Gravity definitions / formulas

What does the concept of a field mean?

A region in which a body (mass, + charge or current) experiences a force

Definition of gravitational field strength

Force per unit mass

What would gravitational field lines look like at a large distance from the earth

Radial. The field obeys the inverse square law

What would gravitational field lines look like when viewed from the surface of the earth

Uniform and down

The relationship between gravitational field strength and distance OUTSIDE the earths surface

Inversely proportional to the distance squared from the centre of the mass.

The relationship between gravitational field strength and distance INSIDE the earths surface.

Directly proportional to the distance

What equation would you use to determine the mass of the planet if you know the acceleration of an object at its surface

M = g r^2 / G

What equation would you use to determine the gravitational field strength OR acceleration at a distance, r, from a mass, m

GM / r^2

Unit for gravitational field strength

ms^-2 or N kg^-1

State Newton's law of gravitation

The attractive force between two masses is directly proportional to the product of the masses and inversely proportional to the distance between the two masses squared

The unit for the gravitational constant, G

N m^2 kg^-2

What equations would you equate when solving problems involving orbiting satellites

G m m / r^2 = m v ^2 / r

How would one derive Keplers 3rd law

G m m / r^2 = m v ^2 / r and sub in v = 2 pi r / T

How would one derive escape velocity

equate energy's 1/2 mv^2 = GmM / r

Define Kepler's 3rd Law

The orbital radius cubed is proportional to the orbital time period squared

Define what is meant by a geostationary satellite

Period = 24hrs Orbits the equator. Always above the same point above the earth Same angular velocity as the earth

What does the gradient of a T^2 (y - axis) Vs r^3 (x - axis) graph correspond to for a satellite in orbit

4π^2 / G M

What does the gradient of a logT (y - axis) Vs log r (x - axis) graph correspond to for a satellite in orbit

3/2

What does the gradient of a log r (y - axis) Vs log T (x - axis) graph correspond to for a satellite in orbit

2/3

What does the ratio of the time periods of two different satellites orbits correspond to. i.e. T1 / T2

(R1 / R2)^3/2

What does the ratio of the radii of two different satellites orbits correspond to. i.e. r1 / r2

(T1 / T2)^2/3

K.E of orbiting satellite which has a radius r

GMm / 2r

Gravitational P.E of an orbiting satellite which has a radius r

-GMm/r

Total energy of an orbiting satellite which has a radius r

-GmM/2r

Escape velocity of a body

root (2GM/r)

Velocity of an orbiting satellite

root (GM/r)

Derive this by equating Newton’s law of gravity and the centripetal force equation

What must you be careful with when using g = G m / r^2 or any other formula involving r?

R is the distance from the centre of the mass (es). You may need to consider the radius of the planet. URGENT: IF THEY GIVE YOU THE ORBITAL RADIUS THEY MEAN FROM THE CENTRE OF THE PLANET TO THE POINT IN QUESTION.

Area of a graph of the gravitational force between two masses (y - axis) Vs distance between two masses (x - axis)

gravitational potential energy between two points = the work done in moving a mass between two points

Definition of Gravitational P.E

Work done in moving a point mass from infinity to that point

Gravitational potential definition

The energy per unit mass required to move a point mass from infinity to that point

Gravitational ptential formula

• V = GM / r

Gravitational potential difference

∆V = final potential - initial potential The work done per unit mass in moving a mass between two points

How to determine the work needed to move a unit mass between two points in a potential well

W = m ∆V = m (V2 - V1)

How to determine the total gravitational potential at a point between two masses

Add the potentials due to the two masses: Total potential = - Gm/d1 - G M/ d2 d1: distance to mass, m d2: distance to mass, M

Equipotential surfaces

A line on which the gravitational potential energy is constant. No work is done when moving a mass along the line

The link between gravitational field lines and Equipotential surfaces

They touch at 90 degrees Gravitational line point towards larger negative potentials

The mathematical link between gravitational field strength and gravitational potential

Gravitational field strength is equal to potential gradient. g = - ∆V / ∆r

Why is gravitational potential always negative?

There is zero attraction between masses at infinity since the range of the gravitational force is infinite. So only at infinity is gravitational potential zero. Since work has to be done in moving it there it must mean that gravitational potential is negative.

Gradient of a graph of potential (y - axis) against distance from a mass (x - axis)?

= gravitational field strength since g = - ∆V / ∆r

The area of a graph of gravitational field strength (y - axis) against distance from a mass (x - axis)?

= change in gravitational potential. since ∆V = - g ∆r

Define escape velocity

The velocity (non mechanical) a body must have in order to escape the gravitational attraction and move to infinity

In order for a rocket to move to a certain orbit it required a certain velocity. State 2 reasons why this is not the escape velocity.

1. The rocket is still within the gravitational field of the planet. It has not escaped the gravitational field to infinity.

2. The rocket applied a constant force along the journey. Escape speed is defined as the speed that must be applied at the surface only . By a non mechanical body.

How to determine the escape velocity of a body when you know the gravitational potential of the body at that point

root (2 ∆V)

How to determine the escape velocity of a body when you know the gravitational field strength at that position

root (2gr)