Which of the following is correct about the gravitational field strength at a point near a planet?

  The gravitational field str ;b20 nx,d;mema2xjc length on the surface of the moon is $\frac{g_E}{6}$. Two objects of different masses m and $2\,m$ are released with zero speed on the moon from heights of ℎh and $2\,h$, respectively, where ℎh is small compared to the radius of the moon.
What are the magnitudes of the accelerations of these objects right after release?

  

  Which of the following graphs shows the variatiol2(uf p0-- k-)b9fl rfstjva jn of the gravitational field strupj (s l-vlr0- 2fk9ajtb -ff)ength of a planet with distance $r$ from the surface of a planet?

  The following statements are given about the forces acting on a satellite in orbit around a planet.

I. The gravitational force on the satellite is proportional to the mass of the planet and the mass of the satellite.
II. The strength of the gravitational field is equal to the weight of the satellite.
III. The centripetal force acting on the satellite is provided by the gravitational force between the planet and the satellite.
Which of these statements are correct?

  A satellite is in an orbit around a planet of radius $R$. The graph shows the variation of different energy quantities against r, which is the distance from the center of the planet. The graph origin represents the surface of the planet.

  

  Spaceship A orbits Earth w-fa k/j97 6ixsey 4zkiith orbital speed $v_A$​ and orbital radius $r$. Spaceship B orbits planet X that has a mass twice that of the earth.
What will be the orbital speed of spaceship B if it were to have the same orbital radius as spaceship A?

  A satellite is in a circbho 7 51jw( wlz+xcc-uular orbit of radius $R$ around a planet of mass $M$. Which of the following graphs represents the relationship between the centripetal acceleration of the satellite and its orbital radius?

  


I. 2 equal masses.
II. 2 equal charges of the same sign.
III. 2 equal charges of opposite sign

  Satellite $A$ of mass $M$ orbits a planet with an orbital speed $v$ and orbital radius $R$. Another satellite $B$ with mass $3M$ orbits the same planet with the same orbital speed.
Knowing that the ratio $\frac{Centripetal force of satellite A​}{​entripetal force of satellite B}\,=\,\frac{1}{3}$, what is the orbital radius of satellite $B$?

A space station X orbits Ear* qxdzf,t1: d h,bh2fo7pynu 3th with orbital radius $R$.

1.State Newton's universal law of gravitation.
2.Explain why an astronaut in the space station feels weightless.
3.The space station changed its position so that its orbital radius is $2R$.
Explain how the gravitational field strength of Earth at this new position compares to that at the orbital radius $R$.
4.Another space station Y with a smaller mass orbits Earth with at the same orbital radius $R$.
Compare the orbital speed of Y to the orbital speed X.

  Geostationary satellites are satellites that complete one circular orbit in the same amount of time it takes for the Earth to rotate once on its axis. A geostationary satellite is placed in an orbit at $3.6\times10^7\,m$ above the Earth's surface, at the equator. The radius of the Earth is $6.4\times10^3\,km$.


The satellite undergoes uniform circular motion.
1.Define gravitational field strength.
2.Show that the linear speed of the satellite is approximately $2.6\times10^3\,ms^{-1}$. v =    $\times10^3\,ms^{-1}$
3.Calculate the gravitational field strength at the point in the orbit of the satellite. g =    $\times10^{-1}\,ms^{-2}$

  1.(1)The Moon orbits the Earth in rnymr.,3xgra l2hkn5,s-zb 6a circular orbit. Explain why a centripetal force is needed 5,, ymslr3 2rx-6nrhbzk .ngafor the Moon to be in its orbit around the Earth.

(2)Identify the origin of this force. v =    $\times10^3\,m$
2.(1)Show that the orbital period T of the Moon around the Earth is given by $T=2 \pi \sqrt{\frac{r^3}{GM}}$
where $M$ is the mass of the Earth and $r$ is the orbital radius.
2.Knowing that
Mass of the Earth = $5.98\times10^{24}\,kg$
The orbital radius = $3.84\times10^8\,m$
Calculate the orbital speed of the Moon around the Earth.
3.(1)A total solar eclipse is seen when the Sun, the Moon and the Earth lie on the same line with the Moon in between the Sun and the Earth.
Knowing that
Mass of the Sun = $1.99\times10^{30}\,kg$
Distance between Sun and Moon during eclipse = $1.49\times10^{11}\,m$
Mass of the Moon = $7.36\times10^{22}\,kg$

Determine whether the Sun or the Earth exerts a greater gravitational force on the Moon.
(2)Explain why the Sun doesn't pull the Moon away from the Earth during a total solar eclipse.

  A spaceship orbits a planet atdk-f-ybx 4c-e a distance of $d$ from the center of the planet. Later the spaceship moves and settles into a new orbit of $\frac{d}{2}$​. which of the following describes the change in kinetic energy, potential energy, and total energy of the spaceship?

  Planet X has half the mass and twice the diameter of planet Y. Tgr3*-n)q/vhx dm d+pmhe escape speed ) md/mdx- n3*q +grhvpfrom the surface of planet X is given by v. What is the escape speed from the surface of planet Y ?

  

  The diagram shows the gravitational fielcbv ley, )w-+:pm )-m 3qxsaptix m0m7d between two masses $m_1$​ and $m_2$​.



Which of the following is correct?

  Planet $X$ has radius $R$ and density $ρ$. The gravitational field strength at the surface of Planet $X$ is $g$.
What is the ratio of the gravitational field strength at the surface of planet $Y$, which has radius $0.25R$ and density $3ρ$, to that at the surface of Planet $X$?

  A proton and another object with charge +e exert electrical and gravitational forces on one another. To the nearest order of magnitude, what mass must the object have to be so that the net force acting on it is zero?

  1.State Newton's law of Gravitation.
2.A geostationary orbit is a special orbit in which satellites follow a circular path and remain above a fixed point above the Earth's surface. A satellite orbits in geostationary orbit at a constant speed of v and orbital radius of R. The mass of the Earth is M.
(1)Show that $\sqrt{\frac{GM}{R}}$
(2)The radius of the satellite's orbit is $4.23 \times10^7\,m$. Use this information to estimate mass of the Earth. M =    $\times10^{24}\,kg$

  A satellite of mass 40 kg is moved frjmv 5+n bf,cv7om one point in space to another for experimental purposes. The graph below shows how the gravitational potential V of the points that the satel,f57vv+cnjm b lite moves through varies with time t.


The change in gravitational potential energy of the satellite is 600 MJ. Which of the following gives the magnitude of the gravitational potential $V_f$​ at the final location of the satellite?

  The centers of three masses lie on the same line. The centers of the masses are separated as shown.


The net gravitational force on m22​ is zero when the value of $d$ is one third of $x$. What is the ratio $\frac{m_1}{m_3}$?

  Planet $A$ has a gravitational field strength $g$ at its surface. Planet $B$ has twice the density and twice the radius of planet $A$.
What is the gravitational field strength at the surface of $B$?

  Satellites $A$ and $B$ orbit the same planet of mass $M$. Satellite $A$ has a mass of $3\,m$ and it is located at a height of $R$ from the surface of the planet. Satellite $B$ has a mass of $m$ and it is located at a height of $2R$ from the surface of the planet.
What is the ratio of the centripetal force acting on $A$ to the centripetal force acting on $B$?

  1.A space probe lands on tiap3k5; ufjy.he surface of a planet which has the same radius as the Earth, and a gravitaku y;ijf. 53aptional field strength of $6.7\, N\,kg^{−1}$ at its surface.
(1)The mass of Earth is given as $5.98\times10^{24}\,kg$. Show that the planet’s mass is approximately $4\times10^{24}\,kg$. $m_{planet}$ =    $\times10^{24}kg$
(2)The average radius of the planet is $6.37\times10^3$ km. Calculate the planet's average density in SI base units.
(3)The planet is at a distance of $1.43\times10^{11}\,m$ from the Earth. Calculate the gravitational force between the Earth and the planet.
3.(1)Calculate the magnitude of the resultant gravitational field strength between the planet and the Earth at point $X$, which is located $\frac{1}{3}$ of the total distance between the planets when measured from the Earth. $g_{planet}$ =    $\times 10^{-9}N\,Kg{-1}$

(2)Suggest a reason why your answer above is only an estimate.
3.(1)The planet has a moon with an orbital radius of $1.20\times10^7\,m$. Show that the acceleration of this moon is approximately $1.9\,ms^{−2}$.
(2)Calculate the angular speed of this moon.
(3)Determine the orbital period of this moon, in hours. h =    $h$

A satellite of mass lx tbw.(oq* s3e3g;4uowey x5 $m$ is launched from the surface and placed in an orbit around a planet of mass $M$ and radius $R$. The height of its orbit from the surface of the planet is ℎh.
The initial speed of the satellite is equal to $\frac{4}{5}​v_{esc}$​.
The planet has no atmosphere.
1.Define gravitational potential energy
2.(1)Show that the initial total energy of the satellite is given by $-\frac{9GMm}{25R}$​.
(2)The satellite is placed in an orbit with orbital radius $r$.
Determine the expression for the total energy of the satellite in its orbit in terms of $G$,$M$,$m$ and $r$.
(3)Use your answers to parts b(i) and b(ii) to determine the height of orbit above the surface of the planet in terms of $R$.
3.The satellite ejects excess fuel opposite to its direction of motion. Suggest the effect of this change on the average orbital radius of the satellite.

  Two masses of $6.2\times10^3\,kg$ and $4.0\times10^3\,kg$ are initially separated by a distance of 4.3 m between their centers.
1.Calculate the gravitational potential energy of the two masses when in this arrangement. $E_g$ =    $\times10^{-4}\,J$
2.Explain why your answer to part (a) is negative.
3.With reference to the gravitational potential due to the $6.2\times10^3\,kg$ mass, suggest how the gravitational potential energy would change if the $4.0\times10^3\,kg$ mass were moved further away.

  The escape speed from the surface of a planetw lof9d7hbflm ,t o93dqm0 1;x of mass $M$ and radius $r$ is given by $v_{esc}$​.
What is the orbital speed of a satellite of mass $m$, at a height of $2r$ from the surface of the same planet?

  1.Define gravitational field+wn+lk ,v8udy strength.
2.The Earth's average radius is given as $6.37\times10^3\,km$. Calculate the height above the Earth's surface at which gravitational field strength becomes half of its surface value.
3.Calculate the gravitational force acting on a satellite of mass $2.63\times10^6\,kg$, placed at the height in part (b). State your answer to the appropriate number of significant figures.
4.Using the available information, calculate the mass of Earth. $M_{earth}$ =    $10^{24}\,kg$

  Two planets X and Y have the same density however the radius of planet X5l.c/4dd2 zdno ,n;byglm+wapv )2i v is larger than that of Y. Two satellites with equal masses A and B orbit X and Y respectively with the same orbital radius. Which ; 5lddi.zdl/b4 y og)vn,+ a2wnc 2mpvof the following quantities is smaller for satellite A?

  


What is the total gravitational potential at X?

  Two point charges are separated by a distance r as shown.






The negative charge's acceleration is 3 times that of the positive charge.
What is the ratio $\frac{Gravitational force​}{Electrostatic force}$ between the two point charges?

  A satellite is in an orbit at a height ℎh above the surface of Earth. The gravi61ziwn 3fy .k nu0oz+vhbcr9p6e 7. wntational potn yowe 7izw09 n.hn1uzkv6f3 b.6cpr+ ential at its location is V.
The satellite is transferred to a different orbit where the gravitational potential is $\frac{V}{2}​$
What can be deduced about the new height of this satellite from the surface of Earth?

  Two stars of equal ma6* /6zmc*th,f,c + ;mobrkd-/bik: bjjbybhcss $M$ are shown in the diagram, distance $d$ apart. A planet is equidistant from the two stars, with distance $\frac{d}{s}$ across the midpoint of the line joining the stars as shown.


What is the resultant gravitational field strength at the position of the planet due to the two star