Question

An astronaut weighs 750 N on the surface of the Earth. What will his weight be on the surface of Saturn, which has a mass 100 times greater than the Earth, and a radius 5 times greater than the Earth?

Answer 1

Answer:

The Equation of Newton’s Law of Gravity

“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.

Newton’s Third Law

Here is something that might surprise you: if you weigh 150 lb, not only is the Earth

attracting you with a force of 150 lb, but you are attracting the Earth with a force of 150

lb too. This is an example of something called “Newton’s third law” – if an object exerts

a force on you, then you exert the same force back on it.

2

The answer is 2.2 lb. Of course, that is the weight of a 1 kg object.

Also, 1 newton ~ 4 ½ pounds, so we could express the answer as about ½ newton.

Explanation:

This is about the newton's law of motion