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Math ahead: Proceed slowly and please use units in all calculations.
Preliminary; This is just a collection of information for me to work with.
A constant force draws all things in the universe to each other. This force is called the Gravitational Constant = g_{c}
3.44 (EE8) ft^{3}/(slug sec^{2})
6.672 (EE11) m^{3}/(slug sec^{2})
A local gravity can be calculated based on the mass of two items, and the distance between them. If a planet has a mass of m_{planet}, the planets radius is r_{planet}, a persons Mass is m_{person}, and we neglect the rotational forces of the planet, we can predict the local gravity g_{l} of the planet.
g_{l} = g_{c} m_{planet} m_{person} / r_{planet}^{2}
This gives Earth a 32.1740 foot/second^{2} acceleration from (Earth's gravity),
9.80665 meter/second^{2} in metric units. Additional considerations are assumed to be measured at sea level elevation and neglecting the rotational effects of the latitude.
g_{earth} = Gravity on Earth is approximately = 32.2 ft/sec^{2} or 9.81 m/sec^{2}
Converting between units: I am trying to make this automatic on the math page. 

1 mile = 
5,280 
feet 
1 Slug = 
9.80665 
Kg 
1 mile = 
1.609 
meters 
1 Slug = 
32.1740 
Lb_{m} 
1 kilometer = 
1,000 
meters 
1 Slug_{us} = 
14.59 
Slug_{m} 
1 kilometer = 
1,000 
meters 
1 Slug_{m} = 
0.06852 
Slug_{us} 
1 kilometer = 
3,281 
feet 
1 Lb_{m} = 
2.205 
Kg 
1 kilometer = 
0.6214 
miles 
1 Kg = 
0.4535924 
Lb_{m} 
Chalenge #1
Find: Calculate the gravitational acceleration of the Earth and Moon.
Given: Assume a mass of 1 unit to be measured. (m_{2} = 1) Use the Gravitational constants as listed above.
Earth: (approximate data) 
Earth's moon: (approximate data) 
orbit: 149,600,000 km = from Sun (Definition) 1.00 AU = 149,600,000 km diameter: 12,743.28 km, 7920 miles radius: 6,371.64 km, 3,960 miles mass: 5.97e24slug_{met}, 4.09e23slug_{us} 
orbit: 384,400 km from Earth 238,866 miles diameter: 3,476 km, 2160 miles radius: 1,738 km, 1080 miles mass: 7.35e22slug_{met}, 5.04e21slug_{us} 
Units: Convert miles to feet or kilometers to meters, be sure all units are in the same measuring system.
g_{c} 
m_{1} slug 
m_{2} slug 
r (Mile or km) 
= r (ft or meter) 

Earth_{us} 
3.44E08 
4.09E+23 
1 
3960 mile 
20,908,800 ft 
Moon_{us} 
3.44E08 
5.04E+21 
1 
1080 mile 
5,702,400 ft 
Earth_{metric} 
6.67E11 
5.97E+24 
1 
6371.64 km 
6,370,000 m 
Moon_{metric} 
6.67E11 
7.35E+22 
1 
1738 km 
1,740,000 m 
Calculate: g_{l} = g_{c} m_{1} m_{2} / r_{planet}^{2}
g_{c} 
m_{1} slug 
m_{2} 
r 
Answer: 

Earth_{us} 
3.44E08 
lb ft^{3} 
4.09E+23 
1 
20,908,800 ft 
32.2 
Ft lb/sec^{2} 
slug^{2} sec^{2} 

Moon_{us} 
3.44E08 
lb ft^{3} 
5.04E+21 
1 
5,702,400 ft 
5.3 
Ft lb/sec^{2} 
slug^{2} sec^{2} 

Earth_{metric} 
6.67E11 
kg m^{3} 
5.97E+24 
1 
6,370,000 m 
9.82 
kg m/sec^{2} 
slug^{2} sec^{2} 

Moon_{metric} 
6.67E11 
kg m^{3} 
7.35E+22 
1 
1,740,000 m 
1.62 
kg m/sec^{2} 
slug^{2} sec^{2} 
Estimate the weight of a 150 lb Earth person landing on the moon. 150 lb * [(5.3 ft/sec^{2}) / (32.2 ft/sec^{2})] = 24.7 lb The person would weigh approximately 24.7 lbs on the moon 
Chalenge #2
Find: Find the force of gravity 150 miles above Earth:
Given: The force of gravity at the surface of Earth is 32.2 ft/sec^{2}
The radius at the surface of Earth is 3,960 Miles or 20,908,800 feet
Units: 150 miles 5280 feet / mile = 792,000 feet above Earth
Calculate: (g_{a} = g_{c} m_{1} m_{2} / r_{planet}^{2 }) and (g_{b} = g_{c} m_{1} m_{2} / (r_{planet+})^{2})
Using basic algebra; g_{a} (r_{planet+})^{2} / (r_{planet})^{2} = g_{b}
32.2 ft/sec^{2} (20,908,800)^{2} / (21,700,800)^{2} = 29.89 ft/sec^{2}
Answer: the force of gravity 150 miles above Earth is 29.89 ft/sec^{2}
Chalenge #3
Find: What is the point of equal gravity between the Earth and the moon?
Given: Moon's orbit: 384,400 km from Earth
Earth Mass = 4.09e23slug_{us}; Earth Radius = 3,960 Miles
Moon's Mass: 5.04e21slug_{us}; Moon's Radius = 1080 Miles
Units: 384,400 km, 238,866 miles (Use miles as a measure)
Calculate: (g_{a} = g_{c} m_{earth} m_{craft} / r_{dist1}^{2 }) = (g_{b} = g_{c} m_{moon} m_{craft} / (r_{dist2})^{2})
Use algebra to cancel m_{craft} (the craft mass is the same for both planets)
Use algebra to cancel g_{c} (the gravitational constant)
r_{dist2} +_{ }r_{dist1} = 238,866 miles or r_{dist} = (238866  r_{dist})
g_{a} = g_{b} = a constant; m_{earth} / r_{dist}^{2 }= m_{moon} / (238,866  r_{dist})^{2}
(4.09e23) ((5.7057e10)  ((2) 238,866 r_{dist}) + (r_{dist}^{2}))  (5.04e21 r_{dist}^{2}) = 0
Apply the quadratic equation r_{dist} = 268,693 and 214,999 Miles.
268,693 exceeds the original distance, 214,999 is the answer.
Answer: r_{dist1} = 214,999 Miles, r_{dist2} = 23,867 Miles.
How do you get the mass of a planet? You start with the radius of the orbit around the sun and work backwards. See circular orbits.
(Approximate) 
English 
Metric 

Planet 
% Earth Mass 
Radius (mi) 
Mass (lb_{m}) 
Radius (km) 
Mass (kg) 

Mercury 
0.055 
1516 
2.25E+22 
2440 
3.29E+23 

Venus 
0.815 
3759 
3.34E+23 
6050 
4.87E+24 

Earth 
1 
3963 
4.09E+23 
6378 
5.97E+24 

moon_{Earth} 
0.01 
1080 
5.04E+21 
1738 
7.35E+22 

Mars 
0.107 
2110 
4.38E+22 
3397 
6.39E+23 

Jupiter 
317.9 
44425 
1.30E+26 
71492 
1.90E+27 

Saturn 
95.2 
37450 
3.90E+25 
60268 
5.69E+26 

Uranus 
14.54 
15876 
5.95E+24 
25550 
8.69E+25 

Neptune 
17.2 
15286 
7.04E+24 
24600 
1.03E+26 

Pluto 
0.002 
994 
8.19E+20 
1600 
1.19E+22 
When you want to test a theory, you will not have a big budget to help. Your experiments must be short and to the point. Gravity is often taken for granted in the world today. Try to eat while hanging upside down, it's a new experience. (Newton's universal law of gravitation & the Cavendish Experiment.  Earth bound testing) 
* Do a web search for more information on Cavendish Experiment.
* Do a web search for more information on the law of gravity.
I will try to make this an interactive page.
The information is being compiled now.
Under Construction 
I have some good ideas to improve this section but I still need time.
Additional reading:.
"Go Forth and Multiply" by Lance Frazer; .
Ad Astra Mag. Jun. 1989.
Space Resources and Space Settlements"
by Gerard K. O'Neill NASA SP428 1979
"Living Aloft" by Connors, Harrison & Akins;
NASA SP483 1985
"An Overview of Artificial Gravity" by Ralph W. Stone
jr.; NASA SP314 1973
References:
Standard Handbook Of Engineering Calculations, Second Edition
Published by McGraw Hill, Edited by Tyler G. Hicks, P.E., 1972,
ISBN 007028735X Pages 8.12 to 8.18
Marks' Standard Handbook for Mechanical Engineers, Ninth Edition
Published by McGraw Hill, Edited by Eugene A. Avallone & Theodore Baumeister III, 1987,
ISBN 007004127X
Section 11.5, Page 1195 to 1197, Rockets
Section 11.6 Astronautics,
Introduction To Flight, Third Edition
Published by McGraw Hill, Written by John D. Anderson, Jr., 1989,
Home References History Rockets Craft Planets Orbits Aliens Future Support Time
Gravity Thrust Friction Satellite Liquid Solid Nuclear Misc.