Gravity Evaluation

The Space Travelers Web Site!

This is not just science fiction. Here is a site map for your convenience

Home References History Rockets Craft Planets Orbits Aliens Future Support Time

Here is a section list to help you visit this section:

Gravity Thrust Friction Satellite Liquid Solid Nuclear Misc.

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 (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 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_planet²

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.

g_earth = 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	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. (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: 5.97e24slug_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	m₁ slug	m₂ slug	r (Mile or km)	= r (ft or meter)
Earth_us	3.44E-08	4.09E+23	1	3960 mile	20,908,800 ft
Moon_us	3.44E-08	5.04E+21	1	1080 mile	5,702,400 ft
Earth_metric	6.67E-11	5.97E+24	1	6371.64 km	6,370,000 m
Moon_metric	6.67E-11	7.35E+22	1	1738 km	1,740,000 m

Calculate: g_l = g_c m₁ m₂ / r_planet²

	g_c		m₁ slug	m₂	r	Answer:
Earth_us	3.44E-08	lb ft³	4.09E+23	1	20,908,800 ft	32.2	Ft lb/sec²
		slug² sec²
Moon_us	3.44E-08	lb ft³	5.04E+21	1	5,702,400 ft	5.3	Ft lb/sec²
		slug² sec²
Earth_metric	6.67E-11	kg m³	5.97E+24	1	6,370,000 m	9.82	kg m/sec²
		slug² sec²
Moon_metric	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: (g_a = g_c m₁ m₂ / r_planet²) and (g_b = g_c m₁ m₂ / (r_planet+)²)

Using basic algebra; g_a (r_planet+)² / (r_planet)² = g_b

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 = 4.09e23slug_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_dist1²) = (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_dist²= m_moon / (238,866 - r_dist)²

(4.09e23) ((5.7057e10) - ((2) 238,866 r_dist) + (r_dist²)) - (5.04e21 r_dist²) = 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 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,

Home References History Rockets Craft Planets Orbits Aliens Future Support Time

Gravity Thrust Friction Satellite Liquid Solid Nuclear Misc.