# Leaving for Mars

As I mentioned at the beginning of the article, our takeoff was at a suitable time for going to Mars. If we power up the transfer MFD now, we should be able to figure out a pretty good transfer orbit.

To see the transfer MFD as it is here, you need to set it up.

• Set the Reference to the Sun (REF button). All the orbits shown will now be orbits around the Sun
• Set Source to Earth (SRC button). You always set this to the planet you are leaving.
• Set target to Mars, as that's where you're going.

All the planets go around in an anticlockwise direction.

Now you need to calculate a hypothetical transfer orbit (HTO). Use the HTO button to switch HTO mode on. A line will appear which is the hypothetical eject time. At first it's on the other side of Earth's orbit from your position, which is wrong, so use the EJ+ and EJ- buttons to adjust the eject time until it's slightly in front of your orbital position as it's shown here.

Then use the DV+ and DV- buttons to increase the energy of your hypothetical orbit until it reaches the orbit of Mars. If the blue line intersects the dotted yellow one as it does here, then you will reach Mars's orbit just as Mars passes the spot, which is what we want. Adjust your Dv until everything lines up as you want it to. This Dv is the speed at which we need to leave Earth behind.

### Calculating the ejection burn.

Of course, in our present orbit, all we are doing is going around the Earth in tight circles. We need to calculate how to change that orbit so that we leave Earth behind, at the right speed and in the right direction.

To do this, we will need to make a fairly long burn in a prograde direction in low earth orbit. This burn needs to give us just enough velocity to escape from Earth's influence, and also to have an extra Dv of 2.433k of speed even after we've climbed away from the Earth. There is a formula for the ejection speed, based on our current orbital speed and the required Dv. This assumes you are in a circular orbit.

Veject = sqrt (2* Vcurrent^2 + Dv^2)

where

• Vcurrent is the speed your spaceship has relative to Earth right now in its low circular orbit
• Dv is the Dv speed which we got from the transfer MFD, and is the speed we want to have once Earth is distant
• Veject is the velocity we need to make that happen

One odd fact about gravity is that your energy in any circular orbit is exactly half the energy you need to escape from the planet altogether. Since energy is proportional to the square of velocity, we can calculate the required speed as above. In this case, our current speed is 7.719k, and our Dv is 2.433k. Veject is therefore 11.18k. This is only a little bit more than Earth's escape velocity.

The other problem we face is choosing the moment to add this extra speed so that we fly away from Earth in the right direction. We want to head in a prograde direction. There are now some add-on instruments that help, but on this occasion, we'll fly it by the seat-of-the pants.

The picture below is of the moment when I chose to apply power. The spacecraft's position in its orbit around the Earth is shown on the left, and the Transfer MFD on the right shows that position again against the backdrop of the Earth's orbit. I switched on prograde alignment with the autopilot and applied power.

Once power is applied, the orbit of the spacecraft around Earth expands outwards in an ellipse. At a speed of 10.17k, the orbit has changed its shape to this.

The orbit continues to expand until the spacecraft finally reaches escape velocity at around 11k. When escape velocity is reached, your orbit is no longer a (long) ellipse - it is a hyperbola, which orbiter displays as below. The change is sudden.

We wait until Vel in the orbit window is the required speed of 11.18k, which happens very quickly for Mars, and thrust is then killed. We have achieved escape velocity, and although Earth is still nearby, we are no longer its prisoner.

You can check your eject by adding the moon onto your target list. This doesn't do anything apart from changing the view of your orbit so you can see a bit more of it. Here we can see, visually at least, that our hyperbolic trajectory away from Earth ( the green line on the orbit window) is almost parallel to the Earth's movement around the Sun as seen in the transfer window.

Things look OK at the moment, but in the next phase of the flight, none of our instruments will help very much. It's best at this point just to coast away from Earth, enjoying the view as you go. Your simulated self won't be this near a planet again for Months.

The cruise