mg<br />I think you're mixing up units but in this case g = 4x10<sup>9</sup>/m but confusingly there's no distance.<br />Metric units <br />Physical constants
 
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