Chapter 7 Gravitational Field Flashcards
(13 cards)
Newton’s law of gravitation
+ Formula of gravitational force
Two point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of separation between them
F = GMm/r^2
G = 6.67 × 10^-11 N m^2 kg^-2
Gravitational field
A region of space in which a mass experiences a force
Gravitational field strength + formula
Gravitational force per unit mass acting on a small test mass placed at that point
g = F/m
Gravitational potential energy and formula
Work done by an external agent in bringing a mass from infinity to that point
U = -GMm/r
Escape velocity
Minimum value of the initial speed such that an object will escape the Earth’s gravitational field and reach infinity
Gravitational potential and formula
Work done per unit mass by an external agent in bringing a small test mass from infinity to that point
Φ = -GM/r
Why is gravitational potential negative (or potential energy)
Gravitational potential at infinity is 0
Since gravitational force is attractive in nature, the direction of external force is opposite to direction of displacement of the mass to bring a mass from infinity to a point in the gravitational field
This results in negative work done by external force
Hence by conservation of energy gravitational potential has a negative value
Relationship between g and Φ
g = -dΦ/dr
Kepler’s third law
The square of the period of revolution of the planets is directly proportional to the cubes of their mean distances from the Sun
Geostationery orbit requirements
The object must:
- rotate about the same axis as Earth in the same plane as the equator
- have an orbital period equal to the Earth’s rotational period
(So that the object and Earth both rotate through the same angular displacement over the same time interval)
Be orbiting from west to east
Advantages of geostationary satellite
Continuous surveillance of the region under it
Easy for ground station to communicate with as it is permanently within view
Ground based antennas can remain fixed in one direction hence geostationary satellites are often used for communication purposes
Satellite can transmit and receive signals over a large area
Disadvantages of geostationary satellite
Distance from Earth’s surface is large compared to low earth orbit (LEO) satellites
Leading to:
significant loss in signal strengths
poorer resolution in imaging satellites
time lag in telecommunication
How does binary star system orbit
Around the center of mass of the system
