19 Selected Topics in Astrophysics
Resources
- Video to Watch: Mechanical Universe – Episode 9 – Moving in Circles
- Extra Help: A-Level Physics Tutor
- Article to Read: Space is a Busy Place and Canada Needs to Be There
Equations Introduced or Used in this Topic:
- [latex]v_{esc}=\sqrt{2GM_o{d}_o}[/latex]
- [latex]R=\dfrac{2GM}{{c}^2}[/latex]
- [latex]\Delta E_p=-\dfrac{Gm_1{m}_2}{t}[/latex]
- [latex]T=2\pi\sqrt{\dfrac{r^3}{GM}}[/latex]
Where…
- [latex]M, M_o, m_1, m_2[/latex] is the Mass of the object, measured in kilograms (kg)
- [latex]v_{esc}[/latex] is the Speed that an object needs to permanently escape the gravitational field of a body, measured in metres per second (m/s)
- [latex]r[/latex] is the Radius of the orbit, measured in metres (m)
- [latex]T[/latex] is the Period of Orbit, measured in seconds (s)
- [latex]G[/latex] is Newton’s Gravitational Constant, currently estimated to be 6.67408(31) × 10−11 Nm2/kg2
- [latex]∆V[/latex] is the Gravitational Potential of a mass measured in joules per kilogram (J/kg)
- [latex]d[/latex] or [latex]d_o[/latex] is the Distance away from the Mass Centre of a Body (gravitational field) or the Distance between Mass Centres of Two Bodies (gravitational fields), measured in metres (m)
- [latex]v_{esc}[/latex] is the Escape Velocity needed to escape the body in metres per second (m/s)
- [latex]r_o[/latex] is the Distance away from the object’s mass centre in metres (m)
- [latex]c[/latex] is the speed of light in meters per second (2.9979 × 108 m/s)
- [latex]R_s[/latex] is the Schwarzschild radius or the event horizon of the black hole
- [latex]T[/latex] is the period of orbit of the satellite measured in meters per second (m/s)
- [latex]r[/latex] is the Orbital Distance between mass centres in metres (m)
One of the challenges of placing satellites in orbit or in manned space missions is the problem of recent human ventures into space, from the planned and protested 2007 Chinese destruction of a satellite to multiple accidental collisions of satellites and space debris.
As of July 2016, the United States Strategic Command tracked a total of 17852 artificial Earth orbit objects. As of January 2019 an estimated 129 million bits of debris were thought to be in orbit around the Earth.
As the number of these bits of debris increases, there exists the risk that the Earth’s orbit will become impassable due to the risk of collisions. Space debris is suspected or known to have damaged or destroyed over nine satellites to date.
The Shuttle Endeavour impact from debris is shown below.
19.1 Escape Velocity
Escape Velocity is the minimum speed needed for an object to permanently escape the influence of the gravitational force of a body, such as a planet, moon or star. The first such object launched from the Earth to achieve escape velocity did so on January 2nd, 1959, launched by the former USSR from the Baikonur Cosmodrome. It eventually reached an orbit around the Sun between the planets Earth and Mars.
The escape v