6.2 – Newton’s law of gravitation

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The centre of the Earth and the Moon are a distance $D$ apart. There is a point X between them where their gravitational fields cancel out. The distance from the centre of the Earth to X is $d$. The mass of the Earth is $M_{\text{E}}$ and the mass of the Moon is $M_{\text{M}}$.

What is correct at X?

A.  $\frac{M_{\text{E}}}{d}=\frac{M_{\text{M}}}{D-d}$

B.  $\frac{M_{\text{E}}}{D-d}=\frac{M_{\text{M}}}{d}$

C.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{{\left(D-d\right)}^2}$

D.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{D^2-d^2}$

The centre of the Earth and the Moon are a distance $D$ apart. There is a point X between them where their gravitational fields cancel out. The distance from the centre of the Earth to X is $d$. The mass of the Earth is $M_{\text{E}}$ and the mass of the Moon is $M_{\text{M}}$.

What is correct at X?

A.  $\frac{M_{\text{E}}}{d}=\frac{M_{\text{M}}}{D-d}$

B.  $\frac{M_{\text{E}}}{D-d}=\frac{M_{\text{M}}}{d}$

C.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{{\left(D-d\right)}^2}$

D.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{D^2-d^2}$

State what is meant by gravitational field strength.

State what is meant by gravitational field strength.

State what is meant by gravitational field strength.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Determine the gravitational field of the planet.

The following data are given:

Mass of planet            $=8.0\times {10}^{24}$ kg
Radius of the planet    $=9.1\times {10}^6$ m.

Determine the gravitational field of the planet.

The following data are given:

Mass of planet            $=8.0\times {10}^{24}$ kg
Radius of the planet    $=9.1\times {10}^6$ m.

Determine the gravitational field of the planet.

The following data are given:

Mass of planet            $=8.0\times {10}^{24}$ kg
Radius of the planet    $=9.1\times {10}^6$ m.

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F