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Gravitational fields are invisible regions around massive objects where other... Show more
Ever wondered why you don't float off into space? Gravitational fields are regions around massive objects where anything with mass experiences an attractive force. Think of them as invisible zones of influence that pull objects together.
Gravity might seem strong when you drop your phone, but it's actually the weakest of all forces. You only notice it between really large objects like planets and stars. The force is always attractive - there's no such thing as gravitational repulsion.
Gravitational field strength tells us how strong the pull is at any point. It's defined as force per unit mass and measured in N/kg. The formula is simple: g = F/m, where F is force and m is mass. Picture field lines radiating outward from a planet - where they're closer together, the field is stronger.
Quick Tip: Field strength decreases as you move further from the centre of mass, which is why astronauts feel weightless in space!
Newton cracked the code on how gravitational force works with his famous equation: F = Gm₁m₂/r². This tells us the force between any two masses depends on their masses and the distance between their centres.
The gravitational constant G is 6.67 × 10⁻¹¹ N/kg - a tiny number that shows how weak gravity really is. The masses (m₁ and m₂) are in kilograms, whilst r is the distance between centres in metres.
Here's the clever bit: by combining Newton's law with the definition of field strength, we get g = GM/r². This means if you know a planet's mass and radius, you can work out its gravitational field strength at the surface.
Remember: This only works for objects that are roughly spherical - Newton assumed uniform spheres, so it's brilliant for planets but rubbish for asteroids!
Let's tackle some real calculations to see how this works in practice. These examples show you exactly what examiners expect in your working.
For a minor planet with mass 2 × 10²² kg and radius 1200 km, we use g = GM/r². First convert the radius to metres (1,200,000 m), then substitute: g = (6.67 × 10⁻¹¹)(2 × 10²²)/(1.2 × 10⁶)² = 0.9 N/kg.
When comparing two stars with the same mass but different radii, you can use ratios. If star 2 has 10 times the radius of star 1, then g₂ = g₁². So g₂ = 300(1/10)² = 3 N/kg.
The trickiest question involves showing that g = ⁴⁄₃πGρr for planets. Start with g = GM/r², substitute M = ρ × ⁴⁄₃πr³ (density times volume), and simplify. The r² cancels with one r from the volume term.
Exam Tip: Always convert units first - kilometres to metres is the most common mistake in gravitational field calculations!
You'll need to memorise several key equations for gravitational fields. The most important is F = Gm₁m₂/r² for the force between two masses, and g = GM/r² for field strength near a planet's surface.
For objects in orbit, velocity relates to gravitational effects through v² = GM/r. This connects orbital motion to the mass of the central body and orbital radius.
Escape velocity calculations use energy principles. The equation ½mv₁² - ½mv₂² = mΔV shows the relationship between kinetic and gravitational potential energy. For escaping a planet completely, mΔV = GMm/r.
Gravitational potential (V) represents energy per unit mass. Near a planet's surface, V = -GM/r (negative because energy is needed to escape). For small height changes, ΔV = gΔh provides a simpler approximation.
Formula Sheet Tip: These equations will be on your data sheet, but knowing when to use each one is the real skill that gets you marks!
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Quotes from every main character
English LiteratureApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Gravitational fields are invisible regions around massive objects where other objects experience attractive forces. Understanding how gravity works helps explain everything from why we stay on Earth to how satellites orbit planets.
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Ever wondered why you don't float off into space? Gravitational fields are regions around massive objects where anything with mass experiences an attractive force. Think of them as invisible zones of influence that pull objects together.
Gravity might seem strong when you drop your phone, but it's actually the weakest of all forces. You only notice it between really large objects like planets and stars. The force is always attractive - there's no such thing as gravitational repulsion.
Gravitational field strength tells us how strong the pull is at any point. It's defined as force per unit mass and measured in N/kg. The formula is simple: g = F/m, where F is force and m is mass. Picture field lines radiating outward from a planet - where they're closer together, the field is stronger.
Quick Tip: Field strength decreases as you move further from the centre of mass, which is why astronauts feel weightless in space!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Newton cracked the code on how gravitational force works with his famous equation: F = Gm₁m₂/r². This tells us the force between any two masses depends on their masses and the distance between their centres.
The gravitational constant G is 6.67 × 10⁻¹¹ N/kg - a tiny number that shows how weak gravity really is. The masses (m₁ and m₂) are in kilograms, whilst r is the distance between centres in metres.
Here's the clever bit: by combining Newton's law with the definition of field strength, we get g = GM/r². This means if you know a planet's mass and radius, you can work out its gravitational field strength at the surface.
Remember: This only works for objects that are roughly spherical - Newton assumed uniform spheres, so it's brilliant for planets but rubbish for asteroids!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Let's tackle some real calculations to see how this works in practice. These examples show you exactly what examiners expect in your working.
For a minor planet with mass 2 × 10²² kg and radius 1200 km, we use g = GM/r². First convert the radius to metres (1,200,000 m), then substitute: g = (6.67 × 10⁻¹¹)(2 × 10²²)/(1.2 × 10⁶)² = 0.9 N/kg.
When comparing two stars with the same mass but different radii, you can use ratios. If star 2 has 10 times the radius of star 1, then g₂ = g₁². So g₂ = 300(1/10)² = 3 N/kg.
The trickiest question involves showing that g = ⁴⁄₃πGρr for planets. Start with g = GM/r², substitute M = ρ × ⁴⁄₃πr³ (density times volume), and simplify. The r² cancels with one r from the volume term.
Exam Tip: Always convert units first - kilometres to metres is the most common mistake in gravitational field calculations!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
You'll need to memorise several key equations for gravitational fields. The most important is F = Gm₁m₂/r² for the force between two masses, and g = GM/r² for field strength near a planet's surface.
For objects in orbit, velocity relates to gravitational effects through v² = GM/r. This connects orbital motion to the mass of the central body and orbital radius.
Escape velocity calculations use energy principles. The equation ½mv₁² - ½mv₂² = mΔV shows the relationship between kinetic and gravitational potential energy. For escaping a planet completely, mΔV = GMm/r.
Gravitational potential (V) represents energy per unit mass. Near a planet's surface, V = -GM/r (negative because energy is needed to escape). For small height changes, ΔV = gΔh provides a simpler approximation.
Formula Sheet Tip: These equations will be on your data sheet, but knowing when to use each one is the real skill that gets you marks!
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Quotes from every main character
English LiteratureApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Physics
Sociology