North East Independent School District



Name_____________________________________________ Date __________________ Period 1 2 3 4 5 6 7 8

Universal Gravitation Activity

Objective

To calculate the gravitational force on a human on various celestial bodies. To calculate the gravitational force between celestial bodies.

Procedure

In order to calculate the force and acceleration caused by gravity on an object while on another planet we must use the Law of Universal Gravitation.

1. First you must find your mass in kg: divide your weight in pounds by 2.2 (my mass is___kg (Myou)

2. The law of universal gravitation states that the force experienced due to gravity depends on the mass of the objects and their distance apart. The distance used in this activity is the radius of a planet because we are interested in the distance from the center of the planet.

3. Research the mass and radius (in meters) of each of the 8 planets, Pluto, and the Moon and enter it in each planets chart.

4. To calculate the force between you and the planet using the formula for the Law of Universal gravitation

a. It will look like this in the calculator

Mercury

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the Acceleration due to gravity on Mercury? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

Questions

1. What is your weight (in pounds) on Earth? ________ On Venus? ________

a. Give 2 reasons why you weigh differently on these planets.

2. Neptune and Uranus have very similar dimensions, but there are slight differences. Uranus is a little larger (larger radius) and Neptune is more massive. What property of the planets could account for the fact that Neptune has more mass but is smaller than Uranus?

3. In your travels as Pluaeoriean Galaxy Oaoerine Miner you visited 2 planets on which you weighed differently but they had the exact same mass. How could this be?

4. One of the things that affect the gravitational force is the distance between you and the center of the planet (the radius). So, what happens to the gravitational force when you increase your distance from the center of the earth (i.e. travel to the top of a mountain or fly in a plane)?

a. Would your weight be different? Why?

b. To calculate your weight at the cruising height of a 747 jet (10,600 meters), what would have to do find the distance you would use in the calculation?

5. Thinking about your answer to 4b, what would have to do to calculate the gravitational force between the earth and the moon other than find their mass and the distance between them?

6. What is the gravitational force between Earth and the Moon if they are 384,393,000 meters apart?

7. Our sun has a radius of 695,500,000 meters and a mass of 1.99 x 1030 kg. What is the gravitational force between the Earth and the Sun if the distance between them is 149,600,000,000 m?

8. Gravitational force does not only exist when celestial bodies like planets and suns are involved. Gravity exists between all objects in the universe. That means that you are attracted to the person sitting next to you! Do the math: if you have a mass of 39 kg and your partner has a mass of 41 kg, what is the magnitude of the gravitational force between you if you are half a meter apart?

a. Compared to the forces experienced when a planet or sun is involved, is this a large amount of force?

i. Why do you think this is true?

Below are 2 tables in which the mass and radius are changed. We will remove the universal constant from the calculations for now. With G removed (as in the equation below), calculate the force in the tables below and answer the questions that follow.

In the calculator:

| |Mass 1 |Mass 2 |Distance |Force |

| |120 kg |120 kg |10 m | |

| |120 kg |240 kg |10 m | |

| |120 kg |360 kg |10 m | |

| |120 kg |480 kg |10 m | |

1. In the table on the left the mass increased each time. What effect did this have on the force?

2. In the table on the right the distance decreased each time. What effect did this have on the force?

3. What has more of an effect on the amount of gravitational force, changes in distance or changes in mass?

a. Look back at the equation for universal gravitation. Why do you think this is true?

4. In the left table, how many times did the mass increase from the 1st to the 4th scenario?

a. This caused the force to increase how many times?

5. In the RIGHT table, how many times did the mass increase from the 1st to the 4th scenario?

a. This caused the force to increase how many times?

6. So if the distance between 2 planets was to be cut in half, how many times would the force between them increase?

-----------------------

|Planet |Radius (m) |Mass |

|Mercury | | |

|Venus | | |

|Earth | | |

|Mars | | |

|Jupiter | | |

|Saturn | | |

|Uranus | | |

|Neptune | | |

|Pluto | | |

|Earth’s Moon | | |

Your mass

Planet mass

M1M2

d2

G

F =

Universal G constant

(6.67x10-11)

Planet radius

6.67E-11 x (Myou x Mplanet) / radius2

Venus

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Venus? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

a = ________

w = ________

w = ________

Saturn

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Saturn? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

w = ________

Mars

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Mars? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

w = ________

Jupiter

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Jupiter? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

w = ________

Earth

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Earth? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

w = ________

Neptune

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Neptune? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

Uranus

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Uranus? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

a = ________

a = ________

w = ________

w = ________

w = ________

a = ________

Earth’s Moon

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on the Moon? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds)

w = ________

a = ________

Pluto

|Universal (G) |Your Mass |Planet Mass |Radius of |Calculated Force|

|gravitational |(Myou) |(Mplanet) |planet |(F) |

|constant | | |(d) | |

|6.67E-11 | | | | |

1. What is the acceleration due to gravity on Pluto? (F = ma)

2. Divide the calculated force in Newtons by 4.4. (this will give your weight in pounds on this planet)

M1M2

d2

(M1 x M2) / d2

F =

| |Mass 1 |Mass 2 |Distance |Force |

| |120 kg |120 kg |40 m | |

| |120 kg |120 kg |20 m | |

| |120 kg |120 kg |13.33 m | |

| |120 kg |120 kg |10 m | |

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