What will happen to the weight of the object if the mass of the Earth is reduced to half of the original mass without a change in its radius?

Before we get into the subject of gravity and how it acts, it's important to understand the difference between weight and mass.

Table of Contents Show

• The Relationship Between Gravity and Mass and Distance
• Low air pressure

We often use the terms "mass" and "weight" interchangeably in our daily speech, but to an astronomer or a physicist they are completely different things. The mass of a body is a measure of how much matter it contains. An object with mass has a quality called inertia. If you shake an object like a stone in your hand, you would notice that it takes a push to get it moving, and another push to stop it again. If the stone is at rest, it wants to remain at rest. Once you've got it moving, it wants to stay moving. This quality or "sluggishness" of matter is its inertia. Mass is a measure of how much inertia an object displays.

Weight is an entirely different thing. Every object in the universe with mass attracts every other object with mass. The amount of attraction depends on the size of the masses and how far apart they are. For everyday-sized objects, this gravitational pull is vanishingly small, but the pull between a very large object, like the Earth, and another object, like you, can be easily measured. How? All you have to do is stand on a scale! Scales measure the force of attraction between you and the Earth. This force of attraction between you and the Earth (or any other planet) is called your weight.

If you are in a spaceship far between the stars and you put a scale underneath you, the scale would read zero. Your weight is zero. You are weightless. There is an anvil floating next to you. It's also weightless. Are you or the anvil mass-less? Absolutely not. If you grabbed the anvil and tried to shake it, you would have to push it to get it going and pull it to get it to stop. It still has inertia, and hence mass, yet it has no weight. See the difference?

The Relationship Between Gravity and Mass and Distance

As stated above, your weight is a measure of the pull of gravity between you and the body you are standing on. This force of gravity depends on a few things. First, it depends on your mass and the mass of the planet you are standing on. If you double your mass, gravity pulls on you twice as hard. If the planet you are standing on is twice as massive, gravity also pulls on you twice as hard. On the other hand, the farther you are from the center of the planet, the weaker the pull between the planet and your body. The force gets weaker quite rapidly. If you double your distance from the planet, the force is one-fourth. If you triple your separation, the force drops to one-ninth. Ten times the distance, one-hundredth the force. See the pattern? The force drops off with the square of the distance. If we put this into an equation it would look like this:

The two "M's" on top are your mass and the planet's mass. The "r" below is the distance from the center of the planet. The masses are in the numerator because the force gets bigger if they get bigger. The distance is in the denominator because the force gets smaller when the distance gets bigger. Note that the force never becomes zero no matter how far you travel. Perhaps this was the inspiration for the poem by Francis Thompson:

All things by immortal power near or far to each other hiddenly linked are. That thou cans't not stir a flower

without troubling a star.

Isaac Newton

This equation, first derived by Sir Isaac Newton, tells us a lot. For instance, you may suspect that because Jupiter is 318 times as massive as the Earth, you should weigh 318 times what you weigh at home. This would be true if Jupiter was the same size as the Earth. But, Jupiter is 11 times the radius of the Earth, so you are 11 times further from the center. This reduces the pull by a factor of 112 resulting in about 2.53 times the pull of Earth on you. Standing on a neutron star makes you unimaginably weighty. Not only is the star very massive to start with (about the same as the Sun), but it is also incredibly small (about the size of San Francisco), so you are very close to the center and r is a very small number. Small numbers in the denominator of a fraction lead to very large results!

What would happen if gravity was reduced by half? – Phoebe, aged 13, London UK

Gravity is a force that pulls things towards each other. It is the reason we walk on the surface of the Earth and don’t float off into space. The gravitational pull of the Earth keeps us on its surface, and makes objects fall towards it – like an apple falling from a tree.

The way gravity works is that it pulls at space, not at you. An object that has mass – that’s made of stuff – changes the shape of the space around it. This creates a shape a bit like a bowl, meaning things would naturally roll towards the middle, where the object with mass is.

If you move sideways fast enough, though, you wouldn’t fall in, but travel around the bowl in a circle. That’s why the Earth goes round the Sun once a year, rather than plunging into it.

Join 175,000 people who subscribe to free evidence-based news.

High jumps

If the Earth’s gravity was only half as strong as it is now, you could jump higher and maybe touch the ceiling. You couldn’t jump nearly as high as you could on the Moon, though, where gravity is six times weaker than on Earth.

We would find it easier to lift things. Instead of one heavy suitcase, you could now carry two. But not a horse, or a train carriage – you wouldn’t turn into a superhero all of a sudden.

Things would seem lighter, and lighter things are moved more easily. You would need less force or energy to get a plane to reach the speed needed to take off.

On the other hand, the microscopic forces that make things rough and sticky, friction, would be weaker because of the reduced weight. This would make walking on slippery surfaces more difficult, and the wind would blow leaves, cars and people about more easily.

Low air pressure

The air would feel lighter, too. Half the gravity would reduce air pressure to half what it is now, which is equivalent to climbing to an altitude of more than 5,000 metres. This is higher than any people live permanently – and we would find it hard to breathe in enough oxygen.

The Moon would pull less strongly at the Earth, and the Earth and Moon would revolve around each other more slowly. This reduces the tides on Earth, which means the sea levels won’t rise and fall as much as they do now.

Likewise, the Sun would pull less strongly at the Earth. As a result, the Earth wouldn’t need to move as fast in its orbit in order to prevent it falling into the Sun. This would lengthen the year to 517 days.

The biggest change would be felt by the Sun – and this would cause the most dramatic change to life on Earth. The reason the Sun shines is because of gravity. Its gravitational pull is incredibly strong, meaning its huge weight presses so hard on the atoms in its centre that they glue together. This is called nuclear fusion, and it creates enormous amounts of energy.

The energy heats up the surface of the Sun to nearly 6,000℃, making it shine very brightly indeed. With only half the gravity, the sun would be like a much smaller star with only half its mass. Such a star would not be twice, but eight times dimmer. This would cool Earth to about -100℃.

But not to worry: we’ve got an Earth “twin” next door, Venus. The same size as Earth, it is closer to the Sun and has a much thicker atmosphere, and at the moment, any day on Venus is a scorching 470℃. But with half the gravity, the Sun would be a lot dimmer and Venus’ atmosphere a lot thinner. It is not unthinkable that it would be rather pleasant on the surface of Venus.

When sending in questions to Curious Kids, make sure you include the asker’s first name, age and town or city. You can:

If so, you’ll be interested in our free daily newsletter. It’s filled with the insights of academic experts, written so that everyone can understand what’s going on in the world. With the latest scientific discoveries, thoughtful analysis on political issues and research-based life tips, each email is filled with articles that will inform you and often intrigue you.

Editor and General Manager

Find peace of mind, and the facts, with experts. Add evidence-based articles to your news digest. No uninformed commentariat. Just experts. 90,000 of them have written for us. They trust us. Give it a go.

If you found the article you just read to be insightful, you’ll be interested in our free daily newsletter. It’s filled with the insights of academic experts, written so that everyone can understand what’s going on in the world. Each newsletter has articles that will inform and intrigue you.