# National Aeronautics and Space Administration

## The Anatomy of Black Holes - Page 25

Gravity is as Gravity Does

Extension:

1. Even though there are exceptions, the data tend to support the generalization that acceleration due to gravity varies directly with the mass of the object. This would be expected from this rearrangement of Newton's Universal Law of Gravitation: g = Gm/r2.

2. The exceptions are that Saturn and Neptune are in reverse order and so are Earth and Uranus.

3. Since acceleration due to gravity is measured at the surface of an object and since gravity increases exponentially as the distance between the surface of an object and its center decreases, an object of lesser mass but smaller radius may possesses a greater acceleration due to gravity than an object of greater mass and greater radius. When a table of planetary radii is consulted, it is found that the radius of Neptune in less than half that of Saturn and the radius of Earth is about 1/4 that of Uranus. Based on the equation given in 2, it is reasonable to conclude that the radii of these objects account for what at first glance appear to be exceptions to the rule.

4. Your weight would change depending on the value for the acceleration due to gravity. Weight is a measure of the force that varies directly with the acceleration due to gravity, or simply F = mg. Thus, the larger the value of g, the greater your weight!

5. Since Pluto possesses the lowest acceleration due to gravity, thus the lowest force of attraction to its surface, less energy would be required to overcome that force than would be the case on any of the other objects.

Testing Einstein 101

1. During a total eclipse the sky would be dark and the stars could be observed. The light from some of the visible stars would pass close to the Sun.

2. If the star was visible in the sky during the day in March, six months earlier it was visible in the night sky. Since the position of stars relative to Earth remains essentially constant, determining the position of the star during the night (six months earlier) provided the scientists with valid data about the star's actual position.

3. Since the observed position of the star was more distant from the Sun's disc than its actual position, the scientists could conclude that light from the star was deflected toward the Sun by its gravitational field. Thus, the experiment supported Einstein's theory.

Crossing the Event Horizon

1. Using the Schwarzschild equation, we input the mass of Jupiter (1.9x1027 kg), the Gravitational constant (G=6.67x10-11 m3/kg-sec2) and the velocity of light (3x108 m/sec) to see that the event horizon of a Jupiter-mass black hole would occur at 2.82 meters.