orbital velocity Archives

In a previous article I investigated what would happen if the Earth stopped turning entirely, either locking to the Sun or the background stars.

If it happened quickly, then results would be catastrophic, turning the whole planet into a blended slurry of mountains, oceans and trees, hurting past a hundreds of kilometers per hour. And if it happened slowly, it would still be unpleasant, as we stopped having a proper day/night cycle. But it wouldn’t be immediately lethal.

But would happen if the Earth somehow just stopped in its tracks as it was orbiting the Sun, as if it ran into an invisible wall? As with the Earth turning question, it’s completely and totally impossible; it’s not going to happen. And with the unspun Earth, it would be totally devastating and super interesting to imagine.

A view of Earth on October 24, 2014 from the Chinese Chang’e-5 T1 spacecraft. Credit: Xinhua News, via UnmannedSpaceflight.com. — Credit: Xinhua News, via UnmannedSpaceflight.com.

Before we begin to imagine the horrifying consequences of a total loss of orbital velocity, let’s examine the physics involved.

The Earth is traveling around the Sun with an orbital velocity of 30 kilometers per second. This is exactly the speed it needs to be going to counteract the force of gravity from the Sun pulling it inward. If the Sun were to suddenly disappear, Earth would travel in a perfectly straight line at 30 km/s. This is how orbits work.

If the Earth’s orbital velocity sped up, then it would go into a higher orbit to compensate. And if the Earth’s orbital velocity slowed down, then it fall into a lower orbit to compensate. And if the Earth’s orbital velocity was slowed all the way down to zero? Now we’re cooking, literally.

First, let’s imagine what would happen if the Earth just suddenly stopped.

As I mentioned above, the Earth’s orbital velocity is 30 km/s, which means that if it suddenly stopped, everything on it would still have 30 km/s worth of inertia. The escape velocity of the Earth is about 11 km/s.

In other words, anything on the Earth’s leading side would fly off into space, continuing along the Earth’s orbital path around the Sun. Anything on the trailing side would be pulverized against the Earth. It would be a horrible, gooey mess.

But even if the Earth slowed gently to a stop, it would still be a horrible mess. Without the outward centripetal force to counteract the inward pull of gravity, the Earth would begin falling towards the Sun.

How long would it take? My integral calculus is a little rusty, so I’ll draw upon the calculations of Dave Rothstein from Cornell’s Ask an Astronomer. According to Dr. Rothstein, the whole journey would take about 65 days. It would take 41 days to cross the orbit of Venus, and on day 57, we’d cross the orbit of Mercury.

As they days went by, the Earth would get hotter and hotter as it got closer to the Sun. Aatish Bhatia over at WIRED did some further calculations to figure out the temperature. A month into the freefall, and the average temperature on Earth would have risen to 50 degrees C. 50 days in and we’d be about 125 C. On the final day, we’d get up to 3,000 C… and then, that would be that.

Of course, this is completely and totally impossible. There’s no force that could just stop the Earth in its tracks like that. There is, however, a plausible scenario that might drag the Earth into the Sun.

In the far future, the Sun will turn into a red giant and expand outward, engulfing the orbits of Mercury and Venus. There’s still an argument among astronomers on whether it’s going to gobble up Earth as well.

Illustration of the red supergiant Betelgeuse, as seen from a fictional orbiting world. © Digital Drew. — Poor Earth. © Digital Drew.

Let’s say it does. In that case, the Earth will be inside the atmosphere of the Sun, and experience a friction from the solar material as it orbits around, and spiral inward. Of course, at this point you’re orbiting inside the Sun, so falling into the Sun already happened.

There you go. If the Earth happened to stop dead in its orbit, it would take about 65 days to plunge down into the Sun, disappearing in a puff of plasma.

Have you ever heard that spacecraft can speed themselves up by performing gravitational slingshot maneuvers? What’s involved to get yourself going faster across the Solar System.

Let’s say you want to go back in time and prevent Kirk from dying on the Enterprise B.

You could use a slingshot maneuver. You’d want to be careful that you don’t accidentally create an alternate reality future where the Earth has been assimilated by the Borg, because Kirk wasn’t in the Nexus to meet up with Professor Picard and Sir Iandalf Magnetopants, while they having the best time ever gallivanting around New York City.

*sigh* Ah, man. I really love those guys. What was I saying? Oh right. One of the best ways to increase the speed of a spacecraft is with a gravitational slingshot, also known as a gravity assist.

There are times that fantasy has bled out too far into the hive mind, and people confuse a made up thing with an actual thing because of quirky similarities, nomenclature and possibly just a lack of understanding.

So, before we go any further a “gravitational slingshot” is a gravity assist that will speed up an actual spacecraft, “slingshot maneuver” is made up bananas nonsense. For example, when Voyager was sent out into the Solar System, it used gravitational slingshots past Jupiter and Saturn to increase its velocity enough to escape the Sun’s gravity.

So how do gravitational assists work? You probably know this involves flying your spacecraft dangerously close to a massive planet. But how does this help speed you up? Sure, as the spacecraft flies towards the planet, it speeds up. But then, as it flies away, it slows down again. Sort of like a skateboarder in a half pipe.

This process nets out to zero, with no overall increase in velocity as your spacecraft falls into and out of the gravity well. So how do they do it? Here’s the trick. Each planet has an orbital speed travelling around the Sun.

As the spacecraft approaches the planet, its gravity pulls the much lighter spacecraft so that it catches up with the planet in orbit. It’s the orbital momentum from the planet which gives the spacecraft a tremendous speed boost. The closer it can fly, the more momentum it receives, and the faster it flies away from the encounter.

To kick the velocity even higher, the spacecraft can fire its rockets during the closest approach, and the high speed encounter will multiply the effect of the rockets. This speed boost comes with a cost. It’s still a transfer of momentum. The planet loses a tiny bit of orbital velocity.

If you did enough gravitational slingshots, such as several zillion zillion slingshots, you’d eventually cause the planet to crash into the Sun. You can use gravitational slingshots to decelerate by doing the whole thing backwards. You approach the planet in the opposite direction that it’s orbiting the Sun. The transfer of momentum will slow down the spacecraft a significant amount, and speed up the planet an infinitesimal amount.

Messenger's complicated flyby trajectory. Credit: NASA — Messenger’s complicated flyby trajectory. Credit: NASA

NASA’s MESSENGER spacecraft made 2 Earth flybys, 2 Venus flybys and 3 Mercury flybys before it was going slowly enough to make an orbital insertion around Mercury. Ulysses, the solar probe launched in 1990, used gravity assists to totally change its trajectory into a polar orbit above and below the Sun. And Cassini used flybys of Venus, Earth and Jupiter to reach Saturn with an efficient flight path.

Nature sure is trying to make it easy for us. Gravitational slingshots are an elegant way to slow down spacecraft, tweak their orbits into directions you could never reach any other way, or accelerate to incredible speeds.

It’s a brilliant dance using orbital mechanics to aid in our exploration of the cosmos. It’s a shining example of the genius and the ingenuity of the minds who are helping to push humanity further out into the stars.

What do you think? What other places is the general comprehension between actual facts and fictional knowledge blurring, just like the “slingshot maneuver” and “gravitational slingshot”?

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Tag: orbital velocity

What if Earth Stopped Orbiting the Sun?

How Do Gravitational Slingshots Work?