D1 SL

Newton’s law states that for spherical masses of uniform density, mass is assumed to be concentrated at its center.
Gravitational Field Strength: Force per unit mass experienced by a small point mass at a specified point.
Resultant gravitational field strength calculations are limited to points along the line joining two bodies.

The law states that gravitational force between two point masses (m and M):
- Proportional to their product
- Inversely proportional to the square of their separation (r).
Universal Gravitational Constant (G): ( G = 6.67 × 10^{−11} ext{N m}^2 ext{kg}^{−2} )
Published in 1687 by Isaac Newton in "Philosophiae Naturalis Principia Mathematica".
Proposition III: The force keeping the moon in orbit is inversely proportional to the square of the distance from Earth's center.

A spherically symmetric body affects external objects as though all mass is at a center point.
Note the significance of how 'r' is defined: from center to center.

Discusses the instantaneous interaction between Earth and Moon despite their distance.
References Einstein's theory: information travels at the speed of light.
Gravitational Field (g) is a property of space, not requiring transmission.

Richard Feynman's perspective: a field is a potential to create a force.
In gravity, it's something providing acceleration felt by any object at that point.
Field as a property of space-time.

Gravitational Field Strength (g): The force per unit mass acting on mass (m) due to mass (M).
- Units: N kg d
For Earth: g = 9.8 N kg-1 or 9.8 m s-2.
Calculation: ( g = F / m ) - Acceleration experienced by mass at a distance from M's center.

Given:
- Mean mass of Earth (M_Earth) = 5.98×10^{24} kg
- Radius of Earth (R_Earth) = 6.37×10^{6} m
(A) When r = R:
- Calculation: ( g_A = \frac{G imes M}{R^2} = (6.67×10^{-11})(5.98×10^{24})/(6.37×10^{6})^2 = 9.83 ext{ N kg}^{-1} )
(B) When r = 3R:
- Calculation: ( g_B = \frac{g_A}{9} = \frac{9.83}{9} = 1.09 ext{ N kg}^{-1} )

Satellite mass: 525 kg.
Calculation at Earth’s surface: ( W_A = m imes g_A = 525 imes 9.83 = 5160 ext{ N} )
Calculation at Altitude: ( W_B = m imes g_B = 525 imes 1.09 = 572.25 ext{ N} )

Draws focus on local spacetime properties caused by mass (M) separated by distance (r).

Questions on gravitational field arrows pointing towards M.
- Do g1 and g2 have the same value? Which one is larger?

Length of arrows represents gravitational field strength: longer arrows = stronger fields.

Density of arrows indicates field strength; denser regions correlate with stronger fields.

Calculation
- Distance (d) = 3.82 x 10^8 m.
- Midpoint Calculation: ( r = \frac{d}{2} = 1.91 x 10^8 ext{ m} ) .
Gravitational field from Moon: ( g_{Moon} = 1.35 × 10^{−4} ext{ N} )
Gravitational field from Earth: ( g_{Earth} = 1.09 × 10^{−2} ext{ N} )
Net gravitational field: ( g = g_{Earth} - g_{Moon} = 1.08 × 10^{−2} ext{ N} ) towards Earth.