Gravity

Question 1

what is newton’s law of universal gravitation?

Answer 1

any 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 their separation

Question 2

define gravitational field strength

Answer 2

gravitational force per unit mass

Question 3

define gravitational potential energy

Answer 3

energy an object has due to its position in a gravitational field

Question 4

define gravitational potential

Answer 4

work done per unit mass to move a mass from infinity to that point

Question 5

what is an equipotential surface?

Answer 5

surface where potential is the same everywhere, no work done to more charge/mass along a equipotential surface

Question 6

how do you calculate the mass of planet being orbited at a distance r from centre with orbital speed w?

Answer 6

m*r*w^2 = G*M*m / r^2
M = r^3*w^2 / G

Question 7

prove that T^2 ~ r^3

Answer 7

GMm / r^2 = mrw^2
GM / r^2 = r(2pi / T)^2
T^2 = 4pi^2r^3 / G*M

Question 8

how do you calculate the speed of a satellite orbiting a planet?

Answer 8

mv^2 / r = GMm / r^2

v = (GM / r)^1/2

Question 9

define geostationary orbit

Answer 9

satellite moves in same direction of earth’s rotation, above the equator with a time period of 24hrs

Question 10

what are low polar orbits used for and why?

Answer 10

mapping land features, monitoring extent of polar ice caps, monitoring ocean currents, tracking cloud coverage, military surveillance

travel at high speeds

Question 11

derive equation for total energy of orbiting satellite

Answer 11

•total energy of orbiting satellite = Ep + Ek
•Ep = gravitational potential x mass = -GMm / r
•Ek: mv^2 /r = GMm / r^2
1/2mv^2 = 1/2GMm / r
therefore Ek = GMm / 2r
•total energy = GMm /2r - GMm /r = -GMm /2r

Question 12

why do satellites in LEO burn up?

Answer 12

affected by earth’s atmosphere which causes air resistance therefore total energy decreases but Ek increases as satellites speed up as they get closer to earth- causes satellite to spiral toward earth and burn up

Question 13

what is escape velocity?

Answer 13

speed at which an object must be travelling away from an astronomical body in order to break free from the gravitational field without any further use of propulsion

Question 14

derive equation for escape velocity

Answer 14

kinetic energy = work done
1/2mv^2 = m•dV = m•GM/r
v = (2GM /r)^1/2