It is the year 2032, and a new planet (Planet Y) is discovered. An astronaut with a mass of 79.00 kg visits the new planet. It is discovered that his weight on the new planet is 740.8 lbs. What is the estimate of the g force on the planet and would the astronaut be heavier on Planet Y or on Earth? (Earth has a g force of 9.81 m/s2 ).

“Newton’s Law of Gravity” gives the gravity force between two objects with masses m

and M separated by distance r:



F  G

m M

r

2

G is called the Gravitational Constant, and has the value



6.671011N m

2

kg2

(N is for

Newton, the physicists’ unit of force) or



1.51011 lbm

2

kg2

.

Let’s go back to the example given in the text: two 150 lb people separated by 1 meter.

The mass of each person is



150lb

2.2

lb

kg

 68kg

. Putting these into the formula gives



F 1.5101 1 lb m

2

kg2



(68kg)

2

(1m)

2

107

lb.

Newton’s Law of Gravity actually gives the force only between two small objects. If one

of the objects is a sphere (such as the Earth) then it turns out that you can still use the

formula, but you must use the distance to the center of the sphere as the value for r. As

an example, let’s put in numbers for a 1 kg object sitting on the surface of the Earth.

Then the force of attraction is given by the gravity equation with m = 1 kg, M = the mass

of the Earth =

24 610

kg, and r = radius of the Earth (that’s the distance to the center of

the sphere). This distance is r = 6371 km ≈

6

610

meters. Without plugging in the

numbers, can you guess what the answer will turn out to be? Guess, and then check this

footnote2

to see if you guessed correctly.

Suppose you weigh 150 lbs on the Earth. Then your mass is



150lb

2.2

lb

kg

 68kg

. What will

you weigh on the Moon? We can calculate that by using Newton’s Law of Gravity, and

putting in the M = the mass of the Moon =

22 7.310

kg, r = the radius of the moon =

6

1.710

meters. The answer is F = 25 lb. That means you will weigh 25 lb. on the

surface of the Moon.

Explanation:

hope this helps :)

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