Let’s Analyze the Physics of New Horizons’ Mission to Pluto

Artist’s impression of New Horizons at Pluto. NASA/Applied Physics Laboratory

I’m going to give you some homework. But before we get to the fun stuff, I want to talk about Pluto. This is nothing new, but I like to give my own view on the topic.

An Ode to Pluto

Let me start with some Pluto haiku.

Sun is dim and faint
Out of darkness it comes
Zoom past. There it goes.

I will be honest. I never thought much of Pluto. It was just that last planet that then became a dwarf planet. But really, who could blame me for not caring about Pluto? What did we even know about it? We knew it’s orbital path, and we had an estimate for its size and mass—but not much more. It was so mysterious that we didn’t even know enough to get excited about it.
For just about my whole life, my only image of Pluto was either just a plain blue dot or some artist’s conception of how Pluto might look. It’s still amazing that until recently, we had no idea about what Pluto actually looked like. Now that we have better images and better data, I’m excited.

But Is Pluto Even a Planet?

My old answer to this question was “no”. Pluto doesn’t fit the pattern of the rest of the planets in our solar system. It clearly isn’t like the Jovian planets (its too small) and it’s not in the same region as the Terrestrial planets. Pluto is just different.
Of course many people were upset that “scientists were mean and didn’t like Pluto”. Honestly, I think they were more upset that the old ways were changing. No one likes change. No one wants to make up a new sentence to memorize the order of the planets (My Very Good Mother Just Served Us Nine Pizzas).
But it doesn’t matter how you label Pluto. It’s still Pluto and it will always be Pluto. Here is an analogy. Suppose there is a 5 foot tall plant outside that has leaves. Would that be a big bush or a small tree? How do you define a tree and a bush? Well, you can make some rules (and trust me, people do make rules about shrubbery vs. trees) but that doesn’t really change that particular plant. It is still a plant no matter what you call it. Pluto is like that plant.

Example Problem

This isn’t exactly an example (well, it could be)—but you might need this for the homework questions. Here is a numerical model showing Pluto, Charon and the New Horizons spacecraft.
I have a few comments regarding this calculation.

• There is are two gravitational forces acting on New Horizons. There is the interaction with Pluto and then there is an interaction with Charon.
• Yes, both Charon and Pluto are orbiting each other. In fact, I started with this earlier model with just Pluto and Charon.
• Technically, New Horizons pulls on both Pluto and New Horizons—however, I didn’t include this interaction because it’s effect is tiny.
• This simulation has everything moving with respect to the Pluto-Charon center of mass. It doesn’t not include the gravitational force from the Sun.
• In order to find the relative positions of Pluto, Charon, and New Horizons I used this program—NASA’s Eyes. It basically lets you move around the solar system to see the locations of different objects. I set the time in the app to New Horizon’s closest approach and then estimated the velocity vector based on the trajectory as seen from two perpendicular views. This also let me get the position of both Charon and Pluto. After that, I just ran the numerical model with a negative time interval (so things went backwards in time) and recorded the new starting positions and momentums for the three objects. I know that seems complicated, but that’s what I did.

Take a look at the program, if you need help with numerical models you can check out this tutorial. Oh, if you want to work on the code in Glowscript or VPython, you should be able to just copy and paste the code.

New Horizons Homework

Now for the homework that you have been waiting for.

• New Horizons passes about 12,000 km from Pluto with a speed of about 13,700 m/s. What is the change in velocity due of New Horizons due to this close pass? You could estimate the deflection or use the numerical model above (or do it both ways).
• Suppose that New Horizons decided to pass Pluto at 5,000 km instead of 12,000 km. If this decision was made 1 week before closest approach, what change in momentum of New Horizons would be needed to make this trajectory change. Hint: estimate the position of New Horizons at 1 week before Pluto and then estimate the change in trajectory angle that would put the spacecraft closer to Pluto. How would your answer be different for a trajectory change that happens 1 day before Pluto?
• Estimate the energy needed to put New Horizons into orbit around Pluto at an altitude of 12,000 km (ignore Charon at first).
• Could New Horizons even orbit Pluto with Charon so close? Could you instead put New Horizons at a Lagrange point?
• Use the diameter and mass estimate of Pluto to estimate the density along with the uncertainty in the density.
• The average data transfer rate for New Horizons to Earth is 2000 bits per second. The claim is that it will take until late 2016 to download all the Pluto data. How much total data would this be? Is it enough to be a feature movie (like Avengers)? What if New Horizons was the Netflix server. How long would it take your movie to buffer before you could start watching it?
• Create a plot of communication delay (due to the speed of light) as a function of distance from New Horizons to Earth. Yes, this one isn’t so difficult.
• Part of the New Horizons mission was to get a speed boost from Jupiter. Make a numerical model of New Horizons flying past Jupiter. How much of a speed boost did the spacecraft get?