One last key concept in Special Relativity is introduced before discussion turns again to black celestial bodies (black holes in particular) that manifest the relativistic effects students have learned about in the previous lectures. The new concept deals with describing events in a coordinate system of space and time. A mathematical explanation is given for how space and time reverse inside the Schwarzschild radius through sign changes in the metric. Evidence for General Relativity is offered from astronomical objects.

The lecture begins with a comprehensive overview of the historical conditions under which Einstein developed his theories. Of particular impact were the urgent need at the turn of the 19th century to synchronize clocks around the world; Einstein's position at a patent office; and a series of experiments that he himself carried out. In 1905 Einstein published three papers that are still considered the greatest papers in the field of physics. The lecture then moves to General Relativity and how it encompasses Newton's laws of gravity.

The lecture begins with the development of post-Newtonian approximations from Newtonian terms. Several problems are worked out in calculating mass, force and energy. A discussion follows about how concepts like mass and velocity are approached differently in Newtonian physics and Relativity. Attention then turns to the discovery that space and time change near the speed of light, and how this realization affected Einstein's theories.

The discussion of black holes continues with an introduction of the concept of event horizon. A number of problems are worked out to familiarize students with mathematics related to black hole event horizons. In a longer question and answer session, Professor Bailyn discusses the more mystifying aspects of the nature of black holes and the possibility of time travel. Finally, the issues of reconciling Newton's laws of motion with Special Relativity, and Newton's law of gravity with General Relativity, are addressed.

The second half of the course begins, focusing on black holes and relativity. In introducing black holes, Professor Bailyn offers a definition, talks about how their existence is detected, and explains why (unlike in the case with exoplanets where Newtonian physics was applied) Einstein's Theory of Relativity is now required when studying black holes. The concepts of escape and circular velocity are introduced. A number of problems are worked out and students learn how to calculate an object's escape velocity.

Midterm Exam 1 covers Lectures 1 through 6.

Class begins with a problem on transits and learning what information astronomers obtain through observing them. For example, radii of stars can be estimated. Furthermore, applying the Doppler shift method, one can find the mass of a star. Finally, a star's density can be calculated. A second method for identifying planets around stars is introduced: the astrometry method. The method allows for an extremely accurate assessment of a star's precise position in the sky. Special features of the astrometry method are discussed and a number of problems are solved.

The class begins with a discussion on transits – important astronomical events that help astronomers to find new planets. The event occurs when a celestial body moves across the face of the star it revolves around and blocks some of its light. By calculating the amount of light that is being obscured astronomers can obtain important information about both star and planet, such as size, density, radial velocity and more. The concept of planetary migration is explained in order to better understand the dramatic differences between bodies in the Inner and Outer Solar System.

Professor Bailyn talks about student responses for a paper assignment on the controversy over Pluto. The central question is whether the popular debate is indeed a "scientific controversy." A number of scientific "fables" are discussed and a moral is associated with each: the demotion of Pluto (moral: science can be affected by culture); the discovery of 51 Peg b (morals: expect the unexpected, and look at your data); the disproof of pulsation as explanation for the Velocity Curves (moral: sometimes science works like science).

The formation of planets is discussed with a special emphasis on the bodies in the Solar System. Planetary differences between the celestial bodies in the Inner and Outer Solar System are observed. Professor Bailyn explains how the outlook of our Solar System can predict what other star systems may look like. It is demonstrated how momentum equations are applied in astronomers' search for exoplanets. Planet velocities are discussed and compared in relation to a planet's mass.