gravitational fields

Question 1

what is newtons law of gravitation

Answer 1

Newtons law of gravitation states that two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

Question 2

what is the formula for the gravitational force

Answer 2

F= GMm/R^2

Question 3

explain what it is meant by a gravitational field

Answer 3

A gravitational field is a region of space in which a mass placed in that region experiences a gravitational force

Question 4

what does the density of the gravitational field lines represent

Answer 4

the strength of the gravitational field

Question 5

define gravitational field strength

Answer 5

The gravitational field strength at a point in space is defined as a gravitational force experienced per unit mass at that point

Question 6

what is the formula for gravitational field strength, theres 2

Answer 6

g= F/m

g= GM/R^2

take note:
gravitational field strength points towards the mass that created it, i.e. the mass that it is being attracted towards.

Question 7

What are some properties from the shell theorem.

Answer 7

For a hollow sphere:

1. Any point inside the hollow sphere has a gravitational field strength of 0
2. Gravitational field strength outside varies with GM/R^2

For uniform solid sphere
1. Assuming that it has constant density (IMPORTANT)
2. Any point inside the uniform solid sphere of constant density, the gravitational field strength varies linearly with distance from center

PROOF:
M= density x volume = density x 4/3pier^3

g= GM/r^2 = G/R^2 (4/3pieR^3 * density) = 4/3GpieR * density `

Question 8

what does gravitational potential energy mean

Answer 8

gravitational potential energy of a mass at a point in the gravitational field is defined as the work done by an external force in bringing the mass from infinity to that point

Question 9

Why is gravitational potential energy negative

Answer 9

As the maximum energy for an object to stay within the gravitational field of the point mass is 0, the total energy has to be less than 0.

Question 10

what is the formula for gravitational potential energy

Answer 10

-GMm/R

Question 11

What is the relationship between gravitational force and gravitational potential energy and what are some characteristics about the relationship

Answer 11

F= -du/dr

1. the magnitude of the force at point R is the gradient of the potential energy curve at R

Question 12

define gravitational potential

Answer 12

The gravitational potential at a point in a gravitational field is defined as the work done per unit mass by an external force in bringing a small test mass from infinity to that point

Question 13

what is the formula of gravitational potential

Answer 13

phi= U/m = -GM/R

Question 14

what is the relationship between field strength and potential

Answer 14

g= -dphi/dr

Question 15

what is the criteria for escape velocity

Answer 15

any object will escape from the gravitational pull when it has a total energy of 0

Question 16

what is the formula for escape velocity

Answer 16

equate ke to gpe and find out what v is

Question 17

what is keplers third law

Answer 17

the square of the period of revolution of planets is directly proportional to the cubes of their mean distances from the sun

Question 18

How is kepler’s third law derived

Answer 18

applying N2L:

Fg = Fc
GMm/r^2 = mrw^2
GM/r^2 = r(2pie/T)^2
T^2 = (4pie^2/GM) * r^3

therefore T^2 = k r^3

Question 19

Derive the KE, GPE and Total Energy of a satellite in a circular orbit

Answer 19

as satellite is in circular orbit, Fg provides for centripetal force

GMm/r^2 = mv^2/r
v^2= GM/r

ke= 1/2 mv^2 = 1/2 * GMm/r

gpe = -GMm/r

Total energy = ke + gpe = 1/2 GMm/r - GMm/r = -1/2 GMm/r

Question 20

what are 3 characteristics of a geostationary satellite

Answer 20

its orbital period is the same as that of the earth about the axis of rotation

its direction of rotation is same as that of the earth about its axis of rotation

its plane of orbit lies in the same plane as the equator

Question 21

What are the advantages of the geostationary satellite

Answer 21

constant surveillance of the region under it

easy for ground station to communicate with it as it is permanently within view. ground based antennas can be fixed in one direction

satellite can receive and transmit signals over a large area due to the high altitude

Question 22

what are the disadvantages of a stationary orbit

Answer 22

significant loss of signal strengths

poorer resolutions in imaging satellites

time lag in telecommunication