When you compute weight (gravitational mass) of an apple, you know that the earth is pulling it from all over the place. But, you should imagine that it is the center of the earth that is pulling it. This is true when you are computing the gravitational force of any spherical object such as earth – the distance between the center of the earth and the center of the apple shown here is the distance between them.
Imagine lifting a 50 kg crate across a smooth floor on earth as shown on the left.
On the Earth the weight of the crate will be 50×10 = 500 N
Gravity changes planet to planet in our solar system.
Now imagine taking the crate to the Moon and lifting it up there. Its mass is still 50 kg but the Moon’s gravitational pull is only about 1/6 of the Earth’s – in other words about 1.6 N/kg. (The Moon has less gravity because it is smaller than the Earth.) This means that the weight of our crate on the Moon will be 50×1.6 = 80 N and so it will be much easier to lift up.
Some examples of other masses are shown in the table.
On other planets the strength of the gravitational field and the acceleration in free fall is different from that on the Earth and so our crate would weigh different amounts if taken to these planets. The table below gives you some weights of our 50 kg crate on other planets.
(Remember that its MASS is the same everywhere including in deep space or in orbit round any planet where it would be weightless!)
Note that larger the planet, more the strength of the gravitational pull on objects towards its center and therefore, more the weight. Jupiter is the largest, therefore, the weight of the 50KG crate is highest there.
It’s interesting to look at the weights of our crate on Earth and on Saturn or Uranus. They are almost the same. That means if you were to go to Saturn or Uranus you would weigh just about the same as you do here. However on Pluto you would be lighter than on the Moon.
What do you think that means about astronauts’ athletic records on Pluto?
Astronauts liked walking on the Moon. They were able to take giant steps because they didn’t weigh as much there. If you were on the Moon you would weigh less than what you do here on the Earth. That is why the astronauts would really like walking on Pluto because they will get a lot lighter because of least gravitational pull, and cover lot more ground compared to other planers with same effort.
On the surface of our Sun the gravity pull is so strong that our crate would weigh an enormous 13 700 N!
- Newton showed that the gravitational effect of a spherically symmetric body is the same as it would be if all its mass were located at its centre (provided that you are outside the body). Planets and stars are nearly spherically symmetric, so one can calculate their gravitational effects using separations from their centres. To prove this requires some mathematics, so we do that in
Later in the 1670’s, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders.
Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.)
Gravitational force acts on all bodies in proportion to their masses. Why, then does not a heavy body fall faster than a light body?
The reason that a heavy body doesn’t fall faster than a light body is because the greater
gravitational force on the heavier body (its weight), acts on a correspondingly greater
FHeavy = mHeavy * a
FLight = mLight * a
The ratio of gravitational force to mass is the same for every body – hence
all bodies in free fall accelerate equally. Since mHeavy > mLight , FHeavy has to be heavier than FLight so that “a” remains the same for both objects.
And it’s true not just near the Earth, but anywhere.