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Lab: Surface Gravity and Weight

CHAPTER 8:  UNIVERSAL GRAVITATION

download lab

Applet Purpose: With this applet you may observe how weights differ from the surface of one planet to another. In other words, it tells you that if something weighs so much on the surface of one planet; it will weigh these amounts on the surfaces of the other planets. 

Click on the following link to access applet: http://library.thinkquest.org/27585/lab/sim_surface.html


How Do I Use It?
To use this applet simply enter a weight into the text box under one of the planets and press the button that says "set" directly below the box. The weights underneath all the other planets will automatically change to be in accordance with what you entered.

 

Things to Try

Underneath Earth enter your weight and press set. What would you weigh on the surface of Jupiter, the Moon or even the Sun? Fill in the table below for each planet, moon, and sun based on your earth weight in pounds.

Table 1.    (My weight in pounds on):

 

Earth

Moon

Mercury

Venus

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Sun

 

 

 

 

 

 

 

 

 

 

 

 

Scale drawing of the relative sizes of planets and moons in the solar system

 

Calculate your mass in kilograms. One kilogram is approximately 2.205 pounds. Your mass = ___________ kg.


Your mass in the universe is a constant and would be the same on each planet, moon, or star listed in the table.
Convert your weight in pounds to
Newtons of force. Note: 1 pound = 4.448 Newtons . State your weight in Newtons on each of the planets, moon and sun.  You will need to convert pounds into Newtons for each value.

 

Table 2.   (My weight in newtons on):

 

Earth

Moon

Mercury

Venus

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Sun

 

 

 

 

 

 

 

 

 

 

 


Determine the acceleration of gravity on each planet, moon, and sun.

The pull of gravity is a force of attraction (called weight) between two objects. One of the objects is usually larger than the other like a planet, moon, or star. This force of gravity causes an object to be accelerated toward the surface of the larger body. The force of gravity (in Newtons ) equals the mass of the smaller body times the gravitational acceleration caused by the larger body. F = mg is the formula that illustrates this relationship. To find the acceleration of gravity on these planets, moon and sun you need to solve this equation for "g". The value "g" will be the acceleration on or near the surface of each planet, moon, or sun. Use this equation to find the acceleration on each surface in the table below.

        Rearrange and you get      

 

 

 

 

Using Newton ís formula of Universal Gravity (chapter 8) and substituting it into the above equation we end up with

 

 

Acceleration of gravity:

 

The acceleration of gravity on any planet can be calculated from Newton 's formula of universal gravity where:

g = acceleration due to gravity (m/s2)
G = universal gravitational constant (m3/kg/s2)
M = mass of the body (kg)
r = radius of the body (m)

 

The value of G is known and has been estimated by scientists as:

G = 6.673 x 10-11 m3/kg/s2 in the Metric system
 

Using this relationship, we can solve for the acceleration due to gravity on any planet so long as we know the planet's size. The acceleration due to gravity of Earth, for example, is known to be about 9.81 m/s2 or 32.2 ft/s2. Let us verify this value by plugging the Earth's mass (ME) and radius (rE) into the above equation.

ME = 5.98 x 1024 kg in the Metric system

rE = 6.375 x 106 m in the Metric system

 

When we do so, we find that the Earth's acceleration due to gravity is indeed about 9.81 m/s2.  Use the table below to calculate the acceleration due to gravity on the sun and planets below.

 

 

Acceleration Due to Gravity Comparison

Body

Mass [kg]

Radius [m]

Acceleration Due
to Gravity, "g" [m/s2]

g / g-Earth

Sun

1.99 x 1030

6.96 x 108

  

  

Mercury

3.18 x 1023

2.43 x 106

 

 

Venus

4.88 x 1024

6.06 x 106

  

 

Earth

5.98 x 1024

6.38 x 106

9.81 m/s2

1

Moon

7.36 x 1022

1.74 x 106

  

 

Mars

6.42 x 1023

3.37 x 106

  

  

Jupiter

1.90 x 1027

6.99 x 107

  

 

Saturn

5.68 x 1026

5.85 x 107

  

 

Uranus

8.68 x 1025

2.33 x 107

  

 

Neptune

1.03 x 1026

2.21 x 107

  

 

Pluto

1.40 x 1022

1.50 x 106

  

 

 

The last column of the table compares the acceleration due to gravity of the body to that of Earth. Divide the acceleration due to gravity on each planet by the value of gravity on Earth. A small body like the Moon only exerts a gravitational acceleration about 1/6th as strong as that of Earth while the massive Sun generates an acceleration nearly 28 times that of Earth. Tiny Pluto, meanwhile, only exerts about 4% the gravity of Earth.

This information is also useful since it directly corresponds to how much an object would weigh on the surface of each of these bodies.  

Lab modified from the following website:

http://www.hazelwood.k12.mo.us/~grichert/sciweb/weight.htm

http://www.aerospaceweb.org/question/astronomy/q0227.shtml

 

H E Y !   M R .  W I L S O N 

Website by Duncan Wilson

Page last updated January 07, 2012

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