The Universe in the Classroom

Up, Up, and Away

To the Red Planet

With this knowledge of orbits, we are ready to plan a trip to Mars. Mapping out the path involves several facts:

The Hohmann transfer orbit from Earth to Mars is very curved (see diagram) because the 107,000 kilometers per hour of the Earth's orbital motion about the Sun combines with 41,200 kilometers per hour imparted by the rocket engines. In a similar fashion, a bomb dropped from a plane makes a curved path due to the speed of the plane and the gravity of Earth. Moving in a straight path from Earth to Mars would take an enormous amount of fuel.

Trip around Mars
Come take a trip around Mars. To get to Mars, first launch yourself into orbit around Earth. Then fire your rockets in the same direction that Earth is moving around the Sun. A speed of about 42,000 kilometers per hour will be enough to escape the Earth's gravity and, when added to the Earth's orbital speed around the Sun, put the spacecraft on a Hohmann transfer orbit to the Red Planet. If you time it right, you'll arrive at the orbit of Mars when the planet is there. At that point, fire the rockets to match your speed to that of Mars. By the way, when you get there, send us a postcard.

Eight months after launch, the spacecraft arrives at Mars, where it must slow down enough to be captured by the martian gravity. The escape velocity of Mars is 18,000 kilometers per hour (11,000 miles per hour), a good deal slower than the escape velocity of Earth, because gravity on Mars is weaker (see table). In the past, Mars-bound space probes have gone into Mars orbit by firing retrorockets to slow down.

Engineers are now working on a technique that does not require a retrorocket. Called aerocapture or aerobraking, the technique aims the craft into the planet's outer atmosphere to slow it down by atmospheric drag. This technique was shown in the movie "2010'' when the Russian spaceship Leonov went into Jupiter orbit. In fall 1994, mission controllers used aerobraking to circularize the orbit of the Venus probe Magellan. Relieved of the need to carry rocket fuel, an aerobraked probe could instead carry twice the payload. Aerocapture might prove dangerous for a manned Mars mission, though, for it would suddenly subject the astronauts to 6 to 8 gs after they had spent months in zero-g. Six to 8 gs would cause a 150-pound astronauts to weigh 900 to 1,200 pounds.

Thanks for the Lift

Another technique that cuts down on the need for rockets is the gravity assist. This uses a planet's gravity and orbital motion to fling a spacecraft in a new direction and at a higher speed. As the spacecraft approaches the planet, it speeds up; after it passes the planet, it slows down. If the planet were sitting still, the process would be symmetrical; the spacecraft would leave with the same speed it had when it came in. Only the direction of the spacecraft would change.

But because the planet is orbiting the Sun, the process is not symmetrical. If mission controllers choose the right approach path, the space probe can have a net gain or loss of speed. The most famous gravity assist sent Voyager 2 from Jupiter to Saturn, Uranus, and Neptune. With each flyby, the path of Voyager was bent and its speed was increased in the direction of the planet's motion. The Galileo probe [see "Here Is My Journey's End,'' The Universe in the Classroom, Fall 1995] swung by Venus once and Earth twice to gain the momentum to reach Jupiter.

The only problems with gravity assists are that they increase the flight time and require waiting for the planets to be lined up in the proper configuration. Voyager made its journey from Earth to Jupiter in just under two years without an assist; Galileo took a little over six years using the assists.

Perhaps one day humans, too, will fly to the planets -- and beyond. But the farther a craft must go, the more problems it will encounter. To escape the Sun's gravity, a starship launched from Earth would have to go at 152,000 kilometers per hour (94,000 miles per hour). Even at that respectable speed, the stars would seem impossibly distant. Stars lie at distances measured in light-years. A light-year is the distance that light travels in one year -- about 9.6 trillion kilometers (5.9 trillion miles). At the above velocity, it would take 30,000 years to reach the nearest star.

Increasing the speed would require special, as-yet- undeveloped types of rocket engine to minimize the amount of fuel the starship would need to carry. By accelerating at 1 g for several months, a starship could make it to the nearest star and back in 30 years. But for this journey, even a "Star Trek''-style antimatter engine would consume 40,000 tons of fuel per ton of payload. The odds seem insurmountable, but remember that just a half century ago, few people seriously thought that we could visit space at all.

JAMES J. SECOSKY is a science teacher at Bloomfield Central School in Bloomfield, N.Y. He used to teach a summer course for kids, "How to Drive the Space Shuttle.'' For more information on space travel, an excellent resource is Thomas Damon's Introduction to Space, published by Krieger Publishing.

How Fast Do You Have to Go?

Speed is the essential ingredient in space travel. If you can go fast enough, you can orbit a planet or escape from it. The velocity required to put a satellite into a circular orbit depends on two things: the mass of the body around which the satellite orbits and the distance of the satellite from the center of the body. Because planets have different masses and sizes, satellites orbit them at different speeds.

The first column in this table gives the velocity of a satellite in low orbit -- that is, an orbit near to the surface of the body. This is the highest speed a satellite of that body can have; farther away, a satellite orbits at a slower speed. The second column gives the escape velocity. Any rocket launched from the surface with this velocity will break free of the body's gravity altogether. Do you notice anything about the two columns of numbers?

Body
Velocity of satellite in low orbit (km/hr)
Escape velocity from surface (km/hr)
Sun 1,570,000 2,220,000
Mercury 7,080 10,000
Venus 21,900 31,000
Earth 28,500 40,300
Moon 6,100 8,640
Mars 12,700 18,000
Asteroid (typical) 71 101
Jupiter 58,200 82,400
Saturn 23,000 32,600
Uranus 19,800 28,000
Neptune 28,000 39,600
Pluto 1,020 1,440

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