Earth's Acceleration Due to Gravity

[spacelifejunkie]

I'm not sure which forum this belongs to so if the moderators move it, I understand. Here's my question...<br /><br />There is great debate concerning the best way to get off of planet earth. We live on the most dense and largest rocky object in the solar system. What if earth's acceleration due to gravity was 10% less? 20%? Can anyone give me some hard data on how much easier it would be to create a space faring society if we only did it on another planet? Keep all other factors constant, just change g = 9.80 m/s^2. <br /><br /><br />SLJ

 

[vogon13]

Lower gravity would help loft a rocket. It would 'balloon' out the atmosphere somewhat so you would have to orbit higher which negates the lower gravity partially. (compare the atmospheric depths of Mars, Venus, and earth)<br /><br />We be all taller in lower gravity, so the manned spacecraft would have to be a little bigger . . .<br /><br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[qso1]

And bigger being a bit more massive kind of puts you back where you started. <div class="Discussion_UserSignature"> <p><strong>My borrowed quote for the time being:</strong></p><p><em>There are three kinds of people in life. Those who make it happen, those who watch it happen...and those who do not know what happened.</em></p> </div>

 

[doubletruncation]

Escape velocity is equal to sqrt(2*g*R) where g is the surface gravity and R is the radius of the planet, or more importantly for our discussion the kinetic energy necessary for an object of mass m to leave the planet is m*g*R. Following vogon and qso's points about people being taller in less gravity, naively I might guess that the mass of a typical person scales inversely as the surface gravity so as to keep the maximum stress that your bones have to handle constant. In that case the most important variable is the radius of the planet. A smaller radius planet (even if it is more massive) should be easier for its citizens to get off of. <div class="Discussion_UserSignature"> </div>

 

[kmarinas86]

<font color="yellow">A smaller radius planet (even if it is more massive) should be easier for its citizens to get off of.</font><br /><br />No...<br /><br />Actually, a more massive planet will be hard to escape, especially if it is dense. An extreme extrapolation of this is the neutron star. It's both massive and smaller than a planet, but it is extremely hard to escape with an escape velocity around 50% the speed of light.<br /><br />If Jupiter were the size of the earth but the same mass, its surface gravity would be greater.

 

[doubletruncation]

If you note, an assumption was made in that statement that the mass of the people who grow up on the planet would be inversely proportional to the surface gravity, so if the mass of the planet is larger the size of the people are smaller. Of course this assumption has its limits (I certainly wouldn't expect it to hold on a neutron star!) - but please note that under this assumption the math works out so that the amount of energy needed to launch the craft depends only on the radius of the planet and is independent of the mass. <div class="Discussion_UserSignature"> </div>

 

[kmarinas86]

<font color="yellow">but please note that under this assumption the math works out so that the amount of energy needed to launch the craft depends only on the radius of the planet and is independent of the mass.</font><br /><br />So if the planet is a huge helium balloon the radius of the earth, will it have the same gravity as earth?<br /><br />Oh please!<br /><br /><font color="yellow">Of course this assumption has its limits (I certainly wouldn't expect it to hold on a neutron star!) </font><br /><br />That's why it's WRONG! The earth is about 81 times heavier than the moon. The gravity at the moon is also 1/6th (actually 1/6.1) that of earth. This implies that radius of the earth divided by the radius of the moon is sqrt((mass of earth/mass of moon)/6) or 3.68 times wider.<br /><br />(6)(3.68)^2 - /> 81<br /><br />The volume of earth is also 49.5 times that of the moon, making it about 8/5ths as dense.

 

[kmarinas86]

<font color="yellow">There is great debate concerning the best way to get off of planet earth. We live on the most dense and largest rocky object in the solar system. What if earth's acceleration due to gravity was 10% less? 20%? Can anyone give me some hard data on how much easier it would be to create a space faring society if we only did it on another planet? Keep all other factors constant, just change g = 9.80 m/s^2.</font><br /><br />If the acceleration due to gravity is 10% less, then the the force due the gravity is 10% less and the energy expenditure is 10% less.<br /><br />GPE = -mgh<br /><br />Where<br /><br />g=GM/r^2=acceleration due to gravity<br />h=r=initial radial distance from the earth's center of mass.<br /><br />Therefore we have:<br />GPE = -m(GM/r) = -GMm/r<br /><br />As r approaches infinity, GPE - /> 0<br /><br />Energy need to escape (considering only earth) = GMm/r = _____ Joules<br /><br />If the acceleration due to gravity is x% less, then the the force due the gravity is x% less and the energy expenditure is x% less.

 

[doubletruncation]

No, of course I agree with you that the kinetic energy that you need is GmM/R and if you hold the mass of the payload (m) constant then it will be larger for a more massive planet or a planet with a smaller radius. But, you've completely missed the point of the argument I was trying to make. If humans were to grow up on Mars for example (which is what I understand the question to be asking) they would quite likely be taller since your height will depend on the stress that your bones can take, with lower surface gravity you can grow bigger, if the planet were more massive you wouldn't grow as big (this is a common theme in many sci-fi stories). To keep the maximum stress on your bones constant a person's mass would be m=m0*R^2/GM where m0 is some constant of proportionality. This is just a rough estimate though - I wouldn't know over what range this holds, it probably wouldn't hold all the way down to 10% of the surface gravity. Now assuming the mass of the ship that you want to launch is proportional to the mass of the creatures (say mship=k*m) then the kinetic energy that you need to launch the ship into orbit would be KE=k*m0*R or just directly proportional to the radius. <div class="Discussion_UserSignature"> </div>

 

[agnau]

Assuming atmospheric pressure is not a factor. I would suspect that the extra 14 psi at sea level does add somewhat to the escape energies required. I do not know how much extra it is. I would assume that the solution doubletruncation gave was due to a similar atmospheric make up as well unless m0 includes that process.