The biggest challenge to rocket design, and for our species’ ability to explore anywhere outside of the little bubble we call Earth, is gravity. Gravity is a force we feel every day – it is what keeps us on the ground – but it is also what makes it so hard to design a rocket that can reach space. It would be pretty easy to launch a rocket very far if nothing was pushing (or in this case, perhaps pulling) it backwards. However, under the force of gravity, the story is completely different. As we’ll soon learn, the force of gravity increases with the mass of an object, and rockets are incredibly massive, often weighing thousands of tons. Overcoming that gravitational pull requires an enormous amount of thrust.
Therefore, truly understanding rocket design also requires understanding how gravity works so we can find ways to overcome it. Yet again, Newton can help us with this. Not only did he observe that the force that keeps Earth in orbit was the same as the force that keeps us on Earth, but he was also able to quantify that force by the equation Fg = GMm/r2. This formula is intuitive: Objects that have more mass, like Earth, create a stronger attractive force, and that force decreases with distance (squared). Just from this formula, you can probably think of a few easy ways to start fighting back against gravity. Lighter rockets will be affected less by gravity, and launching rockets from space instead of Earth’s surface, where r is much larger, also helps significantly. However, while Newton was able to quantify the force of gravity, he was unable to explain where it comes from. Thus, to truly understand how this force works, we must turn to Einstein and Relativity.
Instead of thinking about gravity as a force, Einstein thought of it as a property of space-time itself. Specifically, massive objects bend space around them, creating what he called gravitational wells. The attraction created by gravity arises naturally out of this conception, and works kind of like placing a bowling ball on a taught bedsheet. The mass of the ball creates a well in the sheet (analogous to our gravitational well), and other objects that roll along the sheet will appear to be “pulled” towards the bowling ball due to the well that it creates. The larger the bowling ball, the larger that well will be, and the stronger the attractive force will appear. Amazingly, all of Einstein’s work was exclusively theoretical. Evidence in favor of his theory – such as photons being observed to travel in curved paths, as if attracted by massive objects, despite having no mass themselves – was first observed around 30-40 years after his death.
Illustration by Sain Mary’s University, https://demos.smu.ca/how-tos/160-make-your-own-gravity-well
Activity 2: Demos of Gravity using a Skateboarder and a Bedsheet:
Follow these links:
https://phet.colorado.edu/sims/html/energy-skate-park/latest/energy-skate-park_all.html, and watch the video
And answer the questions below:
What is similar about these demos to a gravitational well? What is different?
- For the skateboard demo only: Can you find a way to get the skateboarder to “escape” the ramp? If so, how did you do it?
- For the skateboard demo only: Using the analogy of the skate ramp as a gravitational well, how might this connect to rockets?
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Just like our skateboarder, any rocket that wants to reach space needs to reach a certain "escape energy" to overcome the gravitational pull that keeps it tethered to Earth. Rockets achieve this by burning fuel to generate propulsion, steadily increasing their kinetic energy until they reach the required speed. To completely break free from Earth’s gravity without needing further thrust, a rocket (or any object) would need to reach what’s called escape velocity, which for Earth is about 11,200 m/s. This enormous speed shows just how challenging it is to design rockets capable of leaving Earth entirely. Even just to enter Low Earth Orbit, a speed of 7,800 m/s is required, still no small task.
Crucial to truly understanding how gravity works is understanding how it is connected to geometry. Specifically, objects under the effect of a gravitational field can only move in four shapes, which are called conic sections: a parabola, an ellipse, a circle, and a hyperbola. Objects that are thrown on the surface of a massive body that don’t have enough velocity to enter orbit travel in a parabola (think of the path followed by a football or basketball). Objects with enough velocity to enter orbit but not enough to escape that orbit travel in elliptical or circular paths, like the moon does around Earth. Finally, objects with enough velocity to escape the gravitational field of a massive body entirely travel in a hyperbola, almost being “slingshotted” off Earth’s gravitational field. Throughout these processes, potential and kinetic energy are continuously being transformed into each other, but the sum of the two – mechanical energy – is always conserved (except for minor losses due to friction and heat). Again, the key is thus to have enough initial kinetic energy to escape from the well of negative energy created by gravity.
Credit to
freeimages.com
