Spaceflight and Einstein's gravity
Gravity governs spaceflight, and Einstein's general relativity refined Newton's picture, predicting phenomena from black holes to gravitational waves.
Getting to orbit
Rockets work by Newton's third law: expelling hot gas backward pushes the rocket forward. Reaching low Earth orbit requires a horizontal speed of about 7.8 km/s. Most rockets launch eastward to gain a boost from Earth's rotation, which is fastest near the equator.
Types of orbits
Low Earth orbit (roughly 160-2,000 km altitude) is used by the ISS and many satellites. Geostationary orbit, about 35,786 km above the equator, has a period of one day, so satellites there stay above the same spot, ideal for communications and weather. GPS satellites orbit at about 20,200 km.
Interplanetary travel
To travel between planets efficiently, spacecraft often use a Hohmann transfer orbit, an ellipse touching both the departure and arrival orbits. A trip to Mars this way takes about 7-9 months, and launch windows occur about every 26 months, when Earth and Mars are suitably aligned.
Gravity assists
Spacecraft can gain or lose speed by flying close to a planet, borrowing a tiny amount of its orbital momentum. Voyager 1 and 2, launched in 1977, used gravity assists from Jupiter and Saturn (and Voyager 2 also Uranus and Neptune). Voyager 1 entered interstellar space in 2012.
Einstein's general relativity
In 1915, Albert Einstein's general theory of relativity described gravity not as a force but as the curvature of spacetime by mass and energy. Physicist John Wheeler summed it up: 'Spacetime tells matter how to move; matter tells spacetime how to curve.' For most situations Newton's laws are an excellent approximation, but relativity is needed for strong gravity and high precision.
Tests of relativity
General relativity explained a small anomaly in Mercury's orbit that Newtonian gravity could not. In 1919, measurements during a solar eclipse showed starlight bending around the Sun by the predicted amount. Gravitational lensing, where massive galaxies bend light from objects behind them, is now a powerful astronomical tool.
Time, GPS, and gravitational waves
Relativity predicts that clocks run slower in stronger gravity and at higher speeds. GPS satellites must correct for both effects, totalling about 38 microseconds per day, or positions would drift by kilometres daily. In 2015, the LIGO detectors first directly detected gravitational waves, ripples in spacetime from two merging black holes, confirming another prediction.
Worked example
A geostationary satellite must orbit with a period of one sidereal day. Using Kepler's third law with Earth's mass gives an orbital radius of about 42,164 km from Earth's centre, or about 35,786 km above the surface. That is why all geostationary satellites sit in a single ring above the equator.
Key takeaways
Rockets use Newton's third law; low Earth orbit needs about 7.8 km/s. Geostationary orbit at about 35,786 km keeps satellites above one spot. Hohmann transfers take about 7-9 months to Mars, with windows every 26 months. Gravity assists sped the Voyagers. Einstein's general relativity (1915) describes gravity as curved spacetime. It explained Mercury's orbit and starlight bending. GPS needs relativistic corrections; LIGO detected gravitational waves in 2015.
Flashcard
Newton's third law
Check your understanding
Why must GPS satellites correct for relativity?