General Relativity: Curved Spacetime and Its Tests · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Gravity as curved spacetime

Science · Astronomy & Astrophysics · ages 21-22
Name ______________________   Date ____________

  1. How does general relativity describe gravity?

    • As an instantaneous Newtonian force acting across flat space
    • Through spacetime geometry shaped by matter and energy
    • As a force acting only on rest mass, never on light or energy

  2. When tidal effects can be neglected, what does local equivalence say about a freely falling laboratory?

    • It behaves like an inertial laboratory far from gravity
    • It behaves like a laboratory accelerating upward in space
    • It detects no spacetime curvature at any distance or time

  3. For stationary clocks at different heights around the same body, the lower-potential clock accumulates less time than the higher-potential clock.

    Circle one:   True   False

  4. Which measurement is Mercury's classical test of general relativity?

    • Its extra perihelion advance beyond Newtonian predictions
    • Its changing surface brightness during each solar orbit
    • Its changing radio frequency caused by Earth's rotation

  5. Why is starlight deflected as it passes near the Sun?

    • The Sun's gravity changes light's locally measured speed
    • The beam follows a null geodesic in curved spacetime
    • The beam is refracted by plasma, with no spacetime curvature

  6. Why must GPS account for relativity in its timing?

    • Only satellite motion changes clock rates
    • Gravity and motion cancel the satellite clock-rate shift
    • Gravity and motion change satellite clock rates

  7. Light travels upward between stationary observers in a static gravitational field. The higher observer measures a lower frequency. What happens to its locally measured wavelength and speed?

    • The wavelength increases and the local speed decreases
    • The wavelength decreases and the local speed stays c
    • The wavelength increases and the local speed stays c

  8. Two initially comoving, freely falling objects develop relative acceleration. In general relativity, which interpretation can explain this?

    • Different fall accelerations show that local equivalence is false
    • Tidal differences in free fall can reveal spacetime curvature
    • The relative acceleration can always be removed by choosing one falling frame
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Answer key

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Gravity as curved spacetime W1-mt_-rZZxZwU2L-s1

  1. Through spacetime geometry shaped by matter and energy · Matter and energy affect spacetime geometry, and that geometry determines free-fall paths.
  2. It behaves like an inertial laboratory far from gravity · Local experiments in free fall reproduce those in an inertial laboratory without gravity, within the stated tidal limit.
  3. True · Under this stationary comparison, lower gravitational potential corresponds to a slower clock rate relative to the higher clock.
  4. Its extra perihelion advance beyond Newtonian predictions · The test measures the extra advance of Mercury's perihelion, about 43 arcseconds per century.
  5. The beam follows a null geodesic in curved spacetime · Light follows the paths determined by spacetime geometry; near the Sun those paths differ from straight lines in flat spacetime.
  6. Gravity and motion change satellite clock rates · GPS uses signal timing. Both gravitational and motion-related clock-rate differences affect that timing.
  7. The wavelength increases and the local speed stays c · Local light speed remains c. Since c = frequency times wavelength, a lower frequency requires a longer wavelength.
  8. Tidal differences in free fall can reveal spacetime curvature · Relative acceleration between freely falling objects can reveal tidal effects. Local equivalence does not remove curvature across an extended region.
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