Q&A: Throwing a Ball to the Moon

Question: My friend told me that if I threw a baseball fast enough at the Moon, it would fall to the ground there and not come back to me. He said the Moon has gravity too, just like Earth. So I asked my teacher Miss Tayk [not real name], and she said that couldn’t happen, because of the rule “what goes up must come down.” Now I’m really confused. I found your blog online, and see you take questions from students, so I was wondering if you could help? — DV, Tucson, AZ

Answer: Sure can, DV. And don’t feel bad about being confused. The problem is people are telling you things that aren’t exactly true. And that includes what your teacher said. I’m sure “Miss Tayk” is a very smart person, or she wouldn’t be a teacher. But the question you asked is very difficult. And gravity can be tricky to understand, especially in situations like this “baseball to the Moon” puzzle.

Let’s start out by understanding the distances involved for throwing a ball from the Earth to the Moon. The graphic above shows the Earth and Moon to the correct scale. That means the view is how it would really look if you went way out in space and looked back at the two objects. The Moon is about a quarter the size of the Earth, and about 30 Earth-diameters away from the Earth. To fit them both in the same view, I had to make them pretty small.

The little yellow dot right next to Earth is where the International Space Station (ISS) orbits. Compared to the Moon, the ISS is fairly close. It’s only 370 km (230 miles) above us. The Moon is about 1000 times farther “up” than the ISS. That’s a long distance, but as I’m sure you know, we’ve already sent many spacecraft to the Moon.

What your teacher told you used to be true … but on October 4th, 1957, something went up that didn’t come down. Launched by the Soviet Union, Sputnik 1 became the first satellite to orbit the Earth. Actually, it did come down eventually, but it stayed up there for about 3 months. All low-flying satellites will fall back to Earth when they start slowing down, and that can take from days to decades, depending on altitude and satellite size and shape.

The first thing that never fell back to Earth was Luna 1, launched on January 2nd, 1959, again by the Soviet Union. It was supposed to hit the Moon, but a malfunction caused it to miss by about 6000 km. It’s still out there today, orbiting around the Sun somewhere between Earth and Mars.

Both these spacecraft had to be moving very fast: Sputnik 1 had a speed of 7.8 km/s (4.8 miles/second) and Luna 1 had a speed of 11.2 km/s (7.0 miles/second). By comparison, the fastest pitch ever thrown in MLB was by Aroldis Chapman (aka “the Cuban Missile”) of the Cincinnati Reds. In 2013, he threw a ball at a world record speed of 169.1 km/hr (105.1 mph). That’s a fast ball, but to compare it to the spacecraft, that baseball was only moving at 0.05 km/s.

If Chapman had thrown that same ball straight upward, it would have reached a height of 113 meters (371 feet). Of course, throwing a ball upward takes a different body motion than a horizontal fastball, so it probably wouldn’t go quite that high. Either way, the distance to the Moon is way beyond that altitude.

But your friend said “IF you threw a ball fast enough,” so lets consider what would happen if you pitched that baseball at 11.2 km/s, the speed Luna 1 needed to reach the Moon. IF the ball left your hand at that speed, it would burst into flames and disintegrate within a fraction of a second. Problem is, you just can’t move that fast through air without heating up from friction with air molecules. Never mind what would happen to your arm. That’s why spacecraft must increase their speed gradually after launch, and only reach those really fast speeds when they get near the vacuum of outer space.

So what IF you could somehow avoid that problem? Imagine away the Earth’s atmosphere, and pitch that ball straight at the Moon with a speed of 11.2 km/s. By the way, that would be a 40,320 km/hr (24,436 mph) fastball. Here’s what would happen. The ball would climb steadily, slowing down because of Earth’s gravity, all the way to the point labeled L1 in the diagram. By that point, the ball would have slowed almost to a stop.

L1 is the point where the Moon’s gravity would take over. It’s about 85% of the way from the Earth to the Moon, since the Moon’s gravity is weaker than Earth’s. At that point the direction of “up” and “down” would change, and the Moon’s gravity would cause the ball to start speeding up, just like any ball does on it’s way back down. It would continue increasing speed until it hit the surface of the Moon.

It’s speed at impact would be about 2.4 km/s (1.47 miles/second), so you probably wouldn’t want to try catching it. At that speed it would go right through your glove (and hand), explode on impact with the ground, and make a new crater.

Next Week in Sky Lights ⇒ The 2014 Vernal Equinox

Gems in the Sky
The 2014 Vernal Equinox