Explainer: Landing Rovers With Newton’s Laws

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How to land a Mars rover when you’re many, many millions of kilometres away.

This resource explains each of Newton’s laws and how they are used to land rovers, like Perseverance, on Mars. It is best suited to Year 7 and 10 Physics students.

Word Count / Video Length: 1118 / 3:25 mins / 2:59 mins

An illustration of NASA’s Perseverance rover landing safely on Mars. Hundreds of critical events must execute perfectly and exactly on time for the rover to land safely on Feb. 18, 2021. Credit: NASA / JPL-Caltech.

It takes a lot of thought and a lot of work to land a rover on Mars. It’s not as if you’re on Earth, where you can check things out, take a few samples and make necessary measurements directly.

To get a lander like Perseverance down, scientists and engineers must take into account such things as the target planet’s gravity, the speed the rover will be travelling and the condition of the landing surface.

Thankfully, one important person has made calculating these things a lot easier: Sir Isaac Newton.

Projectile motion

Landing anything on a foreign planet requires planning, including determining where to land. These missions cost billions of dollars and years of time just to design and construct them. What if there was a storm the day the rover was due to land? Or if there was a quake and the landing site was destroyed?

Good thing there are satellites monitoring storms and quakes on Mars. This means that surface conditions are known in advance – just like us checking the weather forecast before we pick our shoes for the day.

The Chinese rover Tianwen-1 entered Mars’ orbit on 10 February 2021, and will remain in orbit for a couple of months to examine its landing site before deploying its lander and rover for touchdown.

A satellite is also the perfect place for the rovers to send their data before it comes back to Earth.

The more horizontal force an object is given, the further is travels before it lands (A, B, C). With enough force, it will miss Earth and will continue to fall towards it, always missing (D, E, F). This is how satellites remain in orbit around the Earth. Credit: Wikimedia Commons

To understand how satellites orbit, first let us think about throwing a ball. The launched ball will travel both horizontally along and vertically down to the ground. It moves horizontally because you provide it with a horizontal force in the throw and it travels down because of the force due to gravity.

If you throw the ball harder, it will travel further horizontally but it will take the same time to hit the ground because the force due to gravity (9.8 Nkg (or 9.8 ms-2) on Earth) remains the same.

If you take the ball higher, it will also take longer to reach the ground as the vertical distance is larger.

Now, if you take the ball high enough and launch it with enough force, it will move with the same horizontal and vertical motions as our first ball but, will keep missing the Earth since the planet is round. This is exactly how a satellite (including the Moon) stays in orbit: it is always falling towards the Earth but it keeps missing and travels around the planet.

Newton’s first law

As a satellite orbits a planet, the horizontal forces acting on the satellite are balanced. This is because there are virtually no frictional forces. This means that the satellite can continue to orbit, gathering data, without the need for a driving force, like a motor.

Newton’s first law explains this to us.

As part of a Mars sample return mission, a rocket will carry a container of sample tubes with Martian rock and soil samples into orbit around Mars and release it for pick up by another spacecraft. This illustration shows a concept for a Mars Ascent Vehicle (left) releasing a sample container (right) high above the Martian surface. Credit: NASA / JPL-Caltech

The first law states: An object at rest will remain at rest, and an object in motion will remain in motion, travelling at the same speed and direction, unless acted upon by an unbalanced force.

Both the Tianwen-1 and Perseverance communication satellites are moving relative to the surface of Mars and are therefore in motion. As no external unbalanced forces are acting upon them, we know that they will continue at the same horizontal speed as long as we need them to.

When Tianwen-1’s lander and rover are ready to descend, its thrusters will be used. These create an unbalanced force that pushes the lander and rover out of orbit and down to Mars.

The thrusters are also needed to slow it to a stop on the surface so it doesn’t crash onto Mars. Knowing how much force is needed requires Newton’s second and third laws.

Newton’s second law

At the same time as writing his first law, Newton recognised that there was a relationship between the unbalanced force exerted on an object, the mass of that object and the acceleration it would have from the force.

He identified that the larger the unbalanced force, F, applied on an object of mass, m, the higher the acceleration, a, would be.

From this, he deduced and wrote his second law: Force (unbalanced) = mass x acceleration.

The Perseverance lander unit had a mass of 1025 kg and so we can use Newton’s second law to calculate the downward force acting on the lander. Mars has an acceleration due to gravity of 3.69 ms-1 and so the downward force is:

F = 1025 x 3.69 = 3782 N

Note: This is a simplified, ideal scenario where we have ignored any drag or other frictional forces.

A parachute was used to slow Perseverance as it hurtled towards the surface of Mars with this force. The parachute provided an upward force on the lander, which reduce the unbalanced force.

This illustration shows the events that occur in the final minutes of the nearly seven-month journey that NASA’s Perseverance rover takes to Mars. Credit: NASA / JPL-Caltech.

Newton’s third law

To lift a rocket off the Earth, it expels gas towards the ground. Newton’s third law explains how pushing gases downwards, lifts a rocket up.

A United Launch Alliance (ULA) Atlas V rocket carrying the Mars 2020 mission with the Perseverance rover lifts off from Space Launch Complex-41 at 7:50 a.m. EDT on July 30, 2020. Credit: United Launch Alliance

The third law states that every action has an equal (in magnitude) and opposite (in direction) reaction.

So, as the gases are pushed out and down, they push back up on the rocket, lifting it upward. The size of the downward force on the gases will be the same size as the resultant force on the rocket.

If enough upward force is made by the gases, it will be greater than the downward force due to gravity acting on the rocket. This resultant unbalanced force moves the rocket in the direction of the greater force (so in this case, up) as described by Newton’s second law.

Thrusters and boosters were also used to land the rover. Gases were forced down and out of the thrusters and so the gases applied an equal force, in the opposite direction, back onto the thrusters. This slowed the speed of the rover enough to land on Mars without crashing.

Engineers and scientists use very precise calculations to ensure that the downwards force on the rover is only a small amount higher than the upwards force of the thrusters (remember the first law tell us if they were exactly equal, or balanced, the rover would just ‘hover’ where it was). The result was a smooth and gentle landing with no damage to the expensive equipment – and an incredibly cool video.

Spaceship engineers, mathematicians, geologists, astrophysicists, data scientists, fuel chemists and a whole range of other people all had to work together to help Perseverance land on Mars. But they always had Newton in the pilot’s seat.

Now, with the rover safely on the surface of Mars, the next stage of the mission can begin – searching for ancient life!

This article is republished from Cosmos. Read the original article.

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Physical Sciences – Forces

Additional – Careers, Maths, Technology, Engineering.

Concepts (South Australia):

Physical Sciences – Forces and Motion


7 & 10
Learning Connections

Student Skill Summary

Australian Curriculum Connections - Version 8.4

Sub StrandContent Descriptor
Physical SciencesPhysical Sciences is concerned with understanding the nature of forces and motion, and matter and energy. Students gain an understanding of how an object’s motion is influenced by a range of forces such as frictional, magnetic, gravitational and electrostatic forces. They develop an understanding of the concept of energy and how energy transfer is associated with phenomena involving motion, heat, sound, light and electricity. They appreciate that concepts of force, motion, matter and energy apply to systems ranging in scale from atoms to the universe itself.
Sub StrandYear LevelKey IdeaConcept - ACConcept - SAContent TopicContent CodeContent Descriptor
Physical Sciences10Systems | Stability and changeForces and MotionForces and MotionMovement of ObjectsACSSU229The motion of objects can be described and predicted using the laws of physics
ACSSU117Change to an object’s motion is caused by unbalanced forces, including Earth’s gravitational attraction, acting on the object
Sub StrandYear LevelContent TopicContent CodeContent Descriptor
Nature and Development of Science7Scientific Knowledge Changes Our Understanding of the WorldACSHE119Scientific knowledge has changed peoples’ understanding of the world and is refined as new evidence becomes available
7Collaboration and Cultural Diversity Further Scientific KnowledgeACSHE223Science knowledge can develop through collaboration across the disciplines of science and the contributions of people from a range of cultures
10Refinement of Scientific Understanding, Models and Theories EvolvesACSHE191Scientific understanding, including models and theories, is contestable and is refined over time through a process of review by the scientific community
10Advancements in Scientific Understanding Rely on Technological AdvancementsACSHE192Advances in scientific understanding often rely on technological advances and are often linked to scientific discoveries
Use and Influence of Science7Societal and Ethical Impacts of Scientific and Technological SolutionsACSHE120Solutions to contemporary issues that are found using science and technology, may impact on other areas of society and may involve ethical considerations
7Use of Science Understanding and Skills in OccupationsACSHE121People use science understanding and skills in their occupations and these have influenced the development of practices in areas of human activity
10Societal Values and Needs can Influence Scientific ResearchACSHE230Values and needs of contemporary society can influence the focus of scientific research
10Use of Scientific Knowledge Affects Lives and Generates Career OpportunitiesACSHE194People use scientific knowledge to evaluate whether they accept claims, explanations or predictions, and advances in science can affect people’s lives, including generating new career opportunities