Gravitional Field

Question 1

What is newton’s law of gravitation

Answer 1

It states that 2 point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of their separation.

Question 2

What is gravitational force

Answer 2

F = (Gm1m2)/r^2

Question 3

What is a gravitational field

Answer 3

The gravitational field is a region of space where a mass experiences a gravitation force

Question 4

What is gravitational field strength at a point

Answer 4

Gravitational field strength at a point is defined as the gravitational force acting per unit mass at the point

g = GM/r^2

Question 5

What are the factors affecting g measured on earth

Answer 5

1. The non-spherical shape of the earth
   
   • since g α 1/r^2, the value of g is greater at the poles
2. Density of the earth
3. Rotation of the earth
   
   • Apparent weight N at equator
     
     • N = m(g - Rω^2)

Question 6

What is the resultant gravitational field strength

Answer 6

The resultant gravitational field strength at any point is the vector sum of the individual gravitational field strengths

Question 7

What is gravitational potential energy

Answer 7

Gravitational potential energy U at a point is defined as the work done by an external agent in bringing a body from infinity to that point (without any change in its kinetic energy)

U = -(GMm/r)

Question 8

What is gravitational potential

Answer 8

Gravitational potential Φ at a point is defined as the work done per unit mass by an external agent in bringing a body from infinity to that point

Φ = - (GM/r)

Question 9

What is the relationship between F and g

Answer 9

g = F/m

Question 10

What is the relationship between g and Φ

Answer 10

g = -( dΦ/dr)

Question 11

What is the relationship between U and F

Answer 11

F = - (dU/dr)

Question 12

What is the relationship between U and Φ

Answer 12

Φ = U/m

Question 13

What is the resultant gravitational potential

Answer 13

The resultant gravitational potential at the point is given by scalar addition of the potentials due to 2 or more masses present.

Question 14

What is an equipotential surface

Answer 14

Equipotential surfaces are surfaces on which the potential is the same at all points on the surface

Question 15

What is escape speed

Answer 15

Escape speed is the minimum speed at which a body can be projected from the surface of a planet so that it reaches an infinite distance from that point

Question 16

What is the escape speed

Answer 16

v = (2gR)^1/2

Question 17

What is the orbital speed and period for satellites

Answer 17

T = 2π(r^3/GM)^1/2
v = (GM/r)^1/2

Question 18

What are the features of geostationary orbits

Answer 18

1. It is an equatorial orbit
2. It has a period of 24h
3. It moves in the same direction of rotation as the earth

Question 19

What is the radius of a geostationary orbit

Answer 19

r = (GMT^2/4π^2)^1/3