Wednesday, 27 February 2013

Earth to Mars and Back

I haven’t got time to do this, but it got under my skin, after a conversation on Facebook, and I have to get it off my chest!

Going from Earth to Mars seems fairly simple in concept. OK it would take a few months, but it is our next-nearest planet, so what’s the problem?

First let’s point out that while the Sun’s gravitational field dominates the solar system, this is largely overcome by the orbital force requirements of the planets. Any object going between planets is assisted in part by the orbital speed of its launch planet. The Sun becomes a factor in determining the net orbital path of any object such as a space craft.

Going from Earth to Moon is fairly straightforward because, in astronomical terms, the Moon is only a short distance away and the Earth and Moon, being in similar solar orbits, largely cancel out the Sun’s gravitational pull.

Going to Mars is a different story. The space craft effectively has its own solar orbit, the speed of which must overcome the gravitational force of the Sun. It’s going to be hard work to get to Mars, in terms of rocket power, and on the return trip, the problem will be in slowing down, because the space capsule will have been accelerated by the Sun to very high speed, relative to the Earth. Position of the Earth in its orbit at both launch and return will be critical in terms of matching speeds.

Now consider this. During a 501 day trip, in round figures, Mars will complete 0.73 orbits, Earth 1.37, Venus 2.23, Mercury 5.69 and Jupiter 0.12. So, at different points during the trip, all the inner planets will change relative positions significantly and may have a part to play in influencing the space capsule’s progress. You may be surprised that I included Jupiter but it is so massive. The other inner planets although much less massive, could well interpose, in gravitational terms, between the Earth and the capsule at some point in the flight.

I would love to see a computer animated simulation of the 5 inner planets and Sun and their gravitational wells at the various orbital juxtapositions they will occupy during the 501 days of the planned trip.

Here are some interesting comparative numbers (source data from OU modules S282 and S283).
Note: All masses and distances are relative to Earth's. Periods are in days.

The relative gravitation figures are as experienced at Mars’ position. These are mass relative to Earth divided by distance relative to Earth’s orbital radius (Astronomical Unit) squared. Mass of Mars and gravitational constant are common so excluded. We can readily see that Venus’s influence at nearest to Mars (1.27) exceeds Earth’s at its farthest (0.16).

Note that Jupiter’s influence at Mars, even at its farthest distance (7.04), is greater than Earth’s at its nearest (3.70)! Mercury doesn’t figure at all (no surprise there).

The Sun’s dominance is all too clear! You can see what the capsule will be up against!

Then let’s not forget the asteroids flying about.


Relative Orbital  Orbs in Nearest  Relative Farthest Relative
Planet Mass Radius Period 501 days Distance Gravity Distance Gravity
Sun 332775.9 0 0.00 1.52 144033.90 1.52 144033.90
Mercury 0.055 0.39 88.00 5.69 1.13 0.04 1.91 0.02
Venus 0.815 0.72 224.70 2.23 0.8 1.27 2.24 0.16
Earth 1 1 365.30 1.37 0.52 3.70 2.52 0.16
Mars 0.107 1.52 687.00 0.73 0 0
Jupiter 318 5.2 4332.46 0.12 3.68 23.48 6.72 7.04

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