La Gravitation

Question 1

State Newton’s Law of Gravitation

Answer 1

states that 2 pt mass attract each other w force proportional to pdt of their masses, inversely proportional to square of distance btw them

Question 2

Define Gravitational Field

Answer 2

region of space where a mass experience a gravitational force

Question 3

How to quantify as a small test mass?

Answer 3

1. point mass (very small dimension)
2. hv very small mass (m &laquo_space;M) so it does not distort field created by source mass M

Question 4

Define gravitational field strength

Answer 4

gravitational field strength at pt is gravitational force per unit mass on small test mass placed at that pt

Question 5

Define gravitational potential energy

Answer 5

gravitational potential energy, U, of mass m at pt in gravitational field due to mass M is work done by external force in bringing mass m fr infinity to that pt w/o change in Ek

Question 6

Define gravitational potential at a point

Answer 6

work done per unit mass by external force in bringing small test mass fr infinity to that pt w/o change in kinetic energy

Question 7

What are the equations for point mass and any mass for gravitation?

Answer 7

point mass:
- Force, F=GMm/r²
- Field Strength, g=GM/r²
- Potential energy, U= - GMm/r
- Potential, φ= - GM/r

Any mass:
- F=mg
- U=mφ
- F= - dU/dr ≈ - ΔU/Δr
- g= -dφ/dr ≈ - Δφ/Δr

Question 8

What is Kepler’s Third Law?

Answer 8

T² ∝ r³

Where
T is period of orbit,
r is orbital radius

Question 9

What are 3 conditions for geostationary orbit? Elucidate each

Answer 9

1. T of satellite orbit = 24h
   to match T of Earth’s rotat n
2. Satellite directly above equator
   Otherwise, at inclined orbit -> geosynchronous orbit (satellite appear drift north & south equator every 12h)
3. Satellite orbit in same direct n as earth’s rotat n fr west to east

Question 10

Name advantages and disadvantages of geostationary orbit. Explain why

Answer 10

Advantage:
- geostationary satellite appear remain in same pos n in sky when observed fr ground
—> useful for satellites serving particular region that need remain in that area eg telecommunications, weather satellites

Disadvantages:
- geostationary orbit is at considerable dist fr earth. So, resolution of photographs taken from such orbit is limited
- geostationary orbits r near (or directly above) equator
—> satellite limited in ability to serve customers at high latitudes (beyond 60° North or South) vs customers near equator

Question 11

What does negative total energy mean in an orbit? What must be done to escape to infinity?

Answer 11

• Satellite is captured in orbit ant planet, cnt escape to infinity
• to escape to infinite dist fr planet, must hv zero or positive total energy value