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Gravity Evaluation

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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 = gc

3.44 (EE-8) ft3/(slug sec2)

6.672 (EE-11) m3/(slug sec2)

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 mplanet, the planets radius is rplanet, a persons Mass is mperson, and we neglect the rotational forces of the planet, we can predict the local gravity gl of the planet.

gl = gc mplanet mperson / rplanet2

This gives Earth a 32.1740 foot/second2 acceleration from (Earth's gravity),

9.80665 meter/second2 in metric units. Additional considerations are assumed to be measured at sea level elevation and neglecting the rotational effects of the latitude.

gearth = Gravity on Earth is approximately = 32.2 ft/sec2 or 9.81 m/sec2

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

Lbm

1 kilometer =

1,000

meters

1 Slugus =

14.59

Slugm

1 kilometer =

1,000

meters

1 Slugm =

0.06852

Slugus

1 kilometer =

3,281

feet

1 Lbm =

2.205

Kg

1 kilometer =

0.6214

miles

1 Kg =

0.4535924

Lbm

Chalenge #1

Find: Calculate the gravitational acceleration of the Earth and Moon.

Given: Assume a mass of 1 unit to be measured. (m2 = 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: 5.97e24slugmet, 4.09e23slugus

orbit: 384,400 km from Earth

238,866 miles

diameter: 3,476 km, 2160 miles

radius: 1,738 km, 1080 miles

mass: 7.35e22slugmet, 5.04e21slugus

Units: Convert miles to feet or kilometers to meters, be sure all units are in the same measuring system.

gc

m1 slug

m2 slug

r (Mile or km)

= r (ft or meter)

Earthus

3.44E-08

4.09E+23

1

3960 mile

20,908,800 ft

Moonus

3.44E-08

5.04E+21

1

1080 mile

5,702,400 ft

Earthmetric

6.67E-11

5.97E+24

1

6371.64 km

6,370,000 m

Moonmetric

6.67E-11

7.35E+22

1

1738 km

1,740,000 m

Calculate: gl = gc m1 m2 / rplanet2

gc

m1 slug

m2

r

Answer:

Earthus

3.44E-08

lb ft3

4.09E+23

1

20,908,800 ft

32.2

Ft lb/sec2

slug2 sec2

Moonus

3.44E-08

lb ft3

5.04E+21

1

5,702,400 ft

5.3

Ft lb/sec2

slug2 sec2

Earthmetric

6.67E-11

kg m3

5.97E+24

1

6,370,000 m

9.82

kg m/sec2

slug2 sec2

Moonmetric

6.67E-11

kg m3

7.35E+22

1

1,740,000 m

1.62

kg m/sec2

slug2 sec2

Estimate the weight of a 150 lb Earth person landing on the moon.

150 lb * [(5.3 ft/sec2) / (32.2 ft/sec2)] = 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/sec2

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: (ga = gc m1 m2 / rplanet2 ) and (gb = gc m1 m2 / (rplanet+)2)

Using basic algebra; ga (rplanet+)2 / (rplanet)2 = gb

32.2 ft/sec2 (20,908,800)2 / (21,700,800)2 = 29.89 ft/sec2

Answer: the force of gravity 150 miles above Earth is 29.89 ft/sec2

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 = 4.09e23slugus; Earth Radius = 3,960 Miles

Moon's Mass: 5.04e21slugus; Moon's Radius = 1080 Miles

Units: 384,400 km, 238,866 miles (Use miles as a measure)

Calculate: (ga = gc mearth mcraft / rdist12 ) = (gb = gc mmoon mcraft / (rdist2)2)

Use algebra to cancel mcraft (the craft mass is the same for both planets)

Use algebra to cancel gc (the gravitational constant)

rdist2 + rdist1 = 238,866 miles or rdist = (238866 - rdist)

ga = gb = a constant; mearth / rdist2 = mmoon / (238,866 - rdist)2

(4.09e23) ((5.7057e10) - ((2) 238,866 rdist) + (rdist2)) - (5.04e21 rdist2) = 0

Apply the quadratic equation rdist = 268,693 and 214,999 Miles.

268,693 exceeds the original distance, 214,999 is the answer.

Answer: rdist1 = 214,999 Miles, rdist2 = 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 (lbm)

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

moonEarth

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 SP-428 1979

"Living Aloft" by Connors, Harrison & Akins;

NASA SP-483 1985

"An Overview of Artificial Gravity" by Ralph W. Stone

jr.; NASA SP-314 1973

References:

Standard Handbook Of Engineering Calculations, Second Edition

Published by McGraw Hill, Edited by Tyler G. Hicks, P.E., 1972,

ISBN 0-07-028735-X 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 0-07-004127-X

Section 11.5, Page 11-95 to 11-97, Rockets

Section 11.6 Astronautics,

Introduction To Flight, Third Edition

Published by McGraw Hill, Written by John D. Anderson, Jr., 1989,

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