# Gravitational Attraction Between People

by Ron Kurtus (revised 22 January 2018)

You can find the gravitational force of attraction between people—such as between a boy and a girl—by applying the Universal Gravitation Equation, provided you know the mass of each person and their separation.

For example, suppose a boy who weighed 165 lb (74.8 kg-force) sat near a 50 kg-force (110 lb) girl, what would be the gravitational attraction between them, assuming the separation from their centers was 0.5 meters (19.7 in)?

Note that weights are in kilograms-force or newtons (N). To use in the gravitation equation, newtons must be converted to kilogram-mass by dividing by 9.8 m/s2.

Questions you may have include:

• What is the Universal Gravitational Equation?
• How do you determine the mass of each person?
• What is the force of attraction between the boy and the girl?

This lesson will answer those questions. Useful tool: Units Conversion

## Universal Gravitation Equation

The solution requires an application of the Universal Gravitation Equation:

F = GMm/R2

where

• F is the force of attraction between two objects in newtons (N)
• G is the Universal Gravitational Constant = 6.674*10−11 N-m2/kg2
• M and m are the masses of the two objects in kilograms (kg)
• R is the separation in meters (m) between the objects, as measured from their centers of mass

## Determine mass of each person

To calculate the force of attraction, you must first convert the weight on Earth of each person to his or her mass, using the relationship:

W = mg or m = W/g

where

• W is the weight in newtons or pounds
• m is the mass in kilogram-mass or slugs (pound-mass)
• g is the acceleration due to gravity on Earth; g = 9.8 m/s2 or 32 ft/s2

Thus, the mass of the boy is:

M = (74.8 kg-force)/(9.8 m/s2) = 7.6 kg-mass

Th mass of the girl is:

m = (50 kg-force)/(9.8 m/s2) = 5.1 kg-mass

## Substitute values

Next, substitute the values into the equation:

F = GMm/R2

where

• M = 7.6 kg
• m = 5.1 kg
• R = 0.5 m

### Resulting force

The result is:

F = (6.674*10−11 N-m2/kg2)(7.6 kg)(5.1 kg)/(0.5 m)2

F = 258.7*10−11/0.25

F = 1035*10−11 N

F = 1.035*10−8 N

The force of attraction is approximately:

F = 10−8 N

That is a very small gravitational attraction, but it can be measured on a sensitive instrument, such as one using piezoelectric sensors.

## Summary

You can find the gravitational force between a boy and a girl by applying the Universal Gravitation Equation, provided you know the mass of each person and their separation.

The result is a very small gravitational attraction.

Think clearly and logically

## Resources and references

Ron Kurtus' Credentials

### Websites

Measure small forces with high initial load

Weight - Wikipedia

Mass - Wikipedia

Kilogram - Wikipedia

Mass and Weight: the Gravity Force - Engineering Toolbox

Gravitation Resources

### Books

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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www.school-for-champions.com/science/
gravitation_force_people.htm

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