Gravity is the force that pulls objects of mass toward each other. You know from experience that if you drop an object, it falls down toward the ground—not sideways or up—because the gravity created by Earth’s large mass pulls the object down. Gravity acts between any two objects that have mass, even two pencils lying on your desk. Because it is such a weak force, you only notice its effects when at least one of the masses is huge, such as the Earth with its mass of 5.97×1024 kg (or 5,970,000,000,000,000,000,000,000 kg, more than ten trillion times the mass of the world’s population). We also know from experience that the gravitational pull on a 5 kg brick is larger than its pull on a 10 g pencil. These examples show how the strength of the force is proportional to the mass of the objects involved. The strength of the gravitational pull also depends on the distance between the objects; the force gets quickly weaker as the objects get farther apart. As an example, the force of Earth pulling rockets down weakens as their distance from Earth increases.
The solar system is well-suited to explore gravity. Many objects in the solar system are massive: the Sun is 333.000 times the mass of Earth, and although the mass of Mars is 10 times less than the mass of Earth, it is still massive. We can study how gravity holds planets in their orbit while they are moving around the Sun. The planets’ velocity is just so that their paths form an orbit (Figure 1) and not a path away from the Sun (Figure 2, left), or a spiral toward the Sun (Figure 2, right).
Figure 1. Illustration of how the velocity of the planet Earth and the gravitational pull of the Sun on Earth are in a delicate balance that keeps Earth in an orbit around the Sun (this illustration is not drawn to scale).
Figure 2. Illustration of a planet that moves too fast to be pulled into orbit (left), and of a planet that moves too slowly to stay in orbit (right). (These illustrations are not drawn to scale.)
No matter where you are in the solar system, the gravitational pull of the Sun is working on you. You do not notice the gravitational pull of the Sun on you when you are on Earth for two reasons: your mass is small and the Sun is far away. On Earth, you experience the gravity of Earth because this huge mass is close by. The gravitational pull of the Sun has a noticeable effect on Earth even though Earth is as far from the Sun as you are, because Earth is much more massive.
Objects that fly or rise into the air must overcome gravity of whatever planet they are on. The force generated by gravity on an object is called its weight, and the weight of objects changes depending on the planet they are on (See Table 1). For example, the weight of an object on Mars is 37.7% of the weight of the same object on Earth. This difference is due to the combination of the smaller mass of Mars and its smaller radius. This reduced weight makes it is easier to rise into the air from Mars compared to from Earth.
Table 1. Table listing the mass, radius, and weight on different planets compared to the mass, radius, and weight on Earth.
Figure 3. The weight of an object on Earth is greater than its weight on Mars.
Does that mean that it is easier to fly a helicopter on Mars? Not necessarily! Helicopters stay in the air because spinning blades generate an upward push called lift. But helicopter blades need air to create lift. They are made such that when air flows over them, a net upward push (lift) is generated. In general, the denser the air, the harder it can press on surfaces. The Martian atmosphere is 100 times less dense than Earth’s atmosphere. In this thin atmosphere, the same rotating blades will generate much less lift. Unless the lift on the helicopter is greater than its weight, the helicopter will not fly (see Figure 4). So, despite the lower weight on Mars, it is still harder to make a helicopter fly on Mars.
Figure 4. The helicopter will rise only if the lift created by the rotating blades of a helicopter is greater than the helicopter’s weight.
In this lesson, students will build model helicopters out of paper (Figure 5) and investigate how their design can be optimized to make the helicopter fly on Mars. Students will compare their design to NASA’s Ingenuity helicopter (Figure 6), a helicopter that was built to help NASA’s Perseverance rover explore the Martian surface. The Ingenuity is very lightweight, weighing only 4 pounds (on Earth)! Each blade is about 2 ft. (0.6 m) long, and the blades rotate about 2400 times per minute. Will students take the same approach in their designs?
Figure 5. Two examples of paper helicopters.
Figure 6. Rendering of NASA’s Ingenuity helicopter.
A paper helicopters, unlike a real helicopter, does not have a motor to make its blades spin. Due to its special shape, however, the blades still spin as it falls. When you drop a paper helicopter, it will take a fraction of a second for it to start spinning. Once the paper helicopter spins, it should generate lift, which slows its descent to the ground (Figure 7).
Figure 7. Paper helicopters generate lift as their blades rotate, causing the helicopters to slowly float down.
These paper helicopters do not generate enough lift to fly upward, but the lift helps slow their descent. The more lift they generate, the slower they fall. Students will use the time the helicopter spends in the air as a measure of its performance.
There might not be one single design for a paper helicopter that allows it to descend the slowest. That said, adding some mass, such as a paperclip at the bottom of the helicopter, can stabilize the helicopter, making it perform better. Adding more mass than needed will, however, decrease its performance because of the increased weight. Similarly, longer and wider blades that hit the air at an angle are generally better. These changes to the blades generally create more lift, and as a result, slow down the fall of the paper helicopter more. If you change the dimensions of your paper helicopter too drastically, however, the helicopter may actually become unstable and perform worse. Other factors, like changing the shape or angle of the blades, can also influence lift.
For each group of 2–4 students:
- Pencil or pen
- A printout of the Paper Helicopter Template.
Groups should have access to the following shared materials:
- Assortment of paper, e.g. tissue paper, printer paper, notebook paper, construction paper, cardstock, cardboard
- A safe, high place from which to drop the paper helicopters. For example, you could have the students stand on a chair or choose a balcony with a safe railing.
- Optional: A scale to determine the mass of their models